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Population monotonic path schemes for simple games

  • Barış Çiftçi


  • Peter Borm


  • Herbert Hamers


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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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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  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. 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.
  3. 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.
  4. Slikker, M. & Norde, H.W. & Tijs, S.H., 2003. "Information sharing games," Other publications TiSEM fa5460d9-0abc-47e1-a794-7, Tilburg University, School of Economics and Management.
  5. 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.
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