Abstract
We study the cores of non-atomic market games, a class of transferable utility cooperative games introduced by Aumann and Shapley (Values of non-atomic games, 1974), and, more in general, of those games that admit a na-continuous and concave extension to the set of ideal coalitions, studied by Einy et al. (Int J Game Theory 28:1–14, 1999). We show that the core of such games is norm compact and some related results. We also give a Multiple Priors interpretation of some of our findings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aliprantis CD, Border KC (1999) Infinite dimensional analysis. Springer, Berlin Heidelberg New York
Aumann RJ, Shapley LS (1974) Values of non-atomic games. Princeton University Press, Princeton
Barbu V, Precupanu T (1986) Convexity and optimization in Banach spaces. Reidel Publishing Company, Dord recht
Billera LJ, Raanan J (1981) Cores of non-atomic linear production games. Math Oper Res 6:420–423
Chateauneuf A, Maccheroni F, Marinacci M, Tallon J-M (2005) Monotone continuous multiple priors. Econ Theory 26:973–982
Danilov VI, Koshevoy GA (2000) Cores of cooperative games, superdifferentials of functions, and Minkowski difference of sets. J Math Anal Appl 247:1–14
Diestel J, Uhl JJ (1977) Vector measures. American Mathematical Society, Providence
Dunford N, Schwartz JT (1954) Linear operators, part I: general theory. Wiley, London
Einy E, Moreno D, Shitovitz B (1999) The core of a class of non-atomic games which arise in economic applications. Int J Game Theory 28:1–14
Ghirardato P, Marinacci M (2002) Ambiguity made precise: a comparative foundation. J Econ Theory 102:251–289
Gilboa I, Schmeidler D (1989) Maxmin expected utility with a non-unique prior. J Math Econ 18:141–153
Hart S (1977a) Asymptotic values of games with a continuum of players. J Math Econ 4:57–80
Hart S (1977b) Values of non-differentiable markets with a continuum of traders. J Math Econ 4:103–116
Hart S, Neyman A (1988) Values of non-atomic vector measure games. J Math Econ 17:31–40
Hormander L (1954) Sur la fonction d’appui des ensembles convexes dans une espace localement convexe. Arkiv Matematik 3:181–186
Huber PJ, Strassen V (1973) Minimax tests and the Neyman–Pearson lemma for capacities. Ann Stat 1:251–263
Marinacci M, Montrucchio L (2003) Subcalculus for set functions and cores of TU games. J Math Econ 39:1–25
Marinacci M, Montrucchio L (2004) Introduction to the mathematics of ambiguity. In: Gilboa I (ed). Uncertainty in economic theory. Routledge, New York, pp 46–107
Marinacci M, Montrucchio L (2005) Stable cores of large games. Int J Game Theory 33:189–213
Megginson R (1998) An introduction to Banach space theory. Springer, Berlin Heidelberg New York
Mertens JF (1980) Values and derivatives. Math Oper Res 5:523–552
Milchtaich I (1998) Vector measure games based on measures with values in an infinite dimensional vector space. Games Econ Behav 24:25–46
Neyman A (2001) Values of non-atomic vector measure games. Isr J Math 124:1–27
Neyman A (2002) Values of games with infinitely many players. In: Aumann RJ, Hart S (eds) Handbook of game theory, vol III. Elsevier, Amsterdam
Owen G (1975) On the core of linear production games. Math Program 9:358–370
Schmeidler D (1986) Integral representation without additivity. Proc Am Math Soc 97:255–261
Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57:571–587
Wasserman LA, Kadane JB (1990) Bayes’ theorem for Choquet capacities. Ann Stat 18:1328–1339
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Amarante, M., Maccheroni, F., Marinacci, M. et al. Cores of non-atomic market games. Int J Game Theory 34, 399–424 (2006). https://doi.org/10.1007/s00182-006-0029-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-006-0029-2