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.