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Population monotonic path schemes for simple games

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  • 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.
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Suggested Citation

  • Barış Çiftçi & Peter Borm & Herbert Hamers, 2010. "Population monotonic path schemes for simple games," Theory and Decision, Springer, vol. 69(2), pages 205-218, August.
    • Handle: RePEc:kap:theord:v:69:y:2010:i:2:p:205-218
    DOI: 10.1007/s11238-008-9125-z
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    9. Cruijssen, F. & Borm, P.E.M. & Fleuren, H.A. & Hamers, H.J.M., 2005. "Insinking : A Methodology to Exploit Synergy in Transportation," Other publications TiSEM 958be918-e7b4-4e46-9cbe-d, Tilburg University, School of Economics and Management.
    10. 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.
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    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. Takaaki Abe, 2020. "Population monotonic allocation schemes for games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 97-117, March.
    3. Jesús Getán & Jesús Montes & Carles Rafels, 2014. "A note: characterizations of convex games by means of population monotonic allocation schemes," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 871-879, November.
    4. Cruijssen, F., 2006. "Horizontal cooperation in transport and logistics," Other publications TiSEM ab6dbe68-aebc-4b03-8eea-d, Tilburg University, School of Economics and Management.
    5. Cruijssen, Frans & Borm, Peter & Fleuren, Hein & Hamers, Herbert, 2010. "Supplier-initiated outsourcing: A methodology to exploit synergy in transportation," European Journal of Operational Research, Elsevier, vol. 207(2), pages 763-774, December.

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    More about this item

    Keywords

    Cooperative games; Simple games; Population monotonic path schemes; Population monotonic allocation schemes; Coalition formation; Probabilistic values; C71; D72;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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