Game-theoretic analysis of one-stage and two-stage homogeneous good auctions

Forward market is a known instrument for reduction of market power of large producers. This paper examines a two-stage oligopoly environment with constant marginal cost. The outcome at both the forward and the spot market is a Cournot outcome dependent on correspondent demand and supply at the market. Producers aim to maximize their profits via choosing subgame perfect equilibrium of the two-stage game as their strategies. In the first part of the current research we extend the model by Bushnell (2005) considering a capacity constraint. Our results show that the optimal way of market organization in such a model strongly depends on the difference between the maximal production volume and the demand volume at price equal to the marginal cost. In the second part of the paper we consider proportional rationing instead of surplus maximizing rationing at the forward market. We show that for such a model there exists only an SPE in correlated mixed strategies. Producers' behavior should depend on some random variable that determines one of two possibilities for the spot market: either the “bear market”, or the “bull market”. We compare this SPE with Nash equilibria of one-stage markets.