A 3-person game on polyhedral sets

AbstractA problem of a Nash equilibrium point existence and calculating for a 3-person game on polyhedral sets with special payoff functions is considered. It is shown that its existence is equivalent to that of a saddle point in an auxiliary antagonistic game on polyhedral sets and that the saddle point calculating can be done using vector-solutions of a linear and quadratic programming problem formulated on the basis of the master 3-person game