Construction of Stationary Markov Equilibria in a Strategic Market Game

This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time periods, no credit or futures market, and a measure space of agents -- who may differ in their preferences and in the distributions of their (random) endowments. These agents are immortal, and hold fiat money as a means of hedging against the random fluctuations in their endowments of the commodity. In the aggregate, these fluctuations offset each other, and equilibrium prices are constant. We carry out an equilibrium analysis that focuses on distribution of wealth, on consumption, and on price formation. A careful analysis of the one-agent, infinite-horizon optimization problem, and of the invariant measure for the associated optimally controlled Markov chain, leads by aggregation to a stationary noncooperative or competitive equilibrium. This consists of a price for the commodity and of a distribution of wealth across agents which, under appropriate simple strategies for the agents, stay fixed from period to period and preserve the basic quantities of the model. We hope that, in future work, we shall be able to address additional features of the model treated here, such as borrowing and lending at appropriate (endogenously determined) interest rates, the endogenous production of the commodity, overlapping generations of agents, and bankruptcy and treatment of creditors.