Game Theory Gilberto Cmara Earth System Science Center

Game Theory Gilberto Câmara, Earth System Science Center, INPE Licence: Creative Commons By Attribution Non Commercial Share Alike http: //creativecommons. org/licenses/by-nc-sa/2. 5/

Acknowledgments for using previous material q q q 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 Theory GT 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 Theory Explanation: 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 players Strategies: all actions available to all players Payoffs: 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 both Two possible strategies: A party cooperates when he performs value-increasing promises, and defects when he breaches

Modeling choice in non-cooperative games Player 2 Cooperate Player 1 Defect Player 1 Both cooperates, Player 2 defects Player 1 defects, Player 2 cooperates Both defect

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 nada Se os dois jogarem “sete”, não ganham nada.

Prisoners’ Dilemma Two 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 prison 2. 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” “Rebel without a cause” 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.

The hawk-dove game (== chicken game) 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. Maynard Smith and Price, "The logic of animal conflict“ (Nature, 1973 )

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 C D C 10, 10 0, 6 D 6, 0 5, 5 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. . . "

Generalizing. . . 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 C D C b–c -c D b 0 you Payoff matrix other

Terminology Player 2 T = Temptation to defect R = Reward for mutual cooperation P = Punishment for mutual defection S = Sucker's payoff Prisioner’s dillema: T > R > P > S

Generalizing. . . Payoff matrix R: mutual cooperation other P: mutual defection C D C R(1) S(-c) D T(b) P(0) S : sucker’s payoff T : temptation to defect you Taking R = 1 and P = 0

Generalizing. . . Payoff matrix R: mutual cooperation opponent P: mutual defection C D C 1 S D T 0 S : sucker’s payoff T : temptation to defect you Taking R = 1 and P = 0

Different ordering -> Different tensions greed C D C R S D T P fear Chicken game T >1 > S > 0 Stag-hunt game 1>T > 0 > S Prisoner’s dilemma T >1 > 0 > S (Macy&Flache, PNAS 2002)

Spatial Prisioner´s Dillema q q 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.

Spatial Prisioner´s Dillema q q 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.