Bishop-Cannings theorem

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In game theory, the Bishop-Cannings theorem proves that all members of a mixed evolutionarily stable strategy have the same payoff, and that none of these can also be a pure evolutionarily stable strategy.

See also

• Evolutionarily stable strategy
• War of attrition (game)

References

• Bishop, D.T. and C. Cannings. 1978. A generalized war of attrition. Journal of Theoretical Biology 70:85-124.
• Maynard Smith, J.. (1982) Evolution and the Theory of Games. Cambridge University Press. ISBN 0521288843 (Appendix C)

External links

• [Ken Prestwich's annotated version of Maynard Smith's exposition]

[ 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 · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy
Strategies	Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat
Classes of games	Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design
Games	Prisoner's dilemma · Chicken · Stag hunt · Ultimatum game · Coordination game · Matching pennies · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game
Theorems	Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Bishop-Cannings theorem
Related topics	Mathematics · Economics · Behavioral economics · Evolutionary biology · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists

 

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