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Population monotonic paths schemes for simple games

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Author Info
Ciftci, Baris
Borm, Peter
Hamers, Herbert (Tilburg University, Center for Economic Research)

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

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

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior

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References listed on IDEAS
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.:
  1. 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. [Downloadable!] (restricted)
  2. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation, Yale University. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
  4. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  5. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation, Yale University. [Downloadable!]
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  6. 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. [Downloadable!] (restricted)
  7. Cruijssen, Frans & Borm, Peter & Fleuren, Hein & ...,, 2005. "Insinking : a methodology to exploit synergy in transportation," Discussion Paper 121, Tilburg University, Center for Economic Research. [Downloadable!]
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  1. Baris Ciftci & Dinko Dimitrov, 2006. "Stable coalition structures in simple games with veto control," Working Papers 384, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
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