Price-Quantity Strategic Market Games

THIS PAPER IS yet another in a rapidly growing series (e.g. 2-11) on strategic approaches to economic equilibrium. Our aim here is to make precise the remark implicitly due to Bertrand 1 or 10, Ch. 4, 5 that if the agents in an economy use price-setting strategies then the strategic Nash equilibria will, in fact, be Walrasian; and this without any assumption of a large number of small However, in our models, not only prices but also quantities are set by the agents. Thus it might actually be more appropriate to call them Bertrand-Cournot types of models. We begin with a standard Walras exchange economy with a finite number of traders and commodities. This is recast as a game in strategic form in essentially two different ways. There is a trading-post for each commodity to which traders send contingent statements about how much they wish to buy and sell, and at what prices. In Model 1, the trading point is determined by the intersection of the aggregate supply and demand curves. In Model 2, trade takes place so as to meet as many contingent statements as possible. Each buyer whose orders are filled pays the price he quoted, using a fiat money which can be borrowed costlessly and limitlessly. But after trade is over there is a settlement of accounts and a penalty is levied on those who are bankrupt. No attempt is made to model the penalty in any detail. It is simply described in the form of a disutility. But this in turn may be imagined to stem from confiscation of assets (see Remark 5) or the necessity of procuring highly-priced loans, etc. Call a noncooperative equilibrium if it turns out that no trader is isolated, i.e., trapped as the sole buyer or seller at some trading-post. Then our results may be described as follows. In Model 1, the active2 N.E. of the game coincide with the C.E. of the market; furthermore there is a subset of tight, active N.E. which also coincide with the C.E., and each N.E. in this subset is strong