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

cooperation is ubiquitous few individual inequalities in

reproductive potential social rules level reproductive

opportunities and prevent establishment of global controller

Human cooperation

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

based on economic exchanges

Game theory

studies the economics of interacting egoists - non-cooperative game theory

players cooperate, not by the command of a controller or by deference to the group

cooperation based on rules

Game theory cont . . .

Trivers– suggested reciprocation as mutual

assistance– introduced the prisoner’s dilemma

Expansion of Trivers Findings

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.

Axelrod adapted the genetic algorithms of John Holland to simulate the effects of evolutionary trial and error.

Expansion of Trivers finding cont. First application of genetic algorithms to

a genuine evolutionary problem rather than a technical optimization problem

Indirect reciprocity

Alexander (1987) the biological basis for human moral systems

an act of assistance may be returned not to the donor but a third party

Direct Reciprocation

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

Direct Reciprocation

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 . . .

PD game player’s choose simultaneously whether they want to cooperate or defect

assumes that if player starts off by cooperating and then does what ever the other person does

Direct Reciprocation cont . . .

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

the donor does not obtain a return from the recipient

donor receives return from third party 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 . . .

Indirect reciprocity involves reputation and status, and results in everyone in the group continually being assessed and re-assessed (Alexander, 1987)

Nowak and Sigmund (1998)– model of indirect reciprocation

Indirect Reciprocation cont...

in donor who provides there is a cost however, the donor’s score increases if player refuses to play, score decreases 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 . . .

random drift can subvert populations of discriminate altruist by indiscriminate altruist

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

this leads to a cooperative population which is proof against defectors, but not against indiscriminate altruists

chances of two players meeting again is low must know the score of the co-player interaction between two individuals is only

observed by a small subset of the population

Indirect reciprocation cont . . .

only the few on-lookers will update score of donor

For larger groups it is difficult to establish cooperation

for indirect reciprocation to function– compute minimal amount of discriminators– minimal amounts of rounds per generation– maximal size of society

Discussion/Critical Analysis

underestimates kinship and genetic relatedness