Epsilon Cores of Games and Economies With Limited Side Payments.

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 non-empty epsilon-core. Our second result is that, when some degree of side-paymentness within nearly effective small groups is assumed, then all payoffs in the epsilon-core treat all players of the same type approximately eqully. A bound on the distance between epsilon-core payoffs of any two players of the same approximate type is given in terms of the parameters describing the game.