heiko hotz spieltheorie vortrag
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
A Short Introduction to Game Theory
Heiko Hotz
July 13, 2006
Heiko Hotz A Short Introduction to Game Theory
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Table of Contents
1 Introduction
2
Definitions3 Games
4
Evolutionary Game Theory5 Applications
6 Outlook
Heiko Hotz A Short Introduction to Game Theory
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Table of Contents
1 Introduction
2
Definitions3 Games
4
Evolutionary Game Theory5 Applications
6 Outlook
Heiko Hotz A Short Introduction to Game Theory
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Table of Contents
1 Introduction
2
Definitions3 Games
4
Evolutionary Game Theory5 Applications
6 Outlook
Heiko Hotz A Short Introduction to Game Theory
I d i
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Table of Contents
1 Introduction
2
Definitions3 Games
4
Evolutionary Game Theory5 Applications
6 Outlook
Heiko Hotz A Short Introduction to Game Theory
I t d ti
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Table of Contents
1 Introduction
2
Definitions3 Games
4
Evolutionary Game Theory5 Applications
6 Outlook
Heiko Hotz A Short Introduction to Game Theory
Introd ction
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Table of Contents
1 Introduction
2
Definitions3 Games
4
Evolutionary Game Theory5 Applications
6 Outlook
Heiko Hotz A Short Introduction to Game Theory
Introduction
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Game Theory - What is it?Game Theory - Where is it applied?
Introduction
Game Theory - What is it?
Heiko Hotz A Short Introduction to Game Theory
Introduction
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - What is it?
Generally, game theory investigates conflict situations, theinteraction between the agents and their decisions.
A game in the sense of game theory is given by a (mostlyfinite) number of players, who interact according to givenrules.
The subject of game theory are situations, where the result for
a player does not only depend on his own decisions, but also
on the behaviour of the other players.
Heiko Hotz A Short Introduction to Game Theory
Introduction
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - What is it?
Generally, game theory investigates conflict situations, theinteraction between the agents and their decisions.
A game in the sense of game theory is given by a (mostlyfinite) number of players, who interact according to givenrules.
The subject of game theory are situations, where the result for
a player does not only depend on his own decisions, but alsoon the behaviour of the other players.
Heiko Hotz A Short Introduction to Game Theory
Introduction
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IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - What is it?
Generally, game theory investigates conflict situations, theinteraction between the agents and their decisions.
A game in the sense of game theory is given by a (mostlyfinite) number of players, who interact according to givenrules.
The subject of game theory are situations, where the result for
a player does not only depend on his own decisions, but alsoon the behaviour of the other players.
Heiko Hotz A Short Introduction to Game Theory
Introduction
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DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - What is it?
Figure: Johnvon Neumann
Game theory has its historical origin in 1928.By analysing parlour games, John vonNeumann realised very quickly thepracticability of his approaches forthe analysis of economic problems.
In his book Theory of Games andEconomic Behavior, which he wrote together
with Oskar Morgenstern in 1944, he already applied hismathematical theory to economic applications.
The publication of this book is generally seen as the initialpoint of modern game theory.
Heiko Hotz A Short Introduction to Game Theory
Introduction
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DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - What is it?
Figure: Johnvon Neumann
Game theory has its historical origin in 1928.By analysing parlour games, John vonNeumann realised very quickly thepracticability of his approaches forthe analysis of economic problems.
In his book Theory of Games andEconomic Behavior, which he wrote together
with Oskar Morgenstern in 1944, he already applied hismathematical theory to economic applications.
The publication of this book is generally seen as the initialpoint of modern game theory.
Heiko Hotz A Short Introduction to Game Theory
Introduction
http://find/ -
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14/145
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - What is it?
Figure: Johnvon Neumann
Game theory has its historical origin in 1928.By analysing parlour games, John vonNeumann realised very quickly thepracticability of his approaches forthe analysis of economic problems.
In his book Theory of Games andEconomic Behavior, which he wrote together
with Oskar Morgenstern in 1944, he already applied hismathematical theory to economic applications.
The publication of this book is generally seen as the initialpoint of modern game theory.
Heiko Hotz A Short Introduction to Game Theory
IntroductionD fi i i
http://find/ -
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DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Introduction
Game Theory - where is it applied?
Heiko Hotz A Short Introduction to Game Theory
IntroductionD fi iti
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DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - Where is it applied?
When there is competition for a resource to be analysed,game theory can be used either to explain existing behaviouror to improve strategies.
The first is especially applied by sciences which analyselong-term situations, like biology or sociology.
In animality, for example, one can find situations, wherecooperation has developed for the sake of mutual benefits.
The latter is a crucial tool in sciences like economics.Companies use game theory to improve their strategicalsituation in the market.
Many more sciences like sociology, philosophy, psychology andcultural anthropology use game theory as an appropriate tool.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
http://find/ -
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DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - Where is it applied?
When there is competition for a resource to be analysed,game theory can be used either to explain existing behaviouror to improve strategies.
The first is especially applied by sciences which analyselong-term situations, like biology or sociology.
