The Bishop–Cannings theorem is a theorem in evolutionary game theory. It states that (i) all members of a mixed evolutionarily stable strategy (ESS) have the same payoff (Theorem 2), and (ii) that none of these can also be a pure ESS (from their Theorem 3). The usefulness of the results comes from the fact that they can be used to directly find ESSes algebraically, rather than simulating the game and solving it by iteration.
- Bishop, D.T. and Cannings, C. (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.
- Prestwich, K. "The Bishop–Cannings Theorem (an annotated version of John Maynard Smith's exposition of The Bishop–Cannings Theorem)".
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