This concept holds when certain sets are non-empty, convex, compact subsets of a Euclidean space by the Kakutani Fixed Point Theorem, and the utility function is continuous and quasi-concave.  
A variation to this concept that includes perturbations in decision models is known as trembling-hand perfect.  This concept holds when certain sets are non-empty, convex, compact subsets of a Euclidean space by the Kakutani Fixed Point Theorem, and the utility function is continuous and quasi-concave.  A Bayesian one is found by anticipating the plans of others, and they were worked on by Harsanyi and Selten as well as their namesake, who introduced them in the paper Non-Cooperative Games.  For 10 points, name this idea in which each player's strategy choice is a best-response to the strategies played by his rivals, a game theory equilibrium named for a schizophrenic.
A variation to this concept that includes perturbations in decision models is known as trembling-hand perfect.  
Nash equilibrium [accept Nash after "equilibrium" is read, prompt on it before]