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Population Monotonic Path Schemes for Simple Games

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  • Ciftci, B.B.
  • Borm, P.E.M.
  • Hamers, H.J.M.

    (Tilburg University, Center for Economic Research)

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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-113.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:2006113

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Related research

Keywords: cooperative games; simple games; population monotonic path schemes; coalition formation; probabilistic values;

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References

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  1. Norde, H.W. & Reijnierse, J.H., 2000. "A Dual Description of the Class of Games with a Population Monotonic Allocation Scheme," Discussion Paper 2000-99, Tilburg University, Center for Economic Research.
  2. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. 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.
  5. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  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. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
  8. 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.
  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. 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.
  2. Baris Ciftci & Dinko Dimitrov, 2006. "Stable coalition structures in simple games with veto control," Working Papers 384, Bielefeld University, Center for Mathematical Economics.

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