Contingent Contracts and Value Creation

In negotiations in which the potential value creation depends upon external uncertainties, and the players have different beliefs about these uncertainties, it is well known that contingent contracts can enable agreement. But by allowing contingent payments, each player’s expected value capture can, in some situations, be made arbitrarily large. This fact prompts two natural questions. Does the increase in the players’ expected value capture imply an increase in expected value creation? And is there a point at which the contract can become more about making a wager and less about exploiting differences to enable agreement? We address these questions by showing that a player’s expected value capture can be separated into two components: an expected share of ex post value creation and an expected transfer of value from one player to another. The latter can be represented by a zero-sum wager. We show that if contracts are restricted to be ex post individually rational—a natural condition implicit in Arrow (1953) and Raiffa (The art & science of negotiation, Harvard University Press, Cambridge, 1982)—a joint increase in the players’ expected value captures can always be attributed to a division of ex post value creation that better exploits the players’ beliefs rather than to an increase in an embedded zero-sum wager.