Abstract
We consider an extension of glove markets, called T-markets, characterize a family of weighted allocation rules, and define related cooperative games. For the class of T-market games we introduce a new solution concept called the type monotonic allocation scheme. It turns out that the nucleolus and the τ-value generate the same type monotonic allocation scheme with nice extra properties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Apartsin Y, Holzman R (2003) The core and the bargaining set in glove-market games. Int J Game Theory 32: 189–204
Brânzei R, Tijs S, Timmer J (2001) Information collecting situations and bi-monotonic allocation schemes. Math Methods Oper Res 54: 303–313
Fernández C, Borm P, Hendrickx R, Tijs S (2005) Drop out monotonic rules for sequencing situations. Math Methods Oper Res 61: 501–504
Gillies DB (1953) Some theorems on n-person games. PhD Thesis, Princeton University, Princeton
Kalai E, Zemel E (1982) Totally balanced games and games of flow. Math Oper Res 7: 476–478
Muto S, Nakayama M, Potters J, Tijs S (1988) On big boss games. Econ Stud Q 39: 303–321
Owen G (1975) On the core of linear production games. Math Program 9: 358–370
Reijnierse H, Maschler M, Potters J, Tijs S (1996) Simple flow games. Games Econ Behav 16: 238–260
Rosenmüller J, Sudhölter P (2002) Formation of cartels in glove markets and the modiclus. J Econ/Z Nationalökon 76: 217–246
Rosenmüller J, Sudhölter P (2004) Cartels via the modiclus. Discret Appl Math 134: 263–302
Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM J Appl Math 17: 1163–1170
Shapley LS (1953) A value for n-person games. In: Kuhn D, Tucker AW (eds) Contributions to the theory of games, vol II. Annals of mathematics studies, vol 28. Princeton University Press, Princeton, pp 307–317
Shapley LS (1959) The solutions of a symmetric market game. In: Tucker AW, Luce RD (eds) Contributions to the theory of games, vol IV. Annals of mathematics studies, vol 40. Princeton University Press, Princeton, pp 145–162
Shapley LS, Shubik M (1969) On market games. J Econ Theory 1: 9–25
Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utilities. Games Econ Behav 2: 378–394
Tijs SH (1981) Bounds for the core and the τ-value. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North-Holland, Amsterdam, pp 123–132
Voorneveld M, Tijs S, Grahn S (2003) Monotonic allocation schemes in clan games. Math Methods Oper Res 56: 439–449
Author information
Authors and Affiliations
Corresponding author
Additional information
Initial research for this paper was supported by the Hungarian Scientific Research Fund grant OTKA T030945. The authors thank Ruud Hendrickx for his valuable comments. Research of T. Solymosi was also supported in part by OTKA grant T046194.
Rights and permissions
About this article
Cite this article
Brânzei, R., Solymosi, T. & Tijs, S. Type monotonic allocation schemes for a class of market games. TOP 15, 78–88 (2007). https://doi.org/10.1007/s11750-007-0002-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-007-0002-7