On Market Games
An extension to economic models of some recently discovered counterexamples in [n]-person solution theory having to do with games that either have no solutions or have unusually restricted classes of solutions. In this study, the "market games" — games that derive from an exchange economy in which the traders have continuous concave monetary utility functions — are shown to be the same as the "totally balanced games" — games which, with all their subgames, possess cores. (The core of a game is the set of outcomes that cannot be profitably upset by any coalition.) The coincidence of these two classes of games is established with the aid of explicit rules for generating a game from a market and vice versa. It is further shown that any game with a core has the same solutions, in the von Neumann-Morgenstern sense, as some totally balanced game. Thus a market may be found that reproduces the solution behavior of any game with a core. In particular, using a recent result of Lucas (see RM-5518), a ten-trader ten-commodity market is described that has no solution.