Profit sharing in unique Nash equilibrium: Characterization in the two-agent case

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent’s labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker’s (Econometrica, 1992) characterization of their serial mechanism as the unique cost-sharing rule satisfying the same incentives property. We also show that the familiar stand alone test characterizes the class of fixed-path methods (Friedman, Economic Theory, 2002) under our incentives criterion.