Abstract
Cooperative games with large core were introduced by Sharkey (Int. J. Game Theory 11:175–182, 1982), and the concept of Population Monotonic Allocation Scheme was defined by Sprumont (Games Econ. Behav. 2:378–394, 1990). Inspired by these two concepts, Moulin (Int. J. Game Theory 19:219–232, 1990) introduced the notion of large monotonic core giving a characterization for three-player games. In this paper we prove that all games with large monotonic core are convex. We give an effective criterion to determine whether a game has a large monotonic core and, as a consequence, we obtain a characterization for the four-player case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kikuta K (1988) A condition for a game to be convex. Math Jpn 33(3):425–430
Moulin H (1990) Cores and large cores when population varies. Int J Game Theory 19:219–232
Norde H, Reijnierse H (2002) A dual description of the class of games with a population monotonic allocation scheme. Games Econ Behav 41:322–343
Sharkey WW (1982) Cooperative games with large cores. Int J Game Theory 11:175–182
Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ Behav 2:378–394
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Getán, J., Montes, J. On cooperative games with large monotonic core. TOP 18, 493–508 (2010). https://doi.org/10.1007/s11750-009-0077-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-009-0077-4