How John Maynard Smith Applied Game Theory to Evolution

John Maynard Smith revolutionized evolutionary biology by introducing game theory to explain how animal behaviors and strategies evolve over time. By adapting mathematical models originally developed for human economics, he showed that the success of an organism’s behavioral strategy depends on what others in the population are doing. This article explores how Maynard Smith formulated the concept of Evolutionary Stable Strategies (ESS), utilized the famous Hawk-Dove model, and fundamentally changed our understanding of natural selection and animal conflict.

From Rationality to Darwinian Fitness

Traditional game theory, developed by John von Neumann and Oskar Morgenstern, analyzed decisions made by rational human actors trying to maximize their economic gains. Maynard Smith realized that this mathematical framework could be applied to biology by replacing “rational players” with “evolving organisms” and “economic payoffs” with “Darwinian fitness” (survival and reproductive success).

In the biological version of game theory, organisms do not consciously choose their strategies. Instead, their strategies are genetically inherited behaviors. Natural selection acts as the arbiter: strategies that yield higher fitness propagate through the population, while less successful ones are weeded out.

The Evolutionary Stable Strategy (ESS)

In 1973, alongside chemist and geneticist George Price, Maynard Smith introduced the concept of the Evolutionary Stable Strategy (ESS). An ESS is a strategy which, if adopted by a majority of a population, cannot be invaded by any alternative, mutant strategy.

When a population adopts an ESS, natural selection alone is sufficient to prevent new mutant behaviors from successfully spreading. This concept provided a mathematical basis for understanding why certain behaviors, even those that seem suboptimal for the species as a whole, remain stable over evolutionary time.

The Hawk-Dove Game

To illustrate how ESS works, Maynard Smith used the “Hawk-Dove” game, which models animal conflict over a valuable resource (like food or a mate). In this model, individuals can adopt one of two strategies:

• Hawk: Fight aggressively for the resource. A Hawk will only retreat if injured.
• Dove: Display peacefully. A Dove will never fight; it shares the resource if meeting another Dove, and immediately retreats if met by a Hawk.

The payoffs depend on the value of the resource (\(V\)) and the cost of injury from a fight (\(C\)).

• If two Hawks meet, they fight. One wins, one is injured, resulting in an average payoff of \((V - C) / 2\).
• If a Hawk meets a Dove, the Hawk wins the resource (\(V\)) and the Dove gets nothing (\(0\)).
• If two Doves meet, they share the resource, resulting in a payoff of \(V / 2\).

Through mathematical analysis, Maynard Smith showed that if the cost of injury is greater than the value of the resource (\(C > V\)), a pure “Hawk” population is not stable because Doves can easily invade. Conversely, a pure “Dove” population is not stable because a mutant Hawk would dominate. Instead, the population reaches an ESS that consists of a specific ratio of Hawks and Doves, or a “mixed strategy” where individuals randomly choose to act like Hawks or Doves with specific probabilities.

This explained why real-world animal conflicts are often highly ritualized and rarely end in death; natural selection favors balanced, ritualized displays over constant, lethal aggression.

Impact on Modern Biology

Maynard Smith’s application of game theory transformed evolutionary biology by shifting the scientific focus away from “group selection” (the outdated idea that animals behave for the “good of the species”). Instead, it proved that complex social behaviors—such as altruism, cooperation, communication, and territoriality—could be explained through gene-centric self-interest. Today, evolutionary game theory remains a cornerstone of ecology, animal behavior, and evolutionary psychology.