Generic finiteness of outcome distributions for two-person game forms with three outcomes

摘要

A two-person game form is given by nonempty finite sets S-1, S-2 of pure strategies, a nonempty set Omega of outcomes, and a function theta: S-1 x S-2 -> Delta(Omega), where Delta(Omega) is the set of probability measures on Omega. We prove that if the set of outcomes contains just three elements. generically, there are finitely many distributions Omega on induced by Nash equilibria .