Population Monotonic Path Schemes for Simple Games

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages19
Volume2006-113
Publication statusPublished - 2006

Publication series

NameCentER Discussion Paper
Volume2006-113

Keywords

  • cooperative games
  • simple games
  • population monotonic path schemes
  • coalition formation
  • probabilistic values

Cite this

Ciftci, B. B., Borm, P. E. M., & Hamers, H. J. M. (2006). Population Monotonic Path Schemes for Simple Games. (CentER Discussion Paper; Vol. 2006-113). Tilburg: Microeconomics.
Ciftci, B.B. ; Borm, P.E.M. ; Hamers, H.J.M. / Population Monotonic Path Schemes for Simple Games. Tilburg : Microeconomics, 2006. (CentER Discussion Paper).
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Ciftci, BB, Borm, PEM & Hamers, HJM 2006 'Population Monotonic Path Schemes for Simple Games' CentER Discussion Paper, vol. 2006-113, Microeconomics, Tilburg.

Population Monotonic Path Schemes for Simple Games. / Ciftci, B.B.; Borm, P.E.M.; Hamers, H.J.M.

Tilburg : Microeconomics, 2006. (CentER Discussion Paper; Vol. 2006-113).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Population Monotonic Path Schemes for Simple Games

AU - Ciftci, B.B.

AU - Borm, P.E.M.

AU - Hamers, H.J.M.

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N2 - 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.

AB - 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.

KW - cooperative games

KW - simple games

KW - population monotonic path schemes

KW - coalition formation

KW - probabilistic values

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BT - Population Monotonic Path Schemes for Simple Games

PB - Microeconomics

CY - Tilburg

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Ciftci BB, Borm PEM, Hamers HJM. Population Monotonic Path Schemes for Simple Games. Tilburg: Microeconomics. 2006. (CentER Discussion Paper).