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Small group effectiveness, per capita boundedness and nonemptiness of approximate cores
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Wooders, Myrna. (2008) Small group effectiveness, per capita boundedness and nonemptiness of approximate cores. Journal of Mathematical Economics, Vol.44 (No.7-8). pp. 888-906. ISSN 0304-4068
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Official URL: http://dx.doi.org/10.1016/j.jmateco.2007.06.006
Abstract
Small groups of players of a cooperative game with side payments are "effective" if almost all gains to group formation can be realized by groups of players bounded in absolute size. Per capita payoffs are bounded if the average payoff to players has a uniform upper bound, independent of the size of the total player set. It is known that in the context of games with side payments derived from pregames (which induce a common underlying structure on the potential gains to groups of players from cooperation in any game) small group effectiveness implies nonemptiness of approximate cores and the approximation can be made arbitrarily close as the player set is increased in size. Moreover, per capita boundedness, along with thickness (implying that there are many substitutes for each player) yields the same result. In this paper, using extensions of the concepts of small group effectiveness and per capita boundedness to games without side payments (NTU games), we obtain results analogous to those for games with side payments. As the prior results, the results of the current paper can be applied to economies with non-convexities, non-monotonicities, production, indivisibilities, clubs, and local public goods. (C) 2007 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | H Social Sciences > HC Economic History and Conditions Q Science > QA Mathematics H Social Sciences |
| Divisions: | Faculty of Social Sciences > Economics |
| Journal or Publication Title: | Journal of Mathematical Economics |
| Publisher: | Elsevier |
| ISSN: | 0304-4068 |
| Date: | July 2008 |
| Volume: | Vol.44 |
| Number: | No.7-8 |
| Number of Pages: | 19 |
| Page Range: | pp. 888-906 |
| Identification Number: | 10.1016/j.jmateco.2007.06.006 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/29944 |
Data sourced from Thomson Reuters' Web of Knowledge
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