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Balancedness Conditions for Exact Games

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Author Info
Péter Csóka () (Department of Economics, Maastricht University)
P. Jean-Jacques Herings () (Department of Economics, Maastricht University)
László Á. Kóczy () (Budapest Tech)

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Abstract

We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and we provide an alternative proof that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition,but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.

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File URL: http://www.bmf.hu/users/vecseya/RePEc/pkk/wpaper/0805.pdf
File Format: application/pdf
File Function: unpublished
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Publisher Info
Paper provided by Budapest Tech, Keleti Faculty of Economics in its series Working Paper Series with number 0805.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length: 13 pages
Date of creation: Sep 2007
Date of revision: May 2008
Handle: RePEc:pkk:wpaper:0805

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Related research
Keywords: Totally Balanced Games Exact Games Convex Games

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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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. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May. [Downloadable!] (restricted)
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  2. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July. [Downloadable!] (restricted)
  3. Legut, Jerzy, 1990. "On totally balanced games arising from cooperation in fair division," Games and Economic Behavior, Elsevier, vol. 2(1), pages 47-60, March. [Downloadable!] (restricted)
  4. Peter Csoka & P. Jean-Jacques Herings, & Laszlo A. Koczy, 2007. "Stable Allocations of Risk," IEHAS Discussion Papers 0704, Institute of Economics, Hungarian Academy of Sciences. [Downloadable!]
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  5. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June. [Downloadable!] (restricted)
  6. Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer, vol. 27(3), pages 451-459. [Downloadable!] (restricted)
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Cited by:
(explanations, 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. Csóka Péter & Herings P. Jean-Jacques & Kóczy László Á,, 2007. "Stable Allocations of Risk," Research Memoranda 040, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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