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Global Games

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  • Itzhak Gilboa
  • Ehud Lehrer

Abstract

Global games are real-valued functions defined on partitions (rather than subsets) of the set of players. They capture "public good" aspects of cooperation, i.e. situations where the payoff is naturally defined for all players ("the globe") together, as is the cause with issues of environmental clean-up, medical research, and so forth. We analyze the more general concept of lattice functions and apply it to partition functions, set functions and the interrelation between the two. We then use this analysis to define and characterize the Shapley value and the core of global games.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 922.

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Date of creation: Jun 1990
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Handle: RePEc:nwu:cmsems:922

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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References

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  1. Beja, A & Gilboa, Itzhak, 1990. "Values for Two-Stage Games: Another View of the Shapley Axioms," International Journal of Game Theory, Springer, vol. 19(1), pages 17-31.
  2. Itzhak Gilboa & Ehud Lehrer, 1989. "The Value of Information -- An Axiomatic Approach," Discussion Papers 835, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Citations

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Cited by:
  1. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
  3. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
  4. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Computational Statistics, Springer, vol. 65(1), pages 153-167, February.
  5. repec:hal:journl:halshs-00178916 is not listed on IDEAS
  6. repec:hal:journl:halshs-00445171 is not listed on IDEAS
  7. Giovanni Rossi, 2003. "Global Coalitional Games," Department of Economics University of Siena 415, Department of Economics, University of Siena.
  8. Derks, Jean & Peters, Hans, 1997. "Consistent restricted Shapley values," Mathematical Social Sciences, Elsevier, vol. 33(1), pages 75-91, February.
  9. repec:hal:journl:halshs-00179830 is not listed on IDEAS
  10. repec:hal:journl:halshs-00690696 is not listed on IDEAS
  11. J. Bilbao & E. Lebrón & N. Jiménez, 2000. "Simple games on closure spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 43-55, June.
  12. repec:hal:cesptp:hal-00803233 is not listed on IDEAS

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