Bid-Ask Price Competition with Asymmetric Information between Market Makers

We consider the effect of asymmetric information on price formation process in a financial market where private information is held by a market maker. A model is presented where two market makers with two different information partitions compete in prices. At each stage a bid-ask auction between the market makers occur, and the winner trades the asset against liquidity traders. We show that equilibrium prices do not convey all the information present in the market until the last stage. Moreover, we characterize a set of partially revealing equilibria where the informed market maker's prices do not convey his private information. Informed player's expected equilibrium payoffs depends on the beliefs of the market at the beginning of the game.