In animality, for example, one can find situations, wherecooperation has developed for the sake of mutual benefits.
The latter is a crucial tool in sciences like economics.Companies use game theory to improve their strategicalsituation in the market.
Many more sciences like sociology, philosophy, psychology andcultural anthropology use game theory as an appropriate tool.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
http://find/ -
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18/145
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - Where is it applied?
When there is competition for a resource to be analysed,game theory can be used either to explain existing behaviouror to improve strategies.
The first is especially applied by sciences which analyselong-term situations, like biology or sociology.
In animality, for example, one can find situations, wherecooperation has developed for the sake of mutual benefits.
The latter is a crucial tool in sciences like economics.Companies use game theory to improve their strategicalsituation in the market.
Many more sciences like sociology, philosophy, psychology andcultural anthropology use game theory as an appropriate tool.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
http://find/ -
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19/145
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - Where is it applied?
When there is competition for a resource to be analysed,game theory can be used either to explain existing behaviouror to improve strategies.
The first is especially applied by sciences which analyselong-term situations, like biology or sociology.
In animality, for example, one can find situations, wherecooperation has developed for the sake of mutual benefits.
The latter is a crucial tool in sciences like economics.Companies use game theory to improve their strategicalsituation in the market.
Many more sciences like sociology, philosophy, psychology andcultural anthropology use game theory as an appropriate tool.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
http://find/ -
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20/145
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Game Theory - What is it?Game Theory - Where is it applied?
Game Theory - Where is it applied?
When there is competition for a resource to be analysed,game theory can be used either to explain existing behaviouror to improve strategies.
The first is especially applied by sciences which analyselong-term situations, like biology or sociology.
In animality, for example, one can find situations, wherecooperation has developed for the sake of mutual benefits.
The latter is a crucial tool in sciences like economics.Companies use game theory to improve their strategicalsituation in the market.
Many more sciences like sociology, philosophy, psychology andcultural anthropology use game theory as an appropriate tool.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
N l F G
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Normal Form GamesExtensive Form GamesNash Equilibrium
Definitions
Normal Form Games
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
Normal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Normal Form GamesExtensive Form GamesNash Equilibrium
Normal Form Games
A game in normal form consists of:
1
A finite number of players.2 A strategy set assigned to each player.
3 A payoff function, which assigns a certain payoff to eachplayer depending on his strategy and the strategy of the otherplayers.
Both players choose their strategy simultaneously
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
Normal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Normal Form GamesExtensive Form GamesNash Equilibrium
Normal Form Games
A game in normal form consists of:
1
A finite number of players.2 A strategy set assigned to each player.
3 A payoff function, which assigns a certain payoff to eachplayer depending on his strategy and the strategy of the otherplayers.
Both players choose their strategy simultaneously
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
Normal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Normal Form GamesExtensive Form GamesNash Equilibrium
Normal Form Games
A game in normal form consists of:
1
A finite number of players.2 A strategy set assigned to each player.
3 A payoff function, which assigns a certain payoff to eachplayer depending on his strategy and the strategy of the otherplayers.
Both players choose their strategy simultaneously
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GNormal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Normal Form GamesExtensive Form GamesNash Equilibrium
Normal Form Games
A game in normal form consists of:
1
A finite number of players.2 A strategy set assigned to each player.
3 A payoff function, which assigns a certain payoff to eachplayer depending on his strategy and the strategy of the otherplayers.
Both players choose their strategy simultaneously
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GNormal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Extensive Form GamesNash Equilibrium
Payoff Matrix
If the number of players is limited to two and if their sets ofstrategies consist of only a few elements, the outcome of thepayoff function can be represented in a matrix, the so-calledpayoff matrix, which shows the two players, their strategiesand their payoffs:
Player1\Player2 L R
U 3 , 3 0 , 5D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesNormal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Extensive Form GamesNash Equilibrium
Payoff Matrix
If the number of players is limited to two and if their sets ofstrategies consist of only a few elements, the outcome of thepayoff function can be represented in a matrix, the so-calledpayoff matrix, which shows the two players, their strategiesand their payoffs:
Player1\Player2 L R
U 3 , 3 0 , 5D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesNormal Form Games
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Extensive Form GamesNash Equilibrium
Definitions
Extensive Form Games
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesNormal Form Games
G
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Extensive Form GamesNash Equilibrium
Extensive Form Games
Contrary to the normal form game, the rules of an extensive formgame are described such that the agents of the game execute theirmoves consecutively.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesNormal Form GamesE i F G
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GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Extensive Form GamesNash Equilibrium
Definitions
Nash Equilibrium
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IntroductionDefinitions
GamesNormal Form GamesE t i F G
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Evolutionary Game Theory (EGT)Applications
Outlook
Extensive Form GamesNash Equilibrium
Nash Equilibrium
If each player has chosen a strategy and no player can benefit bychanging his strategy while the other players keep theirs
unchanged, then the current set of strategy choices and thecorresponding payoffs constitute a Nash equilibrium.
