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.
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