Repeated games with asymmetric information modeling financial markets with two risky assets^∗

Institute for Economics and Mathematics RAS, 1, Tchaikovsogo st., 191187, St.Petersburg, Russia
doman@emi.nw.ru

Received: 1 February 2012
Accepted: 30 May 2013

Abstract

We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer values. The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G_∞(p). We give the solutions for these games. Optimal strategies of Player 1 generate random walks of transaction prices. But unlike the case of one-type assets, the symmetry of these random walks is broken at the final stages of the game.