A Strategic Market Game with Active Bankruptcy

We construct stationary Markov equilibria for an economy with fiat money, one nondurable commodity, countably-many time periods, and a continuum of agents. The total production of commodity remains constant, but individual agents’ endowments fluctuate in a random fashion from period to period. In order to hedge against these random fluctuations, agents find it useful to hold fiat money which they can borrow or deposit at appropriate rates of interest; such activity may take place either at a central bank (which fixes interest rates judiciously) or through a money-market (in which interest rates are determined endogenously). We carry out an equilibrium analysis, based on a careful study of Dynamic Programming equations and on properties of the invariant measures for associated optimally-controlled Markov chains. This analysis yields the stationary distribution of wealth across agents, as well as the stationary price (for the commodity) and interest rates (for the borrowing and lending of fiat money). A distinctive feature of our analysis is the incorporation of bankruptcy, both as a real possibility in an individual agent’s optimization problem, and as a determinant of interest rates through appropriate balance equations. These allow a central bank (respectively, a money-market) to announce (respectively, to determine endogenously) interest rates in a way that conserves the total money-supply and controls inflation. General results are provided for the existence of such stationary equilibria, and several explicitly solvable examples are treated in detail. ∗Research supported by the Santa Fe Institute, and by the National Science Foundation under grants DMS– 97–32810 (Karatzas) and DMS–97–03285 (Sudderth). We are deeply indebted to the Referee and the Co-Editor for the care with which they read the original version of the paper, and for their many helpful remarks.