Modified multistage bidding model with a countable set of states

A simplified financial market model with two players bidding for one unit of a risky asset for several consecutive stages is considered. First Player (an insider) is informed about the liquidation price of the asset which can take any value in $\mathbb{Z}_{+}$. At the same time Second Player knows only probability distribution $\bar p$ of the price and that First Player is an insider. At each bidding stage the players place integer bids. The higher bid wins and one unit of the asset is transacted to the winning player at the cost equal to a convex combination of the bids with some coefficient $\beta$. After each stage the bids are announced to the players. In this paper we obtain a solution to an infinitely long zero-sum game for distributions $\bar p$ with finite variation. The optimal strategy of the insider player generates a non-symmetric random walk of the asset price which supports the hypothesis that stock price fluctuations have a strategic origin.