Ergodic equilibria in stochastic sequential games

Many dynamic economic situations, including certain markets, can be fruitfully modeled as binary-action stochastic sequential games. Such games have a state variable, which in the case of a market might be the inventory of the good waiting for sale. Conditional on the state, players choose in sequence whether to subtract from it (buy) or add to it (sell). Under two assmptions - called Self-Regulation and Separable Preferences - we can derive the existence of a stationary, sequential equilibrium where the state is geometrically ergodic and stationary, and the two actions are played in the ratio required to avoid drift. We solve for the equilibrium strategies of a particular class of uninformed player. In equilibrium, players must solve a potentially complicated forecasting problem, but our analysis used stationarity to bypass the details of this problem, thus avoiding the (often intractable) dynamic programming usually required to solve stochastic games. This simplification allows us to develop powerful invariance and welfare results, and to provide a microfoundation for market-clearing price adjustment.