Approximating games and economies by markets

It is shown that an arbitrary game with effective small groups is ap-proximately a market game. Small groups are effective if all or almost all gains to collective activities can be achieved by groups bounded in abso-lute size. Market games are games derived from markets where all agents have continuous, concave payoff functions. Bounds on the closeness of the approximation are stated in terms of the extent of substitution — the close-ness of substitutes for each player- and other parameters characterizing the games. In this respect our results resemble those of Starr (1969) and Anderson (1978), for example, on approximate equilibrium and cores in exchange economies. In contrast with the market-game equivalence results of Shubik and Wooders (1982) and Wooders (1993,1994) no topology on the space of player types is required — the results are for arbitrary games