The Alternative to Equilibrium Existence

This paper establishes and interprets a necessary and sucient condition for existence of (countably additive) correlated equilibrium in n-person games, assuming only that utility functions are bounded, measurable. A sequence of deviation profiles is consistent if there exists a correlated strategy that makes every profile in the sequence unprofitable with respect to the sum of utilities. An equilibrium exists if and only if every sequence of deviation profiles has a consistent subsequence. This condition fails to characterize Nash equilibrium. As a direct corollary, existence of (communication) equilibrium is characterized in games with incomplete information on type spaces large enough to include the universal one. Exact conditions for existence of approximate correlated equilibrium are also obtained, as well as a value for two-person zero-sum games.