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Convex Games Versus Clan Games

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Author Info
RODICA BRANZEI (Faculty of Computer Science, Alexandru Ioan Cuza University, Romania)
DINKO DIMITROV (Chair of Microeconomics, Faculty of Law and Economics, University of Bayreuth, Germany)
STEF TIJS (Center and Department of Econometrics and Operations Research, Tilburg University, The Netherlands)

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Abstract

In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games. Furthermore, each monotonic convex game generates a total clan game with zero worth for the clan by a "dualize and extend" procedure. These procedures are also useful for relating core elements and elements of the Weber set of the corresponding games.

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Publisher Info
Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 10 (2008)
Issue (Month): 04 ()
Pages: 363-372
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Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:p:363-372

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Related research
Keywords: Convex games; core; dual games; marginal games; total clan games; Weber set; C71;

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Find related papers by JEL classification:
B4 - Schools of Economic Thought and Methodology - - Economic Methodology
C0 - Mathematical and Quantitative Methods - - General
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D5 - Microeconomics - - General Equilibrium and Disequilibrium
D7 - Microeconomics - - Analysis of Collective Decision-Making
M2 - Business Administration and Business Economics; Marketing; Accounting - - Business Economics

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. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA. [Downloadable!]
  2. Voorneveld, M. & Tijs, S. & Grahn, S., 2000. "Monotonic allocation schemes in clan games," Discussion Paper 80, Tilburg University, Center for Economic Research. [Downloadable!]
  3. Tijs, Stef & Meca, Ana & Lopez, Marco A., 2005. "Benefit sharing in holding situations," European Journal of Operational Research, Elsevier, vol. 162(1), pages 251-269, April. [Downloadable!] (restricted)
  4. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Branzei, R. & Dimitrov, D. & Tijs, S.H., 2004. "A new characterization of convex games," Discussion Paper 109, Tilburg University, Center for Economic Research. [Downloadable!]
  6. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May. [Downloadable!] (restricted)
  7. 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)
  8. Branzei, Rodica & Fragnelli, Vito & Meca, Ana & Tijs, Stef, 2006. "Two classes of cooperative games related to one-object auction situations," Discussion Paper 25, Tilburg University, Center for Economic Research. [Downloadable!]
  9. 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)
  10. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October. [Downloadable!] (restricted)
  11. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September. [Downloadable!] (restricted)
  12. Branzei, R. & Dimitrov, D. & Tijs, S.H., 2004. "The equal split-off set for cooperative games," Discussion Paper 110, Tilburg University, Center for Economic Research. [Downloadable!]
Full references

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. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2007. "Farsighted Coalitional Stability in TU-games," Sonderforschungsbereich 504 Publications 07-57, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
    Other versions:
  2. Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," AUCO Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December. [Downloadable!]
  3. Branzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Discussion Paper 2008-55, Tilburg University, Center for Economic Research. [Downloadable!]
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