Evolutionary game theory

The central concept is the evolutionarily stable strategy (ESS), introduced by John Maynard Smith and George R. Price in 1973.¹ An ESS is a strategy that, if adopted by a population, cannot be invaded by any rare alternative strategy. It is a refinement of the Nash equilibrium, requiring that the strategy is a best reply to itself and that any mutant doing better against the ESS must do worse against itself. This condition ensures long-term stability under frequency-dependent selection.

The classic example is the Hawk-Dove game, where individuals can be aggressive (hawk) or peaceful (dove). The payoff matrix yields a mixed ESS where the population settles at a ratio of hawks to doves determined by the costs and benefits of fighting. This model explains the evolution of ritualized combat and display in animals, where escalated fights are costly and rarely occur.

The replicator equation, introduced by Peter Taylor and Leo Jonker in 1978, formalizes how the frequency of strategies changes over time based on their relative fitness.² It is a deterministic differential equation that describes the dynamics of a population of infinite size with asexual reproduction. The equation has been extended to include mutation, spatial structure, and finite populations, leading to the Moran process and adaptive dynamics.

Evolutionary game theory also connects to population genetics and quantitative genetics, providing a bridge between game-theoretic models and genetic inheritance. The theory has been applied to explain the evolution of cooperation, altruism, and spite, often using the prisoner's dilemma and public goods games as canonical models.³

In biology, evolutionary game theory has been used to explain animal behavior, such as foraging, mating, and territoriality. It has also been applied to the evolution of virulence in pathogens, where the trade-off between transmission and host survival is modeled as a game.⁴ In social science, it has been used to model the emergence of social norms, language, and economic behavior, often in the context of cultural evolution.

The theory has also been influential in evolutionary psychology, explaining human cooperation and moral emotions. It has been used to study the evolution of fairness and punishment, and to analyze the dynamics of social learning and conformity.⁵

Beyond the classic models, evolutionary game theory has been extended to include asymmetric games, where players have different roles or resources, and to multiplayer interactions, such as public goods games with multiple contributors. The concept of the evolutionarily stable set (ESSet) was introduced to handle situations where no single strategy is stable, but a set of strategies is collectively stable.

Another niche area is the application to prebiotic evolution, where game theory has been used to model the competition between self-replicating molecules. The theory has also been applied to the evolution of signaling and communication, including the handicap principle and honest signaling. In addition, evolutionary game theory has been used to analyze the dynamics of cancer, where cells within a tumor are viewed as players in a game of resource competition and cooperation.⁶

Evolutionarily stable strategy (ESS)

A strategy that, if adopted by a population, cannot be invaded by any rare alternative strategy.

Replicator equation

A differential equation describing how the frequency of strategies changes over time based on their relative fitness.

Hawk-Dove game

A model of conflict where individuals choose between aggressive (hawk) and peaceful (dove) behaviors.

Nash equilibrium

A set of strategies where no player can improve their payoff by unilaterally changing their strategy.

Frequency-dependent selection

A type of natural selection where the fitness of a phenotype depends on its frequency relative to other phenotypes.