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 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.cooperative games ; equal treatment ; core convergence ; games without side payments (NTU games) ; large games ; approximate cores ; effective small groups ; parameterized collections of games

An explicit bound on " for nonemptiness of "-cores of games

We consider parameterized collections of games without side payments and determine a bound on E so that all suffciently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can bechosen

"An Explicit Bound on E For Nonemptimess of E-Cores of Games"

We consider parameterized collections of games without side payments and determine a bound on E so that all sufficiently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can be chosen

An explicit bound on epsilon for nonemptiness of Epsilon-cores of games

We consider parameterized collections of games without side payments and determine a bound on epsilon so that all suffciently large games in the collection have non-empty epsilon-cores. Our result makes explicit the relationship between the required size of epsilon for non-emptiness of the epsilon-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the epsilon that can be chosen.cooperative games, games without side payments (NTU games), large games, approximate cores, effective small groups, parameterized collections of games.

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 game with limited side payments has a nonempty epsilon-core. Our main result is that, when some degree of side-paymentness within nearly-effective small groups is assumed, then all payoffs in the epsilon-core treat similar players similarly. A bound on the distance between epsilon-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.

Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another

Monotonicity of Social Optima With Respect to Participation Constraints.

In this paper we consider solutions which select from the core. For games with side payments with at least four players, it is well-known that no core-selection satifies monotonicity for all coalitions; for the particular class of core-selections found by maximizing a social welfare function over the core, we investigate whether such solutions are monotone for a given coalition. It is shown that if this is the case then the solution actually maximizes aggregate coalition payoff on the core. Furthermore, the social welfare function to be maximized exhibits larger marginal social welfare with respect to the payoff of any member of the coalition. The results may be used to show that there are no monotonic core selection rules of this type in the context of games without side payments.coalitional games; monotonicity; core; social welfare

Convex and Exact Games with Non-transferable Utility

We generalize exactness to games with non-transferable utility (NTU). In an exact game for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We study five generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be unified under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of \Pi-balanced, totally \Pi-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.NTU Games, Exact Games, Convex Games

Convex and Exact Games with Non-transferable Utility

We generalize exactness to games with non-transferable utility (NTU). In an exact game for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We study five generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be unified under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of II-balanced, totally II-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.operations research and management science;