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Impalas, Parasites, and the Prisoner’s Dilemma

The existence of the Prisoner’s Dilemma is a good motivation for cooperation–by playing rationally, the two players in the Prisoner’s Dilemma end up with a worse outcome for both of them than if both players had cooperated. (Previous blog posts have pointed out that actual people cooperate more often than would be expected of purely rational players.) In this article, Pavel Stopka and Dominic D.P. Johnson expand on the application of the Prisoner’s Dilemma to real-world natural systems. In a previous study, they noted that although the Prisoner’s Dilemma is frequently used to explain cooperation in nature, slight variations in the payoffs for the players in real-world situations change the actual game being played.

In this study (2012), Stopka and Johnson modeled the cooperative grooming between impalas and the resulting payoffs for individuals, taking into account several factors (like numbers of parasites). By grooming each other, impalas can remove parasites from other impalas. Since we can observe this behavior, it’s clear that the impalas engage in some kind of cooperation rather than selfishly not grooming. It’s harder to identify the game the impalas are playing and the strategy they are using. One possibility is that the impalas are cooperating in the situation of an iterated Prisoner’s Dilemma, where the game is played more than once. At first glance it seems like both impalas should benefit if they groom each other, neither benefits if both impalas do nothing, and if only one cooperates while the other defects, the defector gets the benefit of being groomed without having to do any work. But the authors of this study argue that the impalas are playing a slightly different game. By modeling the impalas, grooming, and parasites, they show that it is beneficial for a parasite-ridden impala to groom another impala, even if the action is not reciprocated, since parasites will move to the more parasite-free host. The game played depends on the number of parasites on individual impalas, and interactions between impalas who have different numbers of parasites. In some cases, the best strategy for the impalas mimics a cooperation strategy for the iterated Prisoner’s Dilemma, despite being a different game.

There are other ways natural systems can deviate from the Prisoner’s Dilemma–for example, in the case of the impalas, the individuals can communicate their intents and respond to the actions of the others. This allows impalas to “parcel”, a behavior described in the article: cooperate as long as the other cooperates, for decreasing periods of time, which allows the impalas to manipulate each others’ decisions and signal how much one individual needs the help of the other.

This article points out an important issue in applying game theory to real-world data: by only looking at observed behaviors of individuals, we can assume that they are playing the wrong game. We often have to take into account variations in payoffs for individuals, communication between individuals, and benefits to the group in addition to benefits to the individuals. And the existence of cooperation in games that look like the Prisoner’s Dilemma doesn’t automatically mean that the players are not playing rationally.

 

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