Joint Production Games And Share Functions

Player i's payoff in a noncooperative game is generally expressed as a function of the vector of strategies of all players. However, in some games - 'simply reducible games' - the payoff of player i is a function of two arguments - the strategy chosen by i, and the sum of the strategies of all players in the game. Cournot oligopoly, public good provision, costand surplus-sharing, and open access resource exploitation are all simply reducible games. We define the 'share function' of a simply reducible game. We indicate its role in the analysis of equilibrium existence, uniqueness and comparative static properties of simply reducible games, and apply it to a model of open access resource exploitation. Finally, we suggest further applications and extensions of our approach.