PRISONER’S DILEMMA BERK EROL «to confess or not to confess»» 13/12/2016

GAME THEORY The study of mathematical models of conflict and cooperation between intelligent rational decision-makers. Mainly used in economics & business, political science, biology, psychology, philosophy, computer science & logic. Umbrella term for the science of logical decision making in humans, animals, and computers. 1/8

GAME TYPES Cooperative / Non-cooperative Symmetric / Asymmetric A game is cooperative if the players are able to form alliances. Symmetric / Asymmetric In a symmetric game, payoffs depend only on the other strategies not on the players. Zero-sum / Non-zero-sum In zero-sum games, a player benefits only at the equal expense of others. Simultaneous / Sequential In sequential games, players have some prior knowledge about earlier actions. Perfect information / imperfect information A game is one of perfect information if all players know all previous moves of others. Others Combinatorial, infinitely long, discrete/continuous, differential, population, pooling games 2/8

PRISONER’S DILEMMA Shows why two completely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so. Characteristics: non-cooperative, symmetric, non-zero-sum, simultaneous, imperfect information. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentences payoffs and named it, "prisoner's dilemma". 3/8

FORMAL PRESENTATION Two members of a criminal gang are arrested and imprisoned. No communication between them (imperfect information). Lack of sufficient evidence. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner have 2 opportunities: cooperate or betray Prisoner B cooperates Prisoner B betrays Prisoner A cooperates Each serves 1 year Prisoner A: 3 years Prisoner B: goes free Prisoner A betrays Prisoner A: goes free Prisoner B: 3 years Each serves 2 years 4/8

GENERALIZED FORM R: cooperation reward P: punishment payoff T: temptation payoff S: sucker’s payoff T > R > P > S Cooperate Betray R, R S, T T, S P, P 5/8

R > P T > R and P > S So the dilemma is For the overall situation, mutual cooperation is superior to mutual defection. T > R and P > S From an individual perspective, rational outcome is defection. So the dilemma is Mutual cooperation yields a better outcome but it is not rational at the individual level. 6/8

ITERATED PRISONER’S DILEMMA The same two players play more than once in succession and they remember previous actions of their opponent and change their strategy accordingly. Requires: 2R > T + S To prevent alternating cooperation and defection giving a greater reward than mutual cooperation. The Evolution of Cooperation (1984) by Robert Axelrod Tournament of the N step prisoner’s dilemma (with N fixed) for which he invited academic colleagues to devise computer strategies. Winning strategy in Axelrod’s tournament: Tit for Tat Cooperate on the first iteration then repeat the opponent’s last action. 7/8

NECESSARY CONDITIONS FOR A SUCCESSUL STRATEGY BY AXELROD Nice (optimistic) Not defect before its opponent does. Retaliation Not always cooperation but also sometimes retaliation. Forgiving Fall back to cooperating if the opponent does not continue to defect. Non-envious Not striving to score more than the opponent. 8/8

REFERENCES https://en.wikipedia.org/wiki/Prisoner's_dilemma http://www.policonomics.com/lp-game-theory2-prisoners- dilemma/ http://science.howstuffworks.com/game-theory1.htm https://plato.stanford.edu/entries/prisoner-dilemma/ http://www.investopedia.com/terms/p/prisoners-dilemma.asp http://www.econlib.org/library/Enc/PrisonersDilemma.html http://www.iterated-prisoners-dilemma.net/ http://www.brembs.net/ipd/ipd.html http://serendip.brynmawr.edu/playground/pd.html