On Simple MIX game

We consider zero-sum game which is called Simple MIX game. Each of two players (I and II) draws a number (x andy respectively) according to a uniform distribution on [0, 1]. After observing his number each player can then choose to offer or not offer to exchange his number for the other player's number. Conditions for an exchange are the following: 1) both players must offer for a trade to occur with certainty; 2) if only one player offers, a trade occurs with probabilityp. A player's payoff is equal to 1, 0 or — 1 if the value of the number which he finally gets is greater, equal or less than the number of his opponent. In the present paper we shall investigate Simple MIX game in which both of the players can obtain additional information about the opponent's number. Besides, we consider two-stage variant of this game.