Figure:John Nash
John Nash showed in 1950, that every game with a
finite number of players and finite numberof strategies has at least one mixed strategyNash equilibrium.
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GamesNormal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Extensive Form GamesNash Equilibrium
Nash Equilibrium
If each player has chosen a strategy and no player can benefit bychanging his strategy while the other players keep theirs
unchanged, then the current set of strategy choices and thecorresponding payoffs constitute a Nash equilibrium.
Figure:John Nash
John Nash showed in 1950, that every game with a
finite number of players and finite numberof strategies has at least one mixed strategyNash equilibrium.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesNormal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Extensive Form GamesNash Equilibrium
Nash Equilibrium
In a pure strategies, one strategy is played with probability 1.
A mixed strategy is a linear combination of at least two purestrategies.
The coefficients denote the probabilities of the pure strategiesto be played.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesG ( G )
Normal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Extensive Form GamesNash Equilibrium
Nash Equilibrium
In a pure strategies, one strategy is played with probability 1.
A mixed strategy is a linear combination of at least two purestrategies.
The coefficients denote the probabilities of the pure strategiesto be played.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
E l ti G Th (EGT)
Normal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Extensive Form GamesNash Equilibrium
Nash Equilibrium
In a pure strategies, one strategy is played with probability 1.
A mixed strategy is a linear combination of at least two purestrategies.
The coefficients denote the probabilities of the pure strategiesto be played.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
E ol tionar Game Theor (EGT)
Normal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Nash Equilibrium
Best Response
The best response is the strategy (or strategies)
which produces the most favorable immediate
outcome for the current player, taking other players
strategies as given.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5
D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form Games
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Evolutionary Game Theory (EGT)Applications
Outlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5
D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form GamesN h E ilib i
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Evolutionary Game Theory (EGT)Applications
Outlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5
D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form GamesN h E ilib i
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Evolutionary Game Theory (EGT)Applications
Outlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5
D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form GamesNash Equilibrium
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y y ( )Applications
Outlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5
D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form GamesNash Equilibrium
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( )Applications
Outlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5
D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)
Normal Form GamesExtensive Form GamesNash Equilibrium
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ApplicationsOutlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)A li i
Normal Form GamesExtensive Form GamesNash Equilibrium
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ApplicationsOutlook
Nash Equilibrium
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)A li ti
Normal Form GamesExtensive Form GamesNash Equilibrium
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ApplicationsOutlook
s q
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)Applications
Normal Form GamesExtensive Form GamesNash Equilibrium
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ApplicationsOutlook
q
Localizing a Nash Equilibrium in a Payoff Matrix
Player1\Player2 L RU 3 , 3 0 , 5D 5 , 0 1 , 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
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ApplicationsOutlook
Games
Prisoners Dilemma
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/http://goback/ -
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ApplicationsOutlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitionsGames
Evolutionary Game Theory (EGT)Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
49/145
ApplicationsOutlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://goforward/http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
50/145
ppOutlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
51/145
ppOutlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
52/145
Outlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
Applications
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
53/145
Outlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsO l k
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
54/145
Outlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsO tl k
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
55/145
Outlook
Prisoners Dilemma
Two suspects arrested
Police has insufficient evidence for a conviction
If both testify:Both receive 2-year sentence
If both stay silent:
Only a six-month-sentence for a minor charge
If one testifies and the other remains silent:Betrayer goes free, accomplice receives 10-year sentence
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
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Outlook
Payoff Matrix of the Prisoners Dilemma
Abbreviations: To testify means to betray the other suspectand thus to defect (D), to remain silent means to cooperate(C) with the other suspect.
We will use positive numbers in the payoff matrix.
Player1\Player2 C D
C 3, 3 0, 5D 5, 0 1, 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
57/145
Outlook
Payoff Matrix of the Prisoners Dilemma
Abbreviations: To testify means to betray the other suspectand thus to defect (D), to remain silent means to cooperate(C) with the other suspect.
We will use positive numbers in the payoff matrix.
Player1\Player2 C D
C 3, 3 0, 5D 5, 0 1, 1
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
58/145
Outlook
Games
Public Good Game
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
59/145
Outlook
Public Good Game
A group of 4 people are given $ 200 each.
They can invest an amount of money in a project.
Every $1 invested will yield $ 2, which would be distributed toall group members.
If everyone invested, each would get $ 400.
However, if only one person invested, that sucker wouldtake home a mere $ 100.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
60/145
Public Good Game
A group of 4 people are given $ 200 each.
They can invest an amount of money in a project.
Every $1 invested will yield $ 2, which would be distributed toall group members.
If everyone invested, each would get $ 400.
However, if only one person invested, that sucker wouldtake home a mere $ 100.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
61/145
Public Good Game
A group of 4 people are given $ 200 each.
They can invest an amount of money in a project.
Every $1 invested will yield $ 2, which would be distributed toall group members.
If everyone invested, each would get $ 400.
However, if only one person invested, that sucker wouldtake home a mere $ 100.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://goforward/http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
62/145
Public Good Game
A group of 4 people are given $ 200 each.
