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 Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex ∗Department of Finance, Corvinus University of Budapest. The author would like to thank Corvinus University of Budapest for the “Kutatási kiválósági” research scholarship. [email protected] †Corresponding author. Department of Economics, Maastricht University, P.O. Box 616, 6200 MD, Maastricht, The Netherlands. The author would like to thank the Netherlands Organisation for Scientific Research (NWO) for financial support. [email protected] ‡Keleti Faculty of Economics, Budapest Tech and Department of Economics, Maastricht University. The author thanks the funding of the OTKA (Hungarian Fund for Scientific Research) under the project NF-72610 and of the European Commission under a Marie Curie Reintegration Grant (PERG-GA-2008-230879). [email protected] §Department of Mathematics, Corvinus University of Budapest. The author thanks the OTKA (Hungarian Fund for Scientific Research) and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences for financial support. [email protected]