A strategic market game with secured lending

We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money market, and a continuum of agents. These Use fiat money in order to offset random fluctuations in their endowments of the commodity, are not allowed to borrow more than they can pay back (secured lending), and maximize expected discounted utility from consumption of the commodity. Their aggregate optimal actions determine dynamically prices and/or interest rates for borrowing and lending, in each period of play. In equilibrium, random fluctuations in endowment levels and wealth-levels offset each other, and prices and interest rates remain constant. As in related recent work, we study in detail the individual agents' dynamic optimization problems, and the invariant measures for the associated, optimally controlled Markov chains. By appropriate aggregation, these individual problems lead to the construction of a stationary Markov competitive equilibrium for the economy as a whole. Several examples are studied in detail, fairly general existence theorems are established, and open questions are indicated for further research.