They can invest an amount of money in a project.
Every $1 invested will yield $ 2, which would be distributed toall group members.
If everyone invested, each would get $ 400.
However, if only one person invested, that sucker wouldtake home a mere $ 100.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
63/145
Public Good Game
A group of 4 people are given $ 200 each.
They can invest an amount of money in a project.
Every $1 invested will yield $ 2, which would be distributed toall group members.
If everyone invested, each would get $ 400.
However, if only one person invested, that sucker wouldtake home a mere $ 100.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
64/145
Payoff Function of the Public Good Game
This is a game in normal form and therefore has a payoff functionfor each player. The payoff function for, lets say, player 1 is givenby
P1 = 2 (s1 + s2 + s3 + s4)4
s1
=2 (s2 + s3 + s4)
4 0, 5 s1
Every investment s1 of player 1 will diminish his payoff.
Therefore, a rational player will choose the strategy sn = 0,i.e. he will invest no money at all.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
65/145
Payoff Function of the Public Good Game
This is a game in normal form and therefore has a payoff functionfor each player. The payoff function for, lets say, player 1 is givenby
P1 = 2 (s1 + s2 + s3 + s4)4
s1
=2 (s2 + s3 + s4)
4 0, 5 s1
Every investment s1 of player 1 will diminish his payoff.
Therefore, a rational player will choose the strategy sn = 0,i.e. he will invest no money at all.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
66/145
Payoff Function of the Public Good Game
This is a game in normal form and therefore has a payoff functionfor each player. The payoff function for, lets say, player 1 is givenby
P1 = 2 (s1 + s2 + s3 + s4)4
s1
=2 (s2 + s3 + s4)
4 0, 5 s1
Every investment s1 of player 1 will diminish his payoff.
Therefore, a rational player will choose the strategy sn = 0,i.e. he will invest no money at all.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
67/145
Payoff Function of the Public Good Game
This is a game in normal form and therefore has a payoff functionfor each player. The payoff function for, lets say, player 1 is givenby
P1 = 2 (s1 + s2 + s3 + s4)4
s1
=2 (s2 + s3 + s4)
4 0, 5 s1
Every investment s1 of player 1 will diminish his payoff.Therefore, a rational player will choose the strategy sn = 0,i.e. he will invest no money at all.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
68/145
Payoff Function of the Public Good Game
This is a game in normal form and therefore has a payoff functionfor each player. The payoff function for, lets say, player 1 is givenby
P1 = 2 (s1 + s2 + s3 + s4)4
s1
=2 (s2 + s3 + s4)
4 0, 5 s1
Every investment s1 of player 1 will diminish his payoff.Therefore, a rational player will choose the strategy sn = 0,i.e. he will invest no money at all.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
69/145
Games
Rock, Paper, Scissors
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
70/145
Rock, Paper, Scissors
Two players form a symbol (rock, paper or scissors) with theirhands
Rock crushes ScissorsScissors cut Paper
Paper covers Rock
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
71/145
Rock, Paper, Scissors
Two players form a symbol (rock, paper or scissors) with theirhands
Rock crushes ScissorsScissors cut Paper
Paper covers Rock
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
R k P S
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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Rock, Paper, Scissors
Two players form a symbol (rock, paper or scissors) with theirhands
Rock crushes ScissorsScissors cut Paper
Paper covers Rock
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Prisoners DilemmaPublic Good GameRock, Paper, Scissors
R k P S i
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
73/145
Rock, Paper, Scissors
Two players form a symbol (rock, paper or scissors) with theirhands
Rock crushes ScissorsScissors cut Paper
Paper covers Rock
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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Evolutionary Game
Theory
Why EGT?
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Wh EGT?
http://find/ -
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Why EGT?
Games can be played repeatedly, and also with a population ofplayers.
Which populations/strategies are stable?
Is it possible for mutants to invade a given population?
How does cooperation arise and evolove?
How does biodeversity emerge?
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Wh EGT?
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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Why EGT?
Games can be played repeatedly, and also with a population ofplayers.
Which populations/strategies are stable?
Is it possible for mutants to invade a given population?
How does cooperation arise and evolove?
How does biodeversity emerge?
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Wh EGT?
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
77/145
Why EGT?
Games can be played repeatedly, and also with a population ofplayers.
Which populations/strategies are stable?
Is it possible for mutants to invade a given population?
How does cooperation arise and evolove?
How does biodeversity emerge?
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Why EGT?
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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Why EGT?
Games can be played repeatedly, and also with a population ofplayers.
Which populations/strategies are stable?
Is it possible for mutants to invade a given population?
How does cooperation arise and evolove?
How does biodeversity emerge?
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Why EGT?
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
79/145
Why EGT?
Games can be played repeatedly, and also with a population ofplayers.
Which populations/strategies are stable?
Is it possible for mutants to invade a given population?
How does cooperation arise and evolove?
How does biodeversity emerge?
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
EGT New Concepts
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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EGT- New Concepts
Evolutionary stable strategy (ESS)
To investigate the stability of populations.Replicator dynamics
To describe the evolution of different species within apopulation over time.
