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 InfoArticle provided by Springer in its journal Theory and Decision.
Volume (Year): 69 (2010)
Issue (Month): 2 (August)
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Web page: http://www.springerlink.com/link.asp?id=100341
Cooperative games; Simple games; Population monotonic path schemes; Population monotonic allocation schemes; Coalition formation; Probabilistic values; C71; D72;
Other versions of this item:
- Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M., 2006. "Population Monotonic Path Schemes for Simple Games," Discussion Paper 2006-113, Tilburg University, Center for Economic Research.
- 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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