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 payoff set of the grand coalition is convex, we show that a game with limited side payments has a nonempty E-core. Our main result is that, when some degree of side-paymentness within nearly-effective small groups is assumed, then all payoffs in the E-core treat similar players similarly. A bound on the distance between E-core payoffs 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 effective groups have the properties of competitive markets
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