Heiko Hotz A Short Introduction to Game Theory
Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
EGT New Concepts
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
81/145
EGT- New Concepts
Evolutionary stable strategy (ESS)
To investigate the stability of populations.Replicator dynamics
To describe the evolution of different species within apopulation over time.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
EGT- New Concepts
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
82/145
EGT- New Concepts
Evolutionary stable strategy (ESS)
To investigate the stability of populations.Replicator dynamics
To describe the evolution of different species within apopulation over time.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
EGT- New Concepts
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
83/145
EGT New Concepts
Evolutionary stable strategy (ESS)
To investigate the stability of populations.Replicator dynamics
To describe the evolution of different species within apopulation over time.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
84/145
Evolutionary Game
Theory
Evolutionary Stable Strategy
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
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Evolutionary Stable Strategy (ESS)
An ESS is a strategy which, if adopted by a population,cannot be invaded by any competing alternative strategy.
An equilibrium refinement to the Nash equilibrium.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
86/145
Evolutionary Stable Strategy (ESS)
An ESS is a strategy which, if adopted by a population,cannot be invaded by any competing alternative strategy.
An equilibrium refinement to the Nash equilibrium.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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y gy ( )
Let E(, ) be the payoff for a player playing against aplayer playing .
For to be an Nash equilibrium it is demanded:E(,) E(, )
For to be an ESS it is demanded:1 E(, ) > E(, ) (equlibrium condition), or2
E(, ) = E(, ) and E(,) > E(, ) (stability condition)
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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y gy ( )
Let E(, ) be the payoff for a player playing against aplayer playing .
For to be an Nash equilibrium it is demanded:E(,) E(, )
For to be an ESS it is demanded:1 E(, ) > E(, ) (equlibrium condition), or2
E(, ) = E(, ) and E(,) > E(, ) (stability condition)
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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y gy ( )
Let E(, ) be the payoff for a player playing against aplayer playing .
For to be an Nash equilibrium it is demanded:E(,) E(, )
For to be an ESS it is demanded:1 E(, ) > E(, ) (equlibrium condition), or2
E(, ) = E(, ) and E(,) > E(, ) (stability condition)
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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y gy ( )
Let E(, ) be the payoff for a player playing against aplayer playing .
For to be an Nash equilibrium it is demanded:E(,) E(, )
For to be an ESS it is demanded:1 E(, ) > E(, ) (equlibrium condition), or2 E
(, ) =E
(, ) andE
(,) >E
(, ) (stability condition)
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Evolutionary Stable Strategy (ESS)
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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( )
Let E(, ) be the payoff for a player playing against aplayer playing .
For to be an Nash equilibrium it is demanded:E(,) E(, )
For to be an ESS it is demanded:1 E(, ) > E(, ) (equlibrium condition), or2 E
(, ) =E
(, ) andE
(,) >E
(, ) (stability condition)
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
92/145
Evolutionary Game
Theory
Hawk-Dove Game
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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Two individuals compete for a resource V.
Each individual follows exactly one of two strategies describedbelow:
Hawk: Initiate aggressive behaviour, not stopping until injuredor until ones opponent backs down.Dove: Retreat immediately if ones opponent initiatesaggressive behaviour.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
94/145
Two individuals compete for a resource V.
Each individual follows exactly one of two strategies describedbelow:
Hawk: Initiate aggressive behaviour, not stopping until injuredor until ones opponent backs down.Dove: Retreat immediately if ones opponent initiatesaggressive behaviour.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
95/145
Two individuals compete for a resource V.
Each individual follows exactly one of two strategies described
below:Hawk: Initiate aggressive behaviour, not stopping until injuredor until ones opponent backs down.Dove: Retreat immediately if ones opponent initiatesaggressive behaviour.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
96/145
Two individuals compete for a resource V.
Each individual follows exactly one of two strategies described
below:Hawk: Initiate aggressive behaviour, not stopping until injuredor until ones opponent backs down.Dove: Retreat immediately if ones opponent initiatesaggressive behaviour.
Heiko Hotz A Short Introduction to Game Theory Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
97/145
We assume
whenever two individuals both initiate aggressive behaviour,conflict eventually results and the two individuals are equally
likely to be injured,the cost of the conflict reduces individual fitness by someconstant value C,
when a hawk meets a dove, the dove immediately retreats andthe hawk obtains the resource, and
when two doves meet the resource is shared equally betweenthem.
Heiko Hot A Short Introd ction to Game Theor Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
98/145
We assume
whenever two individuals both initiate aggressive behaviour,conflict eventually results and the two individuals are equally
likely to be injured,the cost of the conflict reduces individual fitness by someconstant value C,
when a hawk meets a dove, the dove immediately retreats andthe hawk obtains the resource, and
when two doves meet the resource is shared equally betweenthem.
