The existence of equilibria in games with multivalued payoff functions. (Q1432547)

The paper is devoted to the problem of the existence of equilibria in a generalized non-cooperative \(N\)-player game model with multivalued pay-offs. Two approaches to the multivalued pay-off functions are mentioned. The first one considers all values of the function to be achievable with identical probability, while in the second approach only the pay-off values which are really achievable are considered. Each of these approaches is used for the construction of equilibria of two types: extremally weak (called equilibria) and extremally strong (called conditional equilibria). The main results formulate conditions for the existence of equilibria. Some of these conditions are illustrated by an example of a multivalued two-person nonzero-sum game.