Game Theory Application In Cooperation Between Animals

2190 words - 9 pages

The history of evolution is linked by numerous games played between organisms in groups. Because of the limited resources and overcrowded population of animals in a certain group, most of the games resemble Prisoners’ Dilemma, in which the Nash Equilibrium is to cheat on the other player, or to compete against each other. For example, egrets will try to push their brothers or sisters out of the nest to prevent competition for food brought back by the mother bird. In some of the games, however, the players will not choose to compete, but rather cooperate with each other to get higher payoff in total. Here, cooperating strategy is defined as choosing the move that is preferred by the other ...view middle of the document...

(Dugatkin, Lee A. and Hudson K. Reeve, P49-50) by cooperating with others, the player has to share the outcome with other players, with the tradeoff of group work reducing risk of danger. When the risk overweighs the cost of cooperation, the cooperative strategy dominates defective strategy, giving the animals an incentive to cooperate. u_1 (C,C)>u_1 (C,D)>u_1 (D,C)=u_1 (D,D), where C represents “Cooperate” and D represents “Defect”. However, such cooperation may be temporary since it is highly dependent on the changing environment, which may alter animals’ valuation of risk of danger and cost of cooperation.
The cooperative territory defense of Pied wagtail provides a vivid example of by-product mutualism. The birds defend riverside territories in winter since they forage on insects that wash up on the banks. The prey abundance on a territory would increase again after being depleted in a period of time. Some intruders often land on such territories, and sometimes they are tolerated while at other times they are aggressively chased off. This is because if the owner permits the intruder to stay and cooperate with them, a cost in terms of foraging is incurred, but the owner gets more assistance in territory defense. A territory may have a different value to the owner than to an intruder since the intruder does not know which areas have recently been depleted. Thus, on days of low food abundance, the owners have a higher feeding rate if they are alone, so that they would evict the intruders off the territories. On days of high food abundance, however, when there are a lot of intruders around, owners tolerate some intruders to help them defend the territory. Owners are able to increase their feeding rate by such association, since the benefits gained through defense assistance outweigh the cost of sharing the food with another bird. The rank of payoffs from different strategies holds, leading to by-product mutualism where both the owner and the intruder choose to cooperate with each other.
Cooperation may take many forms, especially in repeated games. According to Christopher Stephens, cooperation can be deferred, which means that alternating altruism is also a kind of cooperation. In alternating altruism, one player gets high payoff first, and the other player waits and gets the high payoff later. Specifically, when (u_1 (C,D)+u_1 (D,C))/2>u_1 (C,C), (u_1 (C,D)+u_1 (D,C))/2>u_1 (D,D) , (u_2 (C,D)+u_2 (D,C))/2>u_2 (C,C), and (u_2 (C,D)+u_2 (D,C))/2>u_2 (D,D), in which C is to “Cooperate” and D is to “Defect”, after a period of time, the players may tend to play such strategies that alternate (C,D) and (D,C) repeatedly, so that in total both of the players get higher payoff than constantly playing (C,C), which is a fragile equilibrium that can be broken by any incentive of cheating. The payoff is also higher than sticking to the Nash Equilibrium where both players play defecting all the time, dismissing the time value of the payoff.
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