AN EXACT FORMULA FOR THE LIONS SHARE - A MODEL OF PREPLAY NEGOTIATION

We study a game-theoretic model of preplay negotiation with three play ers, A, B and C. Player A (the leader) can sequentially offer a finite number T of contracts to the other players prior to his (her) choice of an action affecting B and C's payoffs. Contracts simply specify pat h-dependent transfers between the players. The bargaining procedure is a game in extensive form with perfect and complete information. We co mpute the subgame perfect equilibria of this game and provide explicit formulas for equilibrium payoffs. It is shown that if T = 2, player A will contract with B and C sequentially, but that equilibrium actions are not necessarily Pareto-efficient. Equilibria become efficient whe n T = 3. Finally, player A's equilibrium payoff reaches a maximum when T = 4. Thus, the leader's strategic surplus extraction possibilities are exhausted after a finite number of rounds. We show that the model has many economic applications and can be used as a building block to solve more complex problems in which preplay negotiation takes place, such as oligopoly problems. It can be viewed as an attempt to construc t a purely noncooperative theory of collusion, without the help of rep eated play. (C) 1996 Academic Press, Inc.