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Abstract:

We investigate the consequences of formally assuming that players in a game share the belief that they are playing some Nash Equilibrium. In games of perfect information this leads to a refinement of Nash Equilibrium. It always exists but need not be unique. It may not admit Subgame-Perfect Equilibrium (SPE), or the Extensive-Form Rationalizable profile. Imposing subgame perfection (only) on the game restricted to nodes on some equilibrium path leads to uniqueness. Allowing for imperfect information destroys existence. Altogether, our results cast some doubt on the appropriateness of using Nash Equilibrium as a generic solution concept and/or SPE as its refinement.