 On large games with bounded essential coalition sizesEyal Winter () and Myrna Wooders International Journal of Economic Theory, 2008, vol. 4, issue 2, 191-206 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. Date: 2008 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:ijethy:v:4:y:2008:i:2:p:191-206 Ordering information: This journal article can be ordered from Access Statistics for this article International Journal of Economic Theory is currently edited by Kazuo Nishimura and Makoto Yano More articles in International Journal of Economic Theory from The International Society for Economic Theory |
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