On a modification of a multistage bidding model with an insider

This paper is concerned with a modification of a discrete multistage bidding model introduced in [8]. Bidding takes place between two players for one unit of a risky asset. The price of the asset is determined randomly at the start of the bidding and can be either $ m $ with a probability of $ p $ or $ 0 $ with a probability of $ (1 - p) $. The real price of the asset is known to Player 1. Player 2 knows only the probability of a high price and that Player 1 is insider. At each stage of the bidding players make integral bids. The higher bid wins and one unit of the asset is transacted to the winning player. The price of the transaction equals to a convex combination of bids with a coefficient of $ 1/2 $. This model is reduced to the repeated game with incomplete information. The solution for the infinite game with arbitrary $ m $ an $ p $ is found, including optimal strategies for both players and the value of the game.