Spectrum Value for Coalitional Games
AbstractAssuming a `spectrum' or ordering on the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally asymmetric power index in which positioning along the spectrum is critical. We present both a characterisation of this value by means of properties and combinatoric formulae for calculating it. In simple majority games, the greatest power accrues to `moderate' players who are located neither at the extremes of the spectrum nor in its centre. In supermajority games, power increasingly accrues towards the extremes, and in unaninimity games all power is held by the players at the extreme of the spectrum.
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp618.
Length: 19 pages
Date of creation: Aug 2012
Date of revision:
Publication status: Forthcoming in GEB
Other versions of this item:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D46 - Microeconomics - - Market Structure and Pricing - - - Value Theory
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-16 (All new papers)
- NEP-CDM-2012-09-16 (Collective Decision-Making)
- NEP-GTH-2012-09-16 (Game Theory)
- NEP-HPE-2012-09-16 (History & Philosophy of Economics)
- NEP-MIC-2012-09-16 (Microeconomics)
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- Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer, vol. 23(1), pages 43-48.
- Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Discussion Paper 1999-20, Tilburg University, Center for Economic Research.
- Emilio Calvo & Esther Gutierrez, 2011. "A value for cooperative games with a coalition structure," Discussion Papers in Economic Behaviour 0311, University of Valencia, ERI-CES.
- Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer, vol. 18(3), pages 339-56.
- Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
- Emilio Calvo & Esther Gutiérrez, 2013. "The Shapley-Solidarity Value For Games With A Coalition Structure," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1350002-1-1.
- Ziv Hellman & Ron Peretz, 2013. "Graph value for cooperative games," LSE Research Online Documents on Economics 50073, London School of Economics and Political Science, LSE Library.
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