On a modification of the multistage bidding model with continuous bids and asymmetric information

This paper is concerned with a modification of the multistage bidding model with continuous bids. Bidding takes place between two players for one unit of a risky asset. Player 1 knows the real price of the asset while Player 2 only knows probabilities of high and low prices of the asset. At each stage of the bidding players make real valued bids. The higher bid wins, and one unit of the risky asset is transacted to the winning player. The price of the transaction is equal to a convex combination of bids with a coefficient chosen in advance. Optimal strategies and the value of the $n$-stage game are found.