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Abstract
We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility. Under the assumption that the payo® set of the grand coalition is convex, we show that a game with limited side payments has a nonempty "-core. Our main result is that, when some degree of side-paymentness within nearly-e®ective small groups is assumed, then all payo®s in the "-core treat similar players similarly. A bound on the distance between "-core payo®s of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that games with many players and small e®ective groups have the properties of competitive markets.