# Evolutionary Games

# Evolutionary Games

The modeling of evolutionary games has established itself as an important theoretical tool in the social sciences. Evolutionary games have proven useful in deriving descriptively accurate models of human behavior in an economic context, and they have provided important insights regarding the origins of conventions and other social behavior. Indeed, it is a testament to the power of evolutionary games that they have been used productively not only in the social sciences but in biological and philosophical research as well.

The best way to understand the general idea of evolutionary games is by contrasting them with the rational choice methodology in game theory. In a rational choice model, one assumes that people are perfectly rational and self-interested, acting only to increase their own payoffs. These payoffs may be understood as financial rewards or any other positive outcomes.

Although rational choice models are powerful, and often appropriate, it is now known that humans often do not behave in a perfectly rational and self-interested manner. Instead, they often lack the cognitive sophistication required to compute their optimal behavior, while at other times they are motivated by emotional or other “irrational” factors. In such cases, it often turns out that the correct explanation of a particular behavior is etiological—that is, the behavior is the result of short-sighted evolutionary processes or trial-and-error learning, rather than a deliberate rational calculation. Thus, in the context of discussing evolutionary games, the term “evolution” refers generally to any process by which a group of individuals change their behavior in a strategic context.

Accordingly, evolutionary games typically dispense with the assumption that people are rational. Instead, the typical evolutionary game-theoretic model assumes that the agents being examined are myopic, cognitively simple, and not motivated by any self-interest at all. In the most common type of evolutionary game, the agents are simply “hard-wired” to behave in a particular way. The model generates predictions by imposing a dynamic in which the most successful strategies are reproduced according to how successful they are.

The evolutionary game that is undoubtedly the most well known is Robert Axelrod’s famous Prisoner’s Dilemma tournament, in which people were invited to submit strategies for playing the Iterated Prisoner’s Dilemma (1984). This is a game of tremendous importance in the social sciences because it is the simplest nontrivial model of situations in which there is a conflict between self-interested behavior and cooperation with another person. At the conclusion of the tournament, Axelrod considered what would happen in a population containing many copies of the submitted strategies if he introduced a dynamic in which the individuals in the population reproduced, with the most successful individuals having the most offspring, and where each offspring displayed the same behavior as their parent. There is now a large body of formal literature that has extended this idea, of which the best known is the “replicator dynamics” of Peter Taylor and Leo Jonker (1978).

In the replicator dynamics, one mathematically models the evolution of strategies by considering a population that is initially populated, in some arbitrary proportion, by at least two different strategies. In this model, it is assumed that any arbitrary pair of individuals is equally likely to interact. When they do, each will receive a payoff that is defined by the underlying game. Thus, if both the proportion of strategies in the population and the structure of the game are known, then the expected payoff that each strategy will receive in an interaction can be calculated. In the replicator dynamics, it is assumed that if a particular strategy has an expected payoff that is less than the average payoff in the population, the number of individuals using that strategy will gradually diminish. Conversely, if a particular strategy has a higher than average expected payoff, then the number of individuals using that strategy will gradually increase. This behavior is usually represented by a system of differential equations, which is solved to yield a description of the state of the population at any time in its evolution.

In the replicator dynamics, it is often the case that there is some proportion of strategies at which each strategy has the same expected payoff in the population. If this is the case, then the replicator-dynamics model implies that the representation of each strategy in the population will not change. Similarly, it is possible that one strategy will come to predominate in the population, while the other strategies gradually disappear.

Evolutionary games are most explanatory when such stable configurations of strategies exist. Typically, the explanatory strategy is to note that, unless there are powerful external influences on the population, one is most likely to observe a real-world population in a stable state, or approaching a stable state. In this way, an evolutionary model is capable of yielding specific predictions, without the use of the rationality assumptions of rational choice theory.

It is possible, of course, to derive different dynamical models that are best interpreted as models of learning processes, or that employ different assumptions. The best known of these is the “aspiration-imitation” model, which specifically represents the dynamic as a learning process that has various parameters that can be adjusted for the specific model.

Although the term *evolutionary game* is often used in a way that makes it synonymous with the replicator dynamics, it is more accurate to think of evolutionary game theory as a general framework that contains a large variety of different models. These models vary, not only in the specific parameters that define their behavior, but in more dramatic ways as well. The learning process, the cognitive sophistication of the agents, the size of the population, and the speed with which the population evolves are just some of the variables that may be taken into account in an evolutionary game (see Samuelson 1997 for an excellent survey). Evolutionary game theory is thus a flexible tool, and its study is rewarded by the large number of applications to which it can be put.

**SEE ALSO** *Game Theory; Noncooperative Games; Prisoner’s Dilemma (Economics); Rationality; Replicator Dynamics*

## BIBLIOGRAPHY

Axelrod, Robert. 1984. *The Evolution of Cooperation*. New York: Basic Books.

Samuelson, Larry. 1997. *Evolutionary Games and Equilibrium Selection*. Cambridge, MA: MIT Press.

Taylor, Peter, and Leo D. Jonker. 1978. Evolutionarily Stable Strategies and Game Dynamics. *Mathematical Biosciences* 40: 145–156.

*Zachary Ernst*

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