Abstract
This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.
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References
Chang C (2000) Note: remarks on theory of the core. Nav Res Logist 47:456–458
Davis M, Maschler M (1965) The kernel of a cooperative game. Nav Res Logist Q 12:223–259
Driessen T (1991) A survey of consistency properties in cooperative game theory. SIAM Rev 33:43–59
Funaki Y, Yamato T (2001) The core and consistency properties: a general characterization. Int Game Theory Rev 3:175–187
Gillies D (1959) Solutions to general non-zero sum games. In: Tucker A, Luce R (eds) Contributions to the theory of games, vol IV. Annals of mathematical studies, vol 40. Princeton University Press, Princeton, pp 47–58
Hwang Y-A, Sudhölter P (2001) An axiomatization of the core on the universal domain and other natural domains. Int J Game Theory 29:597–623
Keiding H (1986) An axiomatization of the core of a cooperative game. Econ Lett 20:111–115
Llerena F, Rafels C (2006) The vector lattice structure of the n-person TU games. Games Econ Behav 54:373–379
Lucas W (1992) von Neumann–Morgenstern stable sets. In: Aumann R, Hart S (eds) Handbook of game theory, vol I. North-Holland, Amsterdam, pp 543–590
Maschler M (1992) The bargaining set, kernel, and nucleolus. In: Aumann R, Hart S (eds) Handbook of game theory, vol I. North-Holland, Amsterdam, pp 543–590
Milnor J (1952) Reasonable outcomes for n-person games. The Rand Corporation 916
Moulin H (1985) The separability axiom and equal sharing methods. J Econ Theory 36:120–148
Peleg B (1986) On the reduced game property and its converse. Int J Game Theory 15:187–200
Peleg B, Sudhölter P (2003) Introduction to the theory of cooperative games. Kluwer, Boston
Rafels C, Tijs S (1997) On the cores of cooperative games and the stability of the Weber set. Int J Game Theory 26:491–499
Shapley LS (1971) Cores of convex games. Int J Game Theory 1:11–16
Sudhölter P, Peleg B (2000) The positive prekernel of a cooperative game. Int Game Theory Rev 2:287–305
Tadenuma K (1992) Reduced games, consistency, and the core. Int J Game Theory 20:325–334
Thomson W (1998) Consistent allocation rules. Dicussion Paper, Department of Economics, University of Rochester, USA
Voorneveld M, van den Nouweland A (1998) A new axiomatization of the core of games with transferable utility. Econ Lett 60:151–155
Winter E, Wooders M (1994) An axiomatization of the core for finite and continuum games. Soc Choice Welf 11:165–175
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Llerena, F., Rafels, C. Convex decomposition of games and axiomatizations of the core and the D-core. Int J Game Theory 35, 603–615 (2007). https://doi.org/10.1007/s00182-006-0062-1
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DOI: https://doi.org/10.1007/s00182-006-0062-1