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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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    1. Marco Slikker & Henk Norde & Stef Tijs, 2003. "Information Sharing Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-12.
    2. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    3. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    4. 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.
    5. Ciftci, B.B. & Dimitrov, D.A., 2006. "Stable Coalition Structures in Simple Games with Veto Control," Other publications TiSEM fd2410e3-8e9d-4319-86fb-b, Tilburg University, School of Economics and Management.
    6. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    7. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    8. Winter, Eyal, 2002. "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 53, pages 2025-2054, Elsevier.
    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.
    11. 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.
    12. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    13. 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.
    14. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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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. Cruijssen, F., 2006. "Horizontal cooperation in transport and logistics," Other publications TiSEM ab6dbe68-aebc-4b03-8eea-d, Tilburg University, School of Economics and Management.
    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, 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.
    5. 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.

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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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