Game Theory with Applications to Finance and Marketing

mation. In a game-theoretic context with multiple agents, the sameneed not be true. This is the famous Hirshleifer effect; see for exampleNewbery (1984). For example, suppose that A and B will consume asingle commodity at date 2, while their endowments in the commodityin the two equally probable states at date 2 are summarized in thefollowing table:endowments/ states state 1 state 2player A’s endowments 2 0player B’s endowments 0 2Suppose that A and B are endowed with an increasing, strictly concavevon Neumann-Morgenstern utility function u(·) for date-2 consumption.The current time is date 0, and A and B can sign an insurancecontract at date 1.First suppose that no new information arrives at date 1. It is clear thatA and B can benefit from the following insurance contract: if state 1occurs at date 2, then A should give B one unit of the commodity;and if state 2 occurs at date 2, then B should give A one unit of thecommodity. Jensen’s inequality implies that12 u(1) + 1 + 2u(1) = u(1) = u(02 2 ) > 1 2 u(0) + 1 2 u(2),and hence both A and B are better off (have a higher expected utility) atdate 0, in anticipation of the opportunity to sign an insurance contractat date 1.Now suppose instead that some public information arrives at date 1,which reveals completely the state at date 2. If state 1 will prevail atdate 2, A will refuse to trade with B; and if state 2 will prevail at date2, then B will refuse to trade with A. This information destroys thepossibility of insurance! With this information A and B are worse offat date 0.46