Game Theory by James Crissey Luis Mendez James Reid

Complex Adaptive Systems and the Evolution of Reciprocation by Karl Sigmund University of Vienna

Human Societies n cooperation is ubiquitous n few individual inequalities in reproductive potential n social rules level reproductive opportunities and prevent establishment of global controller

Human cooperation n not based on relatedness n Based on reciprocation n based on economic exchanges n human cohesiveness is explained based on economic exchanges

Game theory n studies the economics of interacting egoists - non-cooperative game theory n players cooperate, not by the command of a controller or by deference to the group n cooperation based on rules

Game theory cont... n Trivers –suggested reciprocation as mutual assistance –introduced the prisoner’s dilemma

Expansion of Trivers Findings n 1981 Axelrod and Hamilton applied the evolutionary game theory to players engaged in many rounds of the prisoners dilemma game against randomly chosen co-players. n Axelrod adapted the genetic algorithms of John Holland to simulate the effects of evolutionary trial and error.

Expansion of Trivers finding cont. n First application of genetic algorithms to a genuine evolutionary problem rather than a technical optimization problem

Indirect reciprocity n Alexander (1987) the biological basis for human moral systems n an act of assistance may be returned not to the donor but a third party

Direct Reciprocation n Prisoner’s dilemma is a two-player game where both players have the same two strategies and the same payoff

Direct Reciprocation n Prisoner’s dilemma –two-player game in which both player’s have the same two strategies as well as the same two payoffs –can to cooperate or defect –rewarded based on what they choose

Direct Reciprocation cont... n PD game player’s choose simultaneously whether they want to cooperate or defect n assumes that if player starts off by cooperating and then does what ever the other person does

Direct Reciprocation cont... n Generous Tit for Tat (GTFT) –person retaliates sometimes after players defects –but always cooperates after they cooperate –Pavlov rule, suggests that people will cooperate if they use the same rule in the first round- assumes that players will repeat a move if it leads to high payoff

Indirect Reciprocation n the donor does not obtain a return from the recipient n donor receives return from third party n cost of an altruistic act is offset by a raised ‘score’ or status, which increases chance to subsequently become the recipient of an altruistic act

Indirect Reciprocation cont... n Indirect reciprocity involves reputation and status, and results in everyone in the group continually being assessed and re-assessed (Alexander, 1987) n Nowak and Sigmund (1998) –model of indirect reciprocation

Indirect Reciprocation cont... n in donor who provides there is a cost n however, the donor’s score increases n if player refuses to play, score decreases n if the frequency of less discriminating reaches a certain threshold, then defectors can take over, with the result that cooperation disappears in the population

Indirect discrimination cont... n random drift can subvert populations of discriminate altruist by indiscriminate altruist n once there frequency is too large, defectors can invade; but as soon as defectors reduce the proportion of indiscriminate altruist, the discriminate altruists fight back and eliminate the defectors

Indirect Reciprocation n this leads to a cooperative population which is proof against defectors, but not against indiscriminate altruists n chances of two players meeting again is low n must know the score of the co-player n interaction between two individuals is only observed by a small subset of the population

Indirect reciprocation cont... n only the few on-lookers will update score of donor n For larger groups it is difficult to establish cooperation n for indirect reciprocation to function –compute minimal amount of discriminators –minimal amounts of rounds per generation –maximal size of society

Discussion/Critical Analysis n underestimates kinship and genetic relatedness