Bishop–Cannings theorem
Bishop–Cannings theorem
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 ESSs algebraically, rather than simulating the game and solving it by iteration.
The theorem was formulated by Tim Bishop and Chris Cannings at Sheffield University, who published it in 1978.
A review is given by john-maynard-smith in his book [[evolution-and-the-theory-of-games]], with proof in the appendix.