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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.

Suggested Citation

  • Itzhak Gilboa & Ehud Lehrer, 1990. "Global Games," Discussion Papers 922, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:922
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    References listed on IDEAS

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    1. Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    2. Beja, A & Gilboa, Itzhak, 1990. "Values for Two-Stage Games: Another View of the Shapley Axioms," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 17-31.
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    1. repec:hal:pseose:hal-00803233 is not listed on IDEAS
    2. Borm, Peter & Ju, Yuan & Wettstein, David, 2015. "Rational bargaining in games with coalitional externalities," Journal of Economic Theory, Elsevier, vol. 157(C), pages 236-254.
    3. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 153-167, February.
    4. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 80-88.
    5. 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.
    6. Michel Grabisch, 2006. "Capacities and Games on Lattices: A Survey of Result," Post-Print halshs-00179830, HAL.
    7. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    8. 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;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 43-55, June.
    9. Derks, Jean & Peters, Hans, 1997. "Consistent restricted Shapley values," Mathematical Social Sciences, Elsevier, vol. 33(1), pages 75-91, February.
    10. 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.
    11. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Giovanni Rossi, 2003. "Global Coalitional Games," Department of Economics University of Siena 415, Department of Economics, University of Siena.

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