Algorithm for Solving the Problem of the First Phase in a Game Problem with Arbitrary Situations

Abstract

The game problem of two persons (players) is considered. The two players alternately choose their strategies from the appropriate sets. First, the first player chooses his strategy, then, knowing the strategy of the first player, the second player chooses his strategy. The set of strategies of the second player depends on the strategy of the first player. It is required to determine the following: for any strategy of the first player, does there exist a corresponding strategy of the second player? This problem is solved using a special linear maximin problem with connected variables, the solution of which is reduced to determining the maximum value of the objective function of the problem’s dual to it on special strategies. The algorithm for solving the problem considered is given. Two examples that illustrate the algorithm and the results of numerical experiment is given.

Keywords

• game problem
• first phase problem
• dual problem
• support
• algorithm