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 payoff set of the grand coalition is convex, we show that a large game with limited side payments has a nonempty varepsilon core. Our second result is that, when some degree of side-paymentness within nearly-effective small groups is assumed, then all payoffs in the varepsilon $-core treat all players of the same approximate type approximately equally. A bound on the distance between varepsilon core payoffs of any two players of the same approximate type is given in terms of the parameters describing the game.
Keywords: cooperative games, games without side payments (NTU games), large games, approximate cores, effective small groups, parameterized collections of games
JEL Classification: C10;C62;D71