A difficulty with Nashʹs program: A proof of a special case

Let g be a cooperative game and let N be the set of players of g. According to Nashʹs Program N can find a noncooperative game G such that some Nash equilibrium of G may serve as a solution to g. We show that the implementation of Nashʹs Program might face some difficulties. In this paper we restrict ourselves to finite games. However, we proved in a previous unpublished paper that the same difficulties also appear when infinite games are allowed.