A 2-person game on a polyhedral set of connected strategies

A 2-person zero-sum game with the payoff function being a sum of two linear functions and a bilinear one is considered on a generally unbounded polyhedral set, which is interpreted as a set of pairs of strategies of two players, where the strategies turn out to be connected. The problem of existence and finding a certain equilibrium point of the game along with that of min-max and max-min points for the payoff function is examined. Verifiable necessary and sufficient conditions for solutions to these problems are proposed. These conditions make it possible to find the points by solving an auxiliary system of linear and quadratic constraints (for the equilibrium points), and quadratic programming problems (for the min-max and max-min points) formed on the basis of the master problems.