The number of commodities required to represent a market game

Abstract An n -person game with side payments that can arise from an economic market is called a market game. It is proved here that any n -person market game can be obtained from a market with at most n − 1 commodities. Moreover, no smaller number will suffice in some cases (e.g., the unanimity game). This result is then applied to settle a question regarding market games with a continuum of traders.