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

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;

Egalitarianism in Nontransferable Utility Games

This paper studies egalitarianism in the context of nontransferable utility games by introducing and analyzing the egalitarian value. This new solution concept is based on an egalitarian negotiation procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which it leads to a core element and discuss the egalitarian value for the well-known Roth-Shafer examples. Moreover, we characterize the new value on the class of bankruptcy games and bargaining games