On market games

Abstract

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 out-comes that no coalition can profitably block.) The coincidence of these two classes of games is established with the aid of explicit transformations that generate 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 that has a core. In particular, using a recent result of Lucas, a ten-trader tencommodity market is described that has no solution.