Game Theory and Social Simulation
Gilberto Câmara, Earth System Science Center, INPE
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Acknowledgments for using previous material
Martin Nowak (Harvard University, USA) Francisco C. Santos (Université Libre de Bruxelles, Belgium) Craig Callender (Philosophy, Univ California San Diego, USA) Ana Aguiar (INPE, Brazil) Tiago Carneiro (Federal University of Ouro Preto, Brazil) Guy Brasseur (NCAR, USA)
Game TheoryGT is an analytical tool for social sciences that is used to model
strategic interactions or conflict situations.Strategic interaction: When actions of a player influence payoffs to
other players
Game TheoryExplanation: What is the game to be played?Prediction: What outcome will prevail?Advice or prescription: Which strategies are likely to yield good results
in which situations?
Where can we use Game Theory?
Any situation that requires us to anticipate our rival’s response to our action is a potential context for GT.
Economics, Political science, Biology
What is a Normal Form Game?Players: list of playersStrategies: all actions available to all playersPayoffs: a payoff assigned to every contingency (every possible
strategy profile as the outcome of the game)
John Kennedy and Nikita Khrushchev
Modeling two-party games
Payoffs for each player depend on actions of bothTwo possible strategies: A party cooperates when he performs
value-increasing promises, and defects when he breaches
Cooperate Defect
Cooperate Both cooperatePlayer 1 cooperates, Player 2 defects
DefectPlayer 1 defects, Player 2 cooperates
Both defect
Player 2
Player 1
Modeling choice in non-cooperative games
Silvio Santos e o jogo do “Sete e Meio”
Dois jogadores se enfrentam na TV.Se dois jogarem “meio”, cada um ganha R$ 14 mil.Se um jogar “sete” e o outro “meio”, o primeiro ganha R$ 112
mil e outro não ganha nadaSe os dois jogarem “sete”, não ganham nada.
Prisoners’ DilemmaTwo suspects are caught and put in different rooms (no
communication). They are offered the following deal:1. If both of you confess, you will both get 3 years in prison2. If you confesses whereas the other does not, you will get 1
year and the other gets 5 years in prison .3. If neither of you confess, you both will get 2 years in prison.
The “chicken game”
Two persons drive their cars towards a cliff. They must stop or both may die in the fall. The one that stops first will be called a "chicken," meaning a coward.
“Rebel without a cause”
The hawk-dove game (== chicken game)
Maynard Smith and Price, "The logic of animal conflict“ (Nature, 1973 )
Two individuals compete for a resource (In biological terms, its value increases in the Darwinian fitness of the individual who obtains the resource)
Hawk Initiate aggressive behaviour, not stopping until injured or until one's opponent backs down.
Dove Retreat immediately if one's opponent initiates aggressive behaviour.
The hawk-dove game (== chicken game)
Encyclopedia Britannica
The stag-hunt game: conflict between safety and social cooperation
Two hunters want to kill a stag. Success is uncertain and, if it comes, require the efforts of both. On the other hand, either hunter can forsake his partner and catch a hare with a good chance of success.
The stag-hunt game: conflict between safety and social cooperation
Rousseau, in A Discourse on Inequality:“If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple..."
C D
C 10,10 0,6
D 6,0 5,5
Generalizing...
Payoff matrix
DC
C
D
b – c -c
0 b
other
you
Cooperation requires at least two individuals:A: the one providing cooperation (DONOR)B: the one benefiting from cooperation (RECEIVER)
Donor has a cost c to cooperate and confers a benefit b to other player
Player 2
Terminology
T = Temptation to defect
R = Reward for mutual cooperation
P = Punishment for mutual defection
S = Sucker's payoff
T = Temptation to defect
R = Reward for mutual cooperation
P = Punishment for mutual defection
S = Sucker's payoff
Generalizing...
Payoff matrix R: mutual cooperation
P: mutual defection
S : sucker’s payoff
T : temptation to defect
DC
C
D
R(1) S(-c)
P(0) T(b)
other
you
Taking R = 1 and P = 0
Generalizing...
Payoff matrix R: mutual cooperation
P: mutual defection
S : sucker’s payoff
T : temptation to defect
DC
C
D
1 S
0 T
opponent
you
Taking R = 1 and P = 0
Different ordering -> Different tensions
Chicken game
Stag-hunt game
Prisoner’s dilemma
SP
DCCD R
TT > 1 > 0 > S
1 > T > 0 > S
T > 1 > S > 0 greed fear
(Macy&Flache, PNAS 2002)
Spatial Prisioner´s Dillema
Nowak and May considered a large lattice with each cell occupied by one player. The players engage in one round of the Prisoner’s Dilemma game against each of their neighbors.
Afterward, the next generation is formed: each cell is taken over by a copy of the highest-scoring strategy within the neighborhood.
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