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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)

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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Bibliographic 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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References

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  1. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2001. "Information collecting situations and bi-monotonic allocation schemes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-88210, Tilburg University.
  2. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471, Cowles Foundation for Research in Economics, Yale University.
  3. Tijs, S.H. & Meca, A. & Lopez, M.A., 2005. "Benefit sharing in holding situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142687, Tilburg University.
  4. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "The Equal Split-Off Set for Cooperative Games," Discussion Paper 2004-110, Tilburg University, Center for Economic Research.
  5. Brânzei, R. & Fragnelli, V. & Meca, A. & Tijs, S.H., 2006. "Two Classes of Cooperative Games Related to One-Object Auction Situations," Discussion Paper 2006-25, Tilburg University, Center for Economic Research.
  6. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154241, Tilburg University.
  7. 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.
  8. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  9. 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.
  10. Voorneveld, M. & Tijs, S.H. & Grahn, S., 2003. "Monotonic allocation schemes in clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91573, Tilburg University.
  11. Curiel, I. & Tijs, S.H., 1991. "Minimarg and the maximarg operators," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154226, Tilburg University.
  12. 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.
  13. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  14. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA.
  15. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "A New Characterization of Convex Games," Discussion Paper 2004-109, Tilburg University, Center for Economic Research.
  16. 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.
  17. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154246, Tilburg University.
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Citations

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Cited by:
  1. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
  2. Brânzei, 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.
  3. Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December.

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