Bidding games with several risky assets

Abstract

This paper considers multistep bidding models where several types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These random prices depend on "a state of nature" determined by the initial chance move according to a probability distribution that is known to both players. Player 1 (insider) is aware of the state of nature, but Player 2 is not. Player 2 knows that Player 1 is an insider. The bids may take any integer values. The n-step model is reduced to a zero-sum repeated game with incomplete information of Player 2. It is shown that, if the liquidation prices of shares have finite variances, then the value sequence of n-step games is bounded. This property makes it reasonable to consider the bidding of unlimited duration. The solutions of the corresponding infinite-duration games are constructed. By analogy with the case of two risky assets (see [9]), the optimal strategy of Player 1 induces a random walk of the transaction prices. The symmetry of this random walk is broken at the final steps of the game.