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Evolutionary Game Theory

  • Reference work entry
Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Normal Form Games

Static Notions of Evolutionary Stability

Population Games

Revision Protocols

Deterministic Dynamics

Stochastic Dynamics

Local Interaction

Applications

Future Directions

Acknowledgments

Bibliography

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Abbreviations

Deterministic evolutionary dynamic :

A deterministic evolutionary dynamic is a rule for assigning population games to ordinary differential equations describing the evolution of behavior in the game. Deterministic evolutionary dynamics can be derived from revision protocols, which describe choices (in economic settings) or births and deaths (in biological settings) on an agent-by-agent basis.

Evolutionarily stable strategy (ESS) :

In a symmetric normal form game, an evolutionarily stable strategy is a (possibly mixed) strategy with the following property: a population in which all members play this strategy is resistant to invasion by a small group of mutants who play an alternative mixed strategy.

Normal form game :

A normal form game is a strategic interaction in which each of n players chooses a strategy and then receives a payoff that depends on all agents' choices choices of strategy. In a symmetric two‐player normal form game, the two players choose from the same set of strategies, and payoffs only depend on own and opponent's choices, not on a player's identity.

Population game :

A population game is a strategic interaction among one or more large populations of agents. Each agent's payoff depends on his own choice of strategy and the distribution of others' choices of strategies. One can generate a population game from a normal form game by introducing random matching; however, many population games of interest, including congestion games, do not take this form.

Replicator dynamic:

The replicator dynamic is a fundamental deterministic evolutionary dynamic for games. Under this dynamic, the percentage growth rate of the mass of agents using each strategy is proportional to the excess of the strategy's payoff over the population's average payoff. The replicator dynamic can be interpreted biologically as a model of natural selection, and economically as a model of imitation.

Revision protocol :

A revision protocol describes both the timing and the results of agents' decisions about how to behave in a repeated strategic interaction. Revision protocols are used to derive both deterministic and stochastic evolutionary dynamics for games.

Stochastically stable state :

In Game‑theoretic models of stochastic evolution in games are often described by irreducible Markov processes. In these models, a population state is stochastically stable if it retains positive weight in the process's stationary distribution as the level of noise in agents' choices approaches zero, or as the population size approaches infinity.

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Acknowledgments

The figures in Sects. “Deterministic Dynamics” and “Local Interaction” were created using Dynamo [184] and VirtualLabs [92], respectively. I am grateful to Caltech for its hospitality as I completed this article, and I gratefully acknowledge financial support under NSF Grant SES-0617753.

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  1. Department of Economics, University of Wisconsin, Madison, USA

    William H. Sandholm

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Sandholm, W.H. (2012). Evolutionary Game Theory. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_63

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