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On large games with bounded essential coalition sizes
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Winter, Eyal and Wooders, Myrna Holtz (2008) On large games with bounded essential coalition sizes. International Journal of Economic Theory, Vol.4 (No.2). pp. 191-206. doi:10.1111/j.1742-7363.2008.00079.x
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Official URL: http://dx.doi.org/10.1111/j.1742-7363.2008.00079.x
Abstract
We consider games in characteristic function form where the worth of a group of players depends on the numbers of players of each of a finite number of types in the group. The games have bounded essential coalition sizes: all gains to cooperation can be achieved by coalitions bounded in absolute size (although larger coalitions are permitted they cannot realize larger per-capita gains). We show that the utility function of the corresponding "limit" market, introduced in Wooders (1988, 1994a), is piecewise linear. The piecewise linearity is used to show that for almost all limiting ratios of percentages of player-types, as the games increase in size (numbers of players), asymptotically the games have cores containing only one payoff, and this payoff is symmetric (treats players of the same type identically). We use this result to show that for almost all limiting ratios of percentages of player-types, Shapley values of sequences of growing games converge to the unique limiting payoff.
Item Type: | Journal Item | ||||
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Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics |
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Divisions: | Faculty of Social Sciences > Economics | ||||
Library of Congress Subject Headings (LCSH): | Game theory, Economics -- Mathematical models | ||||
Journal or Publication Title: | International Journal of Economic Theory | ||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||
ISSN: | 1742-7355 | ||||
Official Date: | June 2008 | ||||
Dates: |
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Volume: | Vol.4 | ||||
Number: | No.2 | ||||
Number of Pages: | 16 | ||||
Page Range: | pp. 191-206 | ||||
DOI: | 10.1111/j.1742-7363.2008.00079.x | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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