Solution for one-stage bidding game with incomplete information

We investigate a model of one-stage bidding between two differently informed stockmarket agents where one unit of risky asset (share) is traded. The random liquidation price of a share may take two values: the integer positive $m$ with probability $p$ and $0$ with probability $1-p$. Player 1 (insider) is informed about the price, Player 2 is not. Both players know probability $p$. Player 2 knows that Player 1 is an insider. Both players propose simultaneously their bids. The player who posts the larger price buys one share from his opponent for this price. Any integer bids are admissible. The model is reduced to zero-sum game with lack of information on one side. We construct the solution of this game for any $p$ and $m$: we find optimal strategies of both players and describe recurrent mechanism for calculating game value. The results are illustrated by means of computer simulation.