H ik H t A Sh t I t d ti t G Th Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
99/145
We assume
whenever two individuals both initiate aggressive behaviour,conflict eventually results and the two individuals are equally
likely to be injured,the cost of the conflict reduces individual fitness by someconstant value C,
when a hawk meets a dove, the dove immediately retreats andthe hawk obtains the resource, and
when two doves meet the resource is shared equally betweenthem.
H ik H t A Sh t I t d ti t G Th Introduction
DefinitionsGames
Evolutionary Game Theory (EGT)Applications
Outlook
Why EGT?Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
100/145
We assume
whenever two individuals both initiate aggressive behaviour,conflict eventually results and the two individuals are equally
likely to be injured,the cost of the conflict reduces individual fitness by someconstant value C,
when a hawk meets a dove, the dove immediately retreats andthe hawk obtains the resource, and
when two doves meet the resource is shared equally betweenthem.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
101/145
We assume
whenever two individuals both initiate aggressive behaviour,conflict eventually results and the two individuals are equally
likely to be injured,the cost of the conflict reduces individual fitness by someconstant value C,
when a hawk meets a dove, the dove immediately retreats andthe hawk obtains the resource, and
when two doves meet the resource is shared equally betweenthem.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
102/145
This leads to the following payoff matrix:
Hawk Dove
Hawk 12 (V C),12 (V C) V, 0
Dove 0,V V/2,V/2
Dove is no stable strategy, sinceV2 = E(D,D) < E(H,D) = V.
Because of E(H,H) = 12 (V C) and E(D,H) = 0, H is an
ESS if V C.
But what if V < C?
Neither H nor D is an ESS.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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This leads to the following payoff matrix:
Hawk Dove
Hawk 12 (V C),12 (V C) V, 0
Dove 0,V V/2,V/2
Dove is no stable strategy, sinceV2 = E(D,D) < E(H,D) = V.
Because of E(H,H) = 12 (V C) and E(D,H) = 0, H is an
ESS if V C.
But what if V < C?
Neither H nor D is an ESS.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
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This leads to the following payoff matrix:
Hawk Dove
Hawk 12 (V C),12 (V C) V, 0
Dove 0,V V/2,V/2
Dove is no stable strategy, sinceV2 = E(D,D) < E(H,D) = V.
Because of E(H,H) = 12 (V C) and E(D,H) = 0, H is an
ESS if V C.
But what if V < C?
Neither H nor D is an ESS.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
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This leads to the following payoff matrix:
Hawk Dove
Hawk 12 (V C),12 (V C) V, 0
Dove 0,V V/2,V/2
Dove is no stable strategy, sinceV2 = E(D,D) < E(H,D) = V.
Because of E(H,H) = 12 (V C) and E(D,H) = 0, H is an
ESS if V C.But what if V < C?
Neither H nor D is an ESS.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
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7/28/2019 Heiko Hotz Spieltheorie Vortrag
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This leads to the following payoff matrix:
Hawk Dove
Hawk 12 (V C),12 (V C) V, 0
Dove 0,V V/2,V/2
Dove is no stable strategy, sinceV2 = E(D,D) < E(H,D) = V.
Because of E(H,H) = 12 (V C) and E(D,H) = 0, H is an
ESS if V C.But what if V < C?
Neither H nor D is an ESS.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
Hawk-Dove Game
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
107/145
This leads to the following payoff matrix:
Hawk Dove
Hawk 12 (V C),12 (V C) V, 0
Dove 0,V V/2,V/2
Dove is no stable strategy, sinceV2 = E(D,D) < E(H,D) = V.
Because of E(H,H) = 12 (V C) and E(D,H) = 0, H is an
ESS if V C.But what if V < C?
Neither H nor D is an ESS.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
108/145
Evolutionary Game
Theory
The Replicator Dynamics
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
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7/28/2019 Heiko Hotz Spieltheorie Vortrag
109/145
Let us consider now a population consisting of n types, andlet xi(t) be the frequency of type i at some time t.
The state of the population is given by the vector
x(t) = x1(t), . . . , xn(t).The state of the population will change, since some specieswill get higher payoffs and will reproduce better than others,or others adopt the strategy of the species with the betterfitness.
We want to postulate a law of motion for x(t), i.e. we wantto investigate the evolution of the different species over time.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
110/145
Let us consider now a population consisting of n types, andlet xi(t) be the frequency of type i at some time t.
The state of the population is given by the vector
x(t) = x1(t), . . . , xn(t).The state of the population will change, since some specieswill get higher payoffs and will reproduce better than others,or others adopt the strategy of the species with the betterfitness.
We want to postulate a law of motion for x(t), i.e. we wantto investigate the evolution of the different species over time.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
111/145
Let us consider now a population consisting of n types, andlet xi(t) be the frequency of type i at some time t.
The state of the population is given by the vector
x(t) = x1(t), . . . , xn(t).The state of the population will change, since some specieswill get higher payoffs and will reproduce better than others,or others adopt the strategy of the species with the betterfitness.
We want to postulate a law of motion for x(t), i.e. we wantto investigate the evolution of the different species over time.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
112/145
Let us consider now a population consisting of n types, andlet xi(t) be the frequency of type i at some time t.
