Abstract
In this paper we establish a relationship between the core cover of a compromise admissible game and the core of a particular bankruptcy game: the core cover of a compromise admissible game is, indeed, a translation of the set of coalitionally stable allocations captured by an associated bankruptcy game. Moreover, we analyze the combinatorial complexity of the core cover and, consequently, of the core of a compromise stable game.
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References
Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36: 195–213
Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernitiki 10:119–139 (in Russian)
Curiel I, Maschler M, Tijs S (1987) Bankruptcy games. Math Methods Oper Res 31: A143–A159
Gillies DB (1953) Some theorems on n-person games. PhD thesis, Princeton University, Princeton
González-Díaz J, Sánchez-Rodríguez E (2008) Cores of convex and strictly convex games. Games Econ Behav 62: 100–105
González-Díaz J, Borm P, Hendrickx R, Quant M (2005) A geometric characterisation of the compromise value. Math Methods Oper Res 61: 483–500
Ichiishi T (1981) Super-modularity: applications to convex games and to the greedy algorithm for LP. J Econ Theory 25: 283–286
Mirás-Calvo MA, Sánchez-Rodríguez E (2008) Juegos cooperativos con utilidad transferible usando MATLAB: TUGlab. Servizo de Publicacións da Universidade de Vigo, Vigo
O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2: 345–371
Platz T, Hamers H, Quant M (2011) Characterizing compromise stability of games using larginal vectors. CentER discussion papers 2011-58:195–213, Tilburg University, Tilburg
Quant M, Borm P, Reijnierse H, van Velzen B (2005) The core cover in relation to the nucleolus and the Weber set. Int J Game Theory 33: 491–503
Quant M, Borm P, Hendrickx R, Zwikker P (2006) Compromise solutions based on bankruptcy. Math Soc Sci 51(3): 247–256
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contribution to the theory of games II, vol 28 of Annals of Mathematics Studies. Princeton University Press, Princeton, pp 307–317
Shapley LS (1967) On balanced sets and cores. Naval Res Logist Q 14: 453–460
Shapley LS (1971) Cores of convex games. Int J Game Theory 1: 11–26
Tijs S, Lipperts F (1982) The hypercube and the core cover of the n-person cooperative games. Cahiers du Centre d’Études de Recherche Opérationnelle 24: 27–37
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Estévez-Fernández, A., Fiestras-Janeiro, M.G., Mosquera, M.A. et al. A bankruptcy approach to the core cover. Math Meth Oper Res 76, 343–359 (2012). https://doi.org/10.1007/s00186-012-0409-2
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DOI: https://doi.org/10.1007/s00186-012-0409-2