Evolutionary Games and Population Dynamics

  title={Evolutionary Games and Population Dynamics},
  author={Josef Hofbauer and Karl Sigmund},
Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the… 

Evolutionary Game Theory

This chapter initially summarizes features of matrix games before showing how the theory changes when the two-player game has a continuum of traits or interactions become asymmetric, focusing on the connection between static game-theoretic solution concepts.

Evolutionary Game Theory and Evolutionary Stability

This article discusses generalizations of evolutionary game theory, ESS, and evolutionary stability to several other classes of games, including symmetric population games where payoffs to pure strategies are nonlinear functions of the current population state as well as asymmetric games where players are assigned different roles.

Statistical mechanics of evolutionary dynamics.

The results show that cooperation based on indirect reciprocity is robust with respect to fake reputations and can even be enhanced by them, and it has been found that fraud does not necessarily have a detrimental effect on social systems.

Evolutionary Game Theory

The original models were based on competitions between identical conspecifics, although they now cover a huge range of complex behavioural scenarios such as the adoption of elaborate behaviours or costly physical ornaments by male animals seeking mates or the formation of dominance hierarchies among social groups.

Exploration dynamics in evolutionary games

This work considers a system in which players unconditionally imitate more successful strategies but sometimes also explore the available strategies at random, and term this phenomenon “exploration dynamics” to contrast it with the traditional focus on imitation.

Evolutionary dynamics of multiple games

The results reveal that even when interactions become incredibly complex, their properties can be captured by relatively simple concepts of evolutionary game(s) theory.

Evolutionary dynamics of a smoothed war of attrition game.

Evolutionary games and population dynamics: maintenance of cooperation in public goods games

This model represents natural extension of replicator dynamics to populations of varying densities and feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games.

Learning enables adaptation in cooperation for multi-player stochastic games

Using evolutionary game theory, this work develops a framework of stochastic games that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviours can evolve in the ever-changing group interaction environment, and suggests that in complex social–ecological dilemmas, learning enables the adaptation of individuals to varying environments.

Mathematical and statistical models in evolutionary game theory

Modeling of evolution is becoming increasingly important in biological and social systems. The idea of evolution presents a reasonable and convincible perspective to the problem of long term



Evolution and the Theory of Games

It is beginning to become clear that a range of problems in evolution theory can most appropriately be attacked by a modification of the theory of games, a branch of mathematics first formulated by Von Neumann and Morgenstern in 1944 for the analysis of human conflicts.

Frequency-Dependent Stability for Two-Species Interactions

  • Cressman
  • Biology
    Theoretical population biology
  • 1996
The main focus of the paper is to investigate the application of the ESS (evolutionarily stable strategy) solution concept to dynamic stability when fitnesses are given by random interactions between individuals as opposed to viability selection.

Dynamic Modeling in Behavioral Ecology

This book describes a powerful and flexible technique for the modeling of behavior, based on evolutionary principles. The technique employs stochastic dynamic programming and permits the analysis of

Group selection in predator-prey communities.

  • M. Gilpin
  • Biology
    Monographs in population biology
  • 1975
This book presents a model, based on predator-prey dynamics, wherein nonlinear effects are important, so that small advantages to the selfish individual are nonlinearly amplified into disaster for his group, and shows that group selection can be rapid and powerful.

Evolutionary Game Theory

This text introduces current evolutionary game theory--where ideas from evolutionary biology and rationalistic economics meet--emphasizing the links between static and dynamic approaches and

The rock–paper–scissors game and the evolution of alternative male strategies

MANY species exhibit colour polymorphisms associated with alternative male reproductive strategies, including territorial males and 'sneaker males' that behave and look like females1–3. The

Resource competition and community structure.

  • D. Tilman
  • Environmental Science
    Monographs in population biology
  • 1982
This book builds a mechanistic, resource-based explanation of the structure and functioning of ecological communities and explores such problems as the evolution of "super species," the differences between plant and animal community diversity patterns, and the cause of plant succession.