The Bishop-Cannings theorem, in evolutionary game theory, establishes two properties of a mixed evolutionarily stable strategy: that every pure strategy played with positive probability within it must yield the same payoff, and that none of those component pure strategies can itself also be a stable strategy on its own. The theorem is useful because it allows an evolutionarily stable strategy to be found through algebraic conditions rather than by simulating a game to convergence.
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StatementE(mix, mix) = E(fix(a), mix) = E(fix(b), mix) = E(fix(c), mix) = ... = E(fix(n), mix) 1 Retrieved excerpt confirms the equal payoff condition among mixed ESS components; the theorem's second clause, that no component pure strategy is itself an ESS, was not present in the retrieved text. Classification
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Source Bishop-Cannings theorem (Wikipedia)
Sources
1. Bishop-Cannings Theorem - Holy Cross
Theorem statement section
E(mix, mix) = E(fix(a),mix) = E(fix(b), mix) = E(fix(c), mix) ... E(fix(n), mix)
References section
Bishop, D.T. and C. Cannings. 1978. A generalized war of attrition. J. Theor. Biol.
View the SourceBishop-Cannings theorem (Wikipedia)
- In Branch: Game Theory, Lead sentence
In Group: Equilibria, Bargaining and Cooperative Games, Lead paragraph
The Bishop-Cannings theorem is a theorem in evolutionary game theory.
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