Population Monotonic Path Schemes for Simple Games
AbstractA 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 InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-113.
Date of creation: 2006
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cooperative games; simple games; population monotonic path schemes; coalition formation; probabilistic values;
Other versions of this item:
- 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.
- 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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Slikker, M. & Norde, H.W. & Tijs, S.H., 2000.
"Information Sharing Games,"
2000-100, Tilburg University, Center for Economic Research.
- 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.
- Robert J. Weber, 1977.
"Probabilistic Values for Games,"
Cowles Foundation Discussion Papers
471R, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- 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.
- Norde, H.W. & Reijnierse, J.H., 2000.
"A Dual Description of the Class of Games with a Population Monotonic Allocation Scheme,"
2000-99, Tilburg University, Center for Economic Research.
- 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.
- Baris Ciftci & Dinko Dimitrov, 2006.
"Stable coalition structures in simple games with veto control,"
384, Bielefeld University, Center for Mathematical Economics.
- 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.
- 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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