Evolutionary game theory (EGT) is the application of game theory to interaction dependent strategy evolution in populations. EGT is useful in a biological context by defining a framework of strategies in which adaptive features can be modeled. It originated in 1973 with John Maynard Smith and George R. Price's formalization of evolutionarily stable strategies as an application of the mathematical theory of games to biological contexts^[1], arising from the realization that frequency dependent fitness introduces a strategic aspect to evolution. EGT differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria. Despite its name, evolutionary game theory has become of increasing interest to economists, sociologists, anthropologists, and philosophers.

Contents 1 Basis 2 Models 3 Application 4 See also 5 References 6 External links

[edit] Basis

In Smith's and Price's paper, “The Logic of Animal Conflict,” a computer model was used to show why animals had not adapted a “total war” strategy. Adaptations for males focused on maximizing their ability to compete with each other in order to maximize their dominance over a territory and better compete for mates. Using game theory, they were able to test a variety of evolutionary strategies to see which one emerged with the highest average payoff, explaining why animals have only evolved “limited war” strategy, in which risk of serious injury is low ^[2].

For EGT to be applicable to organisms, they cannot be following a set of random rules, but rather a specific strategy that responds to specific pressures. The value of any particular strategy is always in relation to an organism’s environment^[3]. When applied to an evolutionary context, a payoff for an outcome of a game is analogous to the fitness of an organism.

EGT assumes large populations who interact in randomly matched pairs in repeated games. The game is symmetric in two senses. The first is that players have the same set of strategies to choose from and the payoff for a strategy is the same for any player or organism is the same, irrespective of the features of the other player or organism who chooses an alternative strategy ^[4].

[edit] Models

An important feature of the set of models under the umbrella of evolutionary game theory is repetition. If the games were not repeated, these EGT models would not be able to provide any insight into adaptive behaviors and strategies due to the dynamic nature of the mechanisms of evolution. Further, this biological application is meaningful for economics because it provides an understanding of the adjustments that occur between two equilibria (Samuelson 2002). While game theory provides a framework within which biologists can learn and understand organisms, the observation of evolution and how these strategies are applied helps economics illuminate processes.

A strategy which can survive all "mutant" strategies is considered evolutionary stable. In the context of animal behavior, this usually means such strategies are programmed and heavily influenced by genetics, thus making any player or organism's strategy determined by these biological factors. ^[5]

[edit] Application

The successful application of game theory to evolution has brought further insights to human behavior. Whereas game theory traditionally assumes rational actors, in the real world this almost never describes human behavior. EGT has predicted behaviors in animals where strong assumptions of rationality cannot be made.

The common methodology to study the evolutionary dynamics in games is through replicator equations. These replicator equations in the context of evolutionary biology shows the growth rate of the proportion of organisms using a certain strategy and that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole ^[6]. Continuous replicator equations assume infinite populations, continuous time, complete mixing and that strategies breed true. The attractors (stable fixed points) of the equations are equivalent with evolutionarily stable states.

Evolutionary game theory has been successfully applied to many areas of evolutionary biology with a recent development in the area of co-evolution. In a paper by Carl Bergstrom and Michael Lagmann, they successfully apply evolutionary game theory models to understand the division of benefits in mutualistic interactions between organisms. Darwinian assumptions about fitness are modeled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship will gain a disproportionately high share of the benefits or payoffs. This application of EGT provided an interesting and perhaps unexpected twist on the Red Queen Hypothesis which concludes evolution favored faster rates of evolution ^[7].

[edit] See also

• Adaptive dynamics
• Behavioral ecology
• Dynamical systems
• Evolution and the Theory of Games (book)
• Evolutionary stable strategy
• Gene-centered view of evolution
• Memetics

[edit] References

1. ^ Maynard-Smith, J.; Price, G. R. (1973). "The Logic of Animal Conflict". Nature 246: 15. doi:10.1038/246015a0.  edit
2. ^ Smith, J.M., G.R. Price. 1973. Logic of animal conflict. Nature. 246: 15-18.
3. ^ Slobodkin, L., A. Rapoport. 1974. An optimal strategy of evolution. QRB. 49: 181-200.
4. ^ Samuelson, L. 2002 Evolution and game theory. JEP. 16: 46-66.
5. ^ Weibull, J. W. (1995) Evolutionary game theory, MIT Press
6. ^ Samuelson, L. 2002 Evolution and game theory. JEP. 16: 46-66
7. ^ Bergstrom, C., M. Lachmann. 2003. The red king effect: when the slowest runner wins the coevolutionary race. Nat. Acad. Sci. 100: 593-598.

• Maynard Smith, J. (1982) Evolution and the Theory of Games.
• P. Hammerstein and R. Selten, "Game theory and evolutionary biology", in Handbook of Game Theory with Economic Applications, R. J. Aumann and S. Hart, Eds. (Elsevier, Amsterdam, 1994), vol. 2, pp. 929-993
• Hofbauer, J. and Sigmund, K. (1998) Evolutionary games and population dynamics, Cambridge University Press
• Taylor, P. D. (1979). Evolutionarily Stable Strategies with Two Types of Players J. Appl. Prob. 16, 76-83.
• Taylor, P. D., and Jonker, L. B. (1978). Evolutionarily Stable Strategies and Game Dynamics Math. Biosci. 40, 145-156.
• Weibull, J. W. (1995) Evolutionary game theory, MIT Press

[edit] External links

• EGT at the Stanford Encyclopedia of Philosophy
• Evolving Artificial Moral Ecologies at The Centre for Applied Ethics, University of British Columbia
• Evolutionary game theory at the Open Directory Project

v • d • e Topics in population genetics Key concepts Hardy-Weinberg law · Genetic linkage · Linkage disequilibrium · Fisher's fundamental theorem · Neutral theory · Price equation Selection Natural · Sexual · Artificial · Ecological Effects of selection on genomic variation Genetic hitchhiking · Background selection Genetic drift Small population size · Population bottleneck · Founder effect · Coalescence · Balding–Nichols model Founders R. A. Fisher · J. B. S. Haldane · Sewall Wright Related topics Evolution · Microevolution · Evolutionary game theory · Fitness landscape · Genetic genealogy List of evolutionary biology topics

v • d • e Topics in game theory Definitions Normal-form game · Extensive-form game · Cooperative game · Information set · Preference Equilibrium concepts Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance · Pareto efficiency · Quantal response equilibrium · Self-confirming equilibrium Strategies Dominant strategies · Pure strategy · Mixed strategy · Tit for tat · Grim trigger · Collusion · Backward induction Classes of games Symmetric game · Perfect information · Simultaneous game · Sequential game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Bargaining problem · Stochastic game · Large poisson game · Nontransitive game · Global games Games Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Centipede game · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock-paper-scissors · Pirate game · Dictator game · Public goods game · Blotto games · War of attrition · El Farol Bar problem · Cake cutting · Cournot game · Deadlock · Diner's dilemma · Guess 2/3 of the average · Kuhn poker · Nash bargaining game · Screening game · Trust game · Princess and monster game Theorems Minimax theorem · Purification theorem · Folk theorem · Revelation principle · Arrow's impossibility theorem See also Tragedy of the commons · All-pay auction · List of games in game theory

This game theory article is a stub. You can help Wikipedia by expanding it. v • d • e

or