Joint Production Games with Mixed Sharing Rules

We study joint production games under a mixed sharing rule in which part of the ouput (the mixing parameter) is shared in proportion to inputs and the rest according to exogenously determined shares. We show that this game has a unique Nash equilibrium and discuss comparative statics. When the game is large, we show that players unanimously prefer the same value of the mixing parameter: the equilibrium elasticity of production. At this value, the equilibrium allocation is fully efficient. Our approach heavily exploits the fact that payoffs depend only on a player's input and the aggregate input.