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A special kind of two-person games with incomplete information is considered in the paper. The result of the game can be win or loss and the result is uncertain for both players. Prior to the game, one player, let's call him player A (attacker), assesses the strength, capabilities, etc. of his opponent B (defender). Probability of A's accession to the game depends on this evaluation. If A joins the game, B has to take part in it. Probability of A's winning depends then upon the real power of B. Before A joins the game,
the player B can allocate part of his forces on the additional activities, which we call a bluff, reducing their own strength, but at the same time reducing the probability of A's accession to the game. Player B's aim is to minimize the probability of A's winning. We construct a mathematical model of this type of games and investigate the desirability of using a bluff.
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