The state of the population is given by the vector
x(t) = x1(t), . . . , xn(t).The state of the population will change, since some specieswill get higher payoffs and will reproduce better than others,or others adopt the strategy of the species with the betterfitness.
We want to postulate a law of motion for x(t), i.e. we wantto investigate the evolution of the different species over time.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
113/145
If individuals meet randomly and then engage in a symmetricgame with payoff matrix A, then (Ax)i is the expected payoff
for an individual of type ixTAx is the average payoff in the population state x.
The evolution of x over time is described by the replicatorequation:
xi = xi[(Ax)i xTAx]
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
114/145
If individuals meet randomly and then engage in a symmetricgame with payoff matrix A, then (Ax)i is the expected payoff
for an individual of type ixTAx is the average payoff in the population state x.
The evolution of x over time is described by the replicatorequation:
xi = xi[(Ax)i xTAx]
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
115/145
If individuals meet randomly and then engage in a symmetricgame with payoff matrix A, then (Ax)i is the expected payoff
for an individual of type ixTAx is the average payoff in the population state x.
The evolution of x over time is described by the replicatorequation:
xi = xi[(Ax)i xTAx]
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
116/145
By setting xi = 0, we obtain the evolutionary stable states ofa population.
A population is said to be in an evolutionarily stable state if
its genetic composition is restored by selection after adisturbance, provided the disturbance is not too large.
For V > C, the only evolutionary stable state is a populationconsisting of hawks.
For V < C, a mixed population with a fraction V/C of hawksand a fraction 1 V/C of doves is evolutionary stable.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
117/145
By setting xi = 0, we obtain the evolutionary stable states ofa population.
A population is said to be in an evolutionarily stable state if
its genetic composition is restored by selection after adisturbance, provided the disturbance is not too large.
For V > C, the only evolutionary stable state is a populationconsisting of hawks.
For V < C, a mixed population with a fraction V/C of hawksand a fraction 1 V/C of doves is evolutionary stable.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
118/145
By setting xi = 0, we obtain the evolutionary stable states ofa population.
A population is said to be in an evolutionarily stable state if
its genetic composition is restored by selection after adisturbance, provided the disturbance is not too large.
For V > C, the only evolutionary stable state is a populationconsisting of hawks.
For V < C, a mixed population with a fraction V/C of hawksand a fraction 1 V/C of doves is evolutionary stable.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Why EGT?
Evolutionary Stable Strategy (ESS)Hawk-Dove GameThe Replicator Dynamics
The Replicator Dynamics
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
119/145
By setting xi = 0, we obtain the evolutionary stable states ofa population.
A population is said to be in an evolutionarily stable state if
its genetic composition is restored by selection after adisturbance, provided the disturbance is not too large.
For V > C, the only evolutionary stable state is a populationconsisting of hawks.
For V < C, a mixed population with a fraction V/C of hawksand a fraction 1 V/C of doves is evolutionary stable.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
120/145
Applications
Evolution of Cooperation
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
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7/28/2019 Heiko Hotz Spieltheorie Vortrag
121/145
We have seen, that the logical move in the PrisonersDilemma is to defect
Consider spatially structured populations
Limited local interactions enable cooperators to form clusters
Individuals can outweigh their losses against defectors by gainsfrom interactions within the cluster.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
122/145
We have seen, that the logical move in the PrisonersDilemma is to defect
Consider spatially structured populations
Limited local interactions enable cooperators to form clusters
Individuals can outweigh their losses against defectors by gainsfrom interactions within the cluster.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
123/145
We have seen, that the logical move in the PrisonersDilemma is to defect
Consider spatially structured populations
Limited local interactions enable cooperators to form clusters
Individuals can outweigh their losses against defectors by gainsfrom interactions within the cluster.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
124/145
We have seen, that the logical move in the PrisonersDilemma is to defect
Consider spatially structured populations
Limited local interactions enable cooperators to form clusters
Individuals can outweigh their losses against defectors by gainsfrom interactions within the cluster.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
125/145
Example revealed critical phase transitions.
This falls into the universality class of directed percolation onsquare lattices.
Results for different population structures in the PD arediscussed and related to condensed matter physics.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
126/145
Example revealed critical phase transitions.
This falls into the universality class of directed percolation onsquare lattices.
Results for different population structures in the PD arediscussed and related to condensed matter physics.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Evolution of Cooperation
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
127/145
Example revealed critical phase transitions.
This falls into the universality class of directed percolation onsquare lattices.
Results for different population structures in the PD arediscussed and related to condensed matter physics.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
128/145
Applications
Biodiversity
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
129/145
One of the central aims of ecology is to identify mechanismsthat maintain biodiversity.
Theoretical models have shown that competing species cancoexist if ecological processes such as dispersal, movement,and interaction occur over small spatial scales.
In particular, this may be the case for nontransitivecommunities, that is, those without strict competitive
hierarchies.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
130/145
One of the central aims of ecology is to identify mechanismsthat maintain biodiversity.
