Understanding Biological Interactions via Game Theory
This is an article from Nature, entitled “Game Theory, Evolutionary Stable Strategies and the Evolution of Biological Interactions,” explaining how we can use game theory to model evolutionary behavior.
‘Survival of the fittest’ is a phrase that has often been used to describe natural selection, the mechanism for evolutionary change in nature; this phrase suggests that nature is driven by competition. However, interactions between organisms in nature can also be cooperative, for example altruistic. Altruism is defined as an interaction in which the fitness of the actor is decreased, while the fitness of the other individual increased. For example, when predators are nearing, many species of birds will give a warning call to other birds around them, in the process jeopardizing themselves. We can explain these seemingly counterintuitive phenomena using a game theoretic framework. In particular, we can examine a game between two organisms, where we define payoffs as resources obtained subtracted by the cost or energy spent. As the Nature article above describes, the interaction strategies, also known as phenotypes, can either be competitive, in which case we have Hawk-Dove model, or cooperative, which can be represented by the Prisoner’s Dilemma game. Those organisms which maximize their payoffs have the highest fitness. Furthermore, we can model natural selection by finding the stable Nash equilibria.
In the Hawk-Dove model, two organisms each have an aggressive strategy and a passive strategy. According to the article, the hawk strategy is a stable equilibrium “only if the value of the resource is greater than the cost of the conflict.” Thus, we see that this models the competitive behavior between organisms in nature.
In the Prisoner’s Dilemma game, recall that both prisoners receive the most mutual payoff when they both remain silent. We can apply this to nature where two organisms receive the greatest mutual payoff when they cooperate with each other. Cowden states that we assume that between two players, the game is repeated over “evolutionary time scales”. Through a number of iterations, one organism will use the strategy of the other from the previous iteration, and as a result cooperation can occur as a Nash equilibrium strategy, provided that the individuals meet sufficiently many times.
This article builds off of what we have learned in class, namely two of the most common types of games: Hawk-Dove and Prisoner’s Dilemma, and then finding stable Nash equilibria of them. In particular, this article shows the power and applicability of game theory to very complex phenomena.