James Crissey

Luis Mendez

James Reid

 

Karl Sigmund (2001)Complex Adaptive Systems and the Evolution of Reciprocation

 

††††††††††† In human societies cooperation is ubiquitous.There are few individual inequalities in reproductive potential.A few potentates have managed to obtain an almost unlimited control of their community.These are exceptions, which generally occur at a late and probably transient stage of evolution.In both modern society and bands of hunter-gatherers, social rules tend to level reproductive opportunities and prevent establishment of a global controller.The bulk of human cooperation is based not on relatedness, but reciprocation.It is economic exchanges not genetic ties that explain the cohesion of humans.

††††††††††† This implies that individuals collaborate only if it is for their own good.The mathematical framework for studying the economics of interacting egoists is known as the game theory.This branch of the game theory is somewhat misleading called non-cooperative game theory.The term non-cooperative means in this context that players cannot negotiate binding and enforceable agreements.Players can nevertheless achieve cooperation by following a myopic set of rules.

††††††††††† Robert Trivers was the first to suggest reciprocation as a bias for mutual assistance in animal (human) behavior and to discuss it in terms of the game theory.Trivers introduced the prisonerís dilemma game to bring the problem into focus.Robert Axelrod took one step further when he adapted the genetic algorithms of John Holland to simulate the effects of evolutionary trial and error.This was the first application of genetic algorithms to a genuine evolutionary problem rather than a technical optimization problem.This success has led to many further investigations involving continuous versions of the game.

The Prisonerís Dilemma (PD) is a two-player game in which both players have the same two strategies as well as the same two payoffs. A player can choose to cooperate (C), or defect (D), and is rewarded points based on what they choose. If both players choose C than they both get a small reward, and if both players choose D, than they both get a small punishment in the form of reduction of points. However, if one player chooses D and the other chooses C, than the player that chooses D will get a large reward, while the player that chooses C will get a large punishment, or decrease in points. In this game, it is implied that D dominates C, because no matter what the other player chooses D has the highest probability of earning the most points. In addition, this game also implies that joint cooperation is better than sharing the payoffs after a unilateral defection.

In the repeated PD game, players choose simultaneously whether they want to Cooperate or defect in each round. This game displays a constant probability (W) for each round. In the repeated PD game, strategies can be attributed to simple knee-jerking rules, such as Tit For Tat, TFT, which assumes that a player starts off by cooperating, and then does what ever the other person does. According to Axelrod (1987) these simple rules, such as TFT, are extremely valuable and more than hold there own against more complex strategies.

Investigators have used complex adaptive systems to simulate artificial societies of players engaged in repeated PD games. Axelrod developed the artificial players and used strategy based on what was played in the previous three rounds. The players then engaged in a round robin tournament with accumulating points, which was then transferred over into number of offspring to form the next generation. The researchers discovered that an initial increase in defectors was often followed by a re-emergence of cooperation.

Researchers using the repeated PD game have discovered a strategy called the generous Tit For Tat (GTFT). The GTFT is a strategy in which a person only retaliates some of the time after the presentation of a D, but always cooperates after the presentation of a C. It is important however, that the TFT first be established in a society before the GTFT is able to takeover.

Pavlov, a rule which states that players will cooperate if they used the same rules in the first round, assumes that players will repeat a move if it leads to a high payoff, but will not repeat a move if it does not lead to a payoff. The Pavlov rule, like the GTFT strategy, will only emerge if the TFT strategy has already been used. Essentially the TFT strategy serves as a starting point for cooperation.

Another strategy, the Contrite Tit For Tat (CTFT) strategy, monitors ones own standing and that of the co-player. The CTFT implies that a player standing is good unless he or she defects against a player with good standing. It has been shown that the CTFT strategy is good for invading populations of defectors and establishing a cooperative population.

In the normal PD setup, both players are supposed to move at once, which is the case in a predatory reaction in the wild. However, there are situations of mutual aid in the real world, which call for moving alternatively. In such circumstances the Fair-But-Firm strategy is used, which states that people will defect only after the unwarranted defection by a co-player. In addition to this information, it has been determined that if players are able choose, and refuse partners, than cooperation.

In addition to direct reciprocation, Sigmund mentions another strategy based on reciprocity. He refers to this other strategy as indirect reciprocation. Based on this idea, the individual donor does not obtain a return from the recipient, rather from a third party. Donorís, according to Sigmund, provide help if the recipient has helped others in the past. In essence, the altruistís help their probability of being helped in the future because theyíve assisted in the past, thus augmenting the probability of otherís helping them.

††††††††††† The idea behind this type of reciprocation is that if an individual engages in an altruistic act, the individual losses- cost. However, for the simple act that the individual engaged in providing they increase their score because they will potentially be helped in the future. If an individual refuses to play, they decrease their score.

††††††††††† Sigmund goes on to suggest that random drift can subvert populations of discriminate altruists by indiscriminate altruists; once their frequency is large, defectors can invade; but as soon as the defectors have reduced the proportion of indiscriminate altruists, the discriminate altruists can fight back and eliminate the defectors.

††††††††††† An important point posited by Sigmund is that cooperation is more robust if the society is challenged more frequently by invasion attempts of defectors. In addition he mention that degree of acquaintanceship, which is the probability that a player knows the score of the co-player, is larger than the cost-to-benefit ratio. He states that that the degree of acquaintanceship is analogous with Hamiltonís rule, which sates that the degree of relatedness (the probability that an allele in the playerís genome is also present in the co-player) must exceed the cost-to-benefit ratio.

 

Game Theory

 

 

 

 

 

I.                     Introduction

 

A.      Human Societies

-cooperation is ubiquitous

-social rules prevent establishment of a global conroller

B.       Human Cooperation

-not based on relatedness

-Based on reciprocation

C.       Game Theory

-studies the economics of interacting egoists

-cooperation based on rules

II.                   Direct Reciprocation

A.      Prisoners dillema

-two player game where both players have the same two strategies and the same payoff

-given options to cooperate or defect

-rewarded based on what they choose

B.       Tit for Tat

-person retaliates sometimes after players defect

-but always cooperate after they cooperate

III.                 Indirect Reciprocation

A.      Indirect Reciprocation

-donor does not obtain a return from the recipient

-donor recieves return from third party

-donor who provides there is a cost

-however donors score increases

-if player refuses to play score decreases

-chance of two players meeting again is low

-must know the score of theco-player

B.Indirect reciprocation to function

-compute minimal amount of discriminators

-minimal amount of rounds per generation

-maximal size of society

IV.                 Critical Analysis/Discusion

A.      Underestimates kinship and genetic relatedness

 

 

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††