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Population monotonic path schemes for simple games

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Author Info

  • Barış Çiftçi

    ()

  • Peter Borm

    ()

  • Herbert Hamers

    ()

Abstract

A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path.A path scheme is called population monotonic if a player's payoff does not decrease as the path coalition grows.In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand.We show that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced.Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition.Extensions of these results to other probabilistic values are discussed.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s11238-008-9125-z
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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 69 (2010)
Issue (Month): 2 (August)
Pages: 205-218

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Handle: RePEc:kap:theord:v:69:y:2010:i:2:p:205-218

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Cooperative games; Simple games; Population monotonic path schemes; Population monotonic allocation schemes; Coalition formation; Probabilistic values; C71; D72;

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  1. Slikker, M. & Norde, H.W. & Tijs, S.H., 2003. "Information sharing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-117078, Tilburg University.
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  3. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
  4. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151 Elsevier.
  5. Norde, Henk & Reijnierse, Hans, 2002. "A dual description of the class of games with a population monotonic allocation scheme," Games and Economic Behavior, Elsevier, vol. 41(2), pages 322-343, November.
  6. Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076 Elsevier.
  7. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  8. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  9. Cruijssen, F.C.A.M. & Borm, P.E.M. & Fleuren, H.A. & Hamers, H.J.M., 2005. "Insinking: A Methodology to Exploit Synergy in Transportation," Discussion Paper 2005-121, Tilburg University, Center for Economic Research.
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Cited by:
  1. Ciftci, B.B. & Dimitrov, D.A., 2006. "Stable Coalition Structures in Simple Games with Veto Control," Discussion Paper 2006-114, Tilburg University, Center for Economic Research.
  2. Cruijssen, F.C.A.M., 2006. "Horizontal Cooperation in Transport and Logistics," Open Access publications from Tilburg University urn:nbn:nl:ui:12-189742, Tilburg University.

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