Theoretical models have shown that competing species cancoexist if ecological processes such as dispersal, movement,and interaction occur over small spatial scales.
In particular, this may be the case for nontransitivecommunities, that is, those without strict competitive
hierarchies.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
131/145
One of the central aims of ecology is to identify mechanismsthat maintain biodiversity.
Theoretical models have shown that competing species cancoexist if ecological processes such as dispersal, movement,and interaction occur over small spatial scales.
In particular, this may be the case for nontransitivecommunities, that is, those without strict competitive
hierarchies.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)Applications
Outlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
132/145
There exist three strains of Escherichia coli bacteria.
Type A releases toxic colicin and produces, for its ownprotection, an immunity protein.
Type B produces the immunity protein only.
Type C produces neither toxin nor immunity.
The production of the toxic colicin and the immunity proteincauses some higher costs.
Thus B beats A, C beats B and A beats C.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
133/145
There exist three strains of Escherichia coli bacteria.
Type A releases toxic colicin and produces, for its ownprotection, an immunity protein.
Type B produces the immunity protein only.
Type C produces neither toxin nor immunity.
The production of the toxic colicin and the immunity proteincauses some higher costs.
Thus B beats A, C beats B and A beats C.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
134/145
There exist three strains of Escherichia coli bacteria.
Type A releases toxic colicin and produces, for its ownprotection, an immunity protein.
Type B produces the immunity protein only.
Type C produces neither toxin nor immunity.
The production of the toxic colicin and the immunity proteincauses some higher costs.
Thus B beats A, C beats B and A beats C.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/http://goback/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
135/145
There exist three strains of Escherichia coli bacteria.
Type A releases toxic colicin and produces, for its ownprotection, an immunity protein.
Type B produces the immunity protein only.
Type C produces neither toxin nor immunity.
The production of the toxic colicin and the immunity proteincauses some higher costs.
Thus B beats A, C beats B and A beats C.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
136/145
There exist three strains of Escherichia coli bacteria.
Type A releases toxic colicin and produces, for its ownprotection, an immunity protein.
Type B produces the immunity protein only.
Type C produces neither toxin nor immunity.
The production of the toxic colicin and the immunity proteincauses some higher costs.
Thus B beats A, C beats B and A beats C.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
137/145
There exist three strains of Escherichia coli bacteria.
Type A releases toxic colicin and produces, for its ownprotection, an immunity protein.
Type B produces the immunity protein only.
Type C produces neither toxin nor immunity.
The production of the toxic colicin and the immunity proteincauses some higher costs.
Thus B beats A, C beats B and A beats C.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Evolution of CooperationBiodiversity
Biodiversity
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
138/145
green: resistant strainred: colicin producing strainblue: sensitive strain
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
139/145
Outlook
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Outlook
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
140/145
Most evolutionary game dynamics have been studied in thecontext of infinitely large populations. We expect that finitepopulation size effects will lead to surprising outcomes and
might question the importance of traditional evolutionarystability.
Emerging fields as diverse as metabolic control networkswithin cells and evolutionary psychology, for example, should
benefit from game theory.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Outlook
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
141/145
Most evolutionary game dynamics have been studied in thecontext of infinitely large populations. We expect that finitepopulation size effects will lead to surprising outcomes and
might question the importance of traditional evolutionarystability.
Emerging fields as diverse as metabolic control networkswithin cells and evolutionary psychology, for example, should
benefit from game theory.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
GamesEvolutionary Game Theory (EGT)
ApplicationsOutlook
Outlook
C lt al i te etatio s of e licato d a ics ofte ass e
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
142/145
Cultural interpretations of replicator dynamics often assumethat successful strategies spread by imitation or learning, butthe learning of complicated strategies from behavioralobservations is a nontrivial task that needs specific
investigation.
Interactions among genes, viruses, cells, and humans are ofteninstances of evolutionary games that are amenable toempirical and theoretical investigation.
Game theory is the appropriate tool whenever the success ofan individual depends on others.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
Games
Evolutionary Game Theory (EGT)Applications
Outlook
Outlook
Cultural interpretations of replicator dynamics often assume
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
143/145
Cultural interpretations of replicator dynamics often assumethat successful strategies spread by imitation or learning, butthe learning of complicated strategies from behavioralobservations is a nontrivial task that needs specific
investigation.
Interactions among genes, viruses, cells, and humans are ofteninstances of evolutionary games that are amenable toempirical and theoretical investigation.
Game theory is the appropriate tool whenever the success ofan individual depends on others.
Heiko Hotz A Short Introduction to Game Theory
IntroductionDefinitions
Games
Evolutionary Game Theory (EGT)Applications
Outlook
Outlook
Cultural interpretations of replicator dynamics often assume
http://find/ -
7/28/2019 Heiko Hotz Spieltheorie Vortrag
144/145
Cultural interpretations of replicator dynamics often assumethat successful strategies spread by imitation or learning, butthe learning of complicated strategies from behavioralobservations is a nontrivial task that needs specific
investigation.Interactions among genes, viruses, cells, and humans are ofteninstances of evolutionary games
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