Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is st...

We simulate the prisoner’s dilemma and hawk-dove games on a real social acquaintance network. Using a discrete analogue of replicator dynamics, we show that surprisingly high levels of cooperation can be achieved, contrary to what happens in unstructured mixing populations. Moreover, we empirically show that cooperation in this network is stable with respect to invasion by defectors.

We introduce the class of anti-coordination games, including the hawk-dove game as a special case. A symmetric two-player game is said to have the anti-coordination property if any worst response to a mixed strategy is in the support of that mixed strategy. Every anti-coordination game has a unique interior Nash equilibrium. We investigate stability of the static equilibrium under several dynam...

The hawk-dove game famously introduced strategic game theory thinking into biology and forms the basis of arguments for limited aggression in animal populations. However, aggressive 'hawks' and peaceful 'doves', with strategies inherited in a discrete manner, have never been documented in a real animal population. Thus, the applicability of game-theoretic arguments to real populations might be ...

In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker replicator equation that describes dynamics of pure strategy frequencies. I then investigate the evolution of not only frequencies of pure strategies but also of to...

The paper presents an attempt to integrate the classical evolutionary game theory based on replicator dynamics and state-based approach of Houston McNamara. In new approach, individuals have different heritable strategies; however, carrying same strategy can differ in terms state, role or situation which they act. Thus, is completed by additional subsystem differential equations describing tran...

A systematic analysis of the effects of spatial extension on the equilibrium frequency of cooperators and defectors in games is presented and compared to well mixed populations where spatial extension can be neglected. We demonstrate that often spatial extension is indeed capable of promoting cooperative behavior. This holds in particular for the prisoner’s dilemma for a small but important par...

A systematic analysis of the effects of spatial extension on the equilibrium frequency of cooperators and defectors in 2× 2 games is presented and compared to well mixed populations where spatial extension can be neglected. We demonstrate that often spatial extension is indeed capable of promoting cooperative behavior. This holds in particular for the prisoner’s dilemma for a small but importan...

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an nxn payoff matrix. Players can use mixed strategies, which are given by the vector (p(1),...,p(n)). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entri...