2,248 research outputs found
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;
Coalitions in Cooperative Wireless Networks
Cooperation between rational users in wireless networks is studied using
coalitional game theory. Using the rate achieved by a user as its utility, it
is shown that the stable coalition structure, i.e., set of coalitions from
which users have no incentives to defect, depends on the manner in which the
rate gains are apportioned among the cooperating users. Specifically, the
stability of the grand coalition (GC), i.e., the coalition of all users, is
studied. Transmitter and receiver cooperation in an interference channel (IC)
are studied as illustrative cooperative models to determine the stable
coalitions for both flexible (transferable) and fixed (non-transferable)
apportioning schemes. It is shown that the stable sum-rate optimal coalition
when only receivers cooperate by jointly decoding (transferable) is the GC. The
stability of the GC depends on the detector when receivers cooperate using
linear multiuser detectors (non-transferable). Transmitter cooperation is
studied assuming that all receivers cooperate perfectly and that users outside
a coalition act as jammers. The stability of the GC is studied for both the
case of perfectly cooperating transmitters (transferrable) and under a partial
decode-and-forward strategy (non-transferable). In both cases, the stability is
shown to depend on the channel gains and the transmitter jamming strengths.Comment: To appear in the IEEE Journal on Selected Areas in Communication,
Special Issue on Game Theory in Communication Systems, 200
Size Monotonicity and Stability of the Core in Hedonic Games
We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games.Core, Hedonic Games, Monotonicity, Stable Sets
Effectivity functions and associated game correspondences
Game Theory;game theory
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