Economic Theory

, Volume 60, Issue 2, pp 315–343 | Cite as

Sharing the surplus in games with externalities within and across issues

  • Effrosyni Diamantoudi
  • Inés Macho-Stadler
  • David Pérez-CastrilloEmail author
  • Licun Xue
Research Article


We consider issue-externality games in which agents can cooperate on multiple issues and externalities are present both within and across issues, that is, the amount a coalition receives in one issue depends on how the players are organized on all the issues. Examples of such games are several firms competing in multiple markets, and countries negotiating both a trade agreement (through, e.g., WTO) and an environmental agreement (e.g., Kyoto Protocol). We propose a way to extend (Shapley) values for partition function games to issue-externality games. We characterize our proposal through axioms that extend the Shapley axioms to our more general environment. The solution concept that we propose can be applied to many interesting games, including inter-temporal situations where players meet sequentially.


Externalities Cooperative game theory Shapley value Linked issues 

JEL Classification

C71 D62 


  1. Albizuri, M.J., Arin, J., Rubio, J.: An axiom system for a value for games in partition function form. Int. Game Theory Rev. 7, 63–73 (2005)CrossRefGoogle Scholar
  2. Beja, A., Gilboa, I.: Values for two-stage games: another view of the Shapley axioms. Int. J. Game Theory 19, 17–31 (1990)CrossRefGoogle Scholar
  3. Bloch, F., de Clippel, G.: Core of combined games. J. Econ. Theory 145, 2424–2434 (2010)CrossRefGoogle Scholar
  4. Bolger, E.M.: A set of axioms for a value for partition function games. Int. J. Game Theory 18, 37–44 (1989)CrossRefGoogle Scholar
  5. Bulow, J.I., Geanakoplos, J.D., Klemperer, P.D.: Multimarket oligopoly: strategic substitutes and complements. J. Polit. Econ. 93, 488–511 (1985)CrossRefGoogle Scholar
  6. de Clippel, G., Serrano, R.: Marginal contributions and externalities in the value. Econometrica 76, 1413–1436 (2008)CrossRefGoogle Scholar
  7. Dutta, B., Ehlers, L., Kar, A.: Externalities, potential, value and consistency. J. Econ. Theory 134, 2380–2411 (2010)CrossRefGoogle Scholar
  8. Feldman, B.E.: Bargaining, coalition formation, and value. Ph.D. thesis, State University of New York at Stony Brook (1996)Google Scholar
  9. Harsanyi, J.C.: A bargaining model for the cooperative \(n\)-person game. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games IV, pp. 325–355. Princeton University Press, Princeton (1959)Google Scholar
  10. Hart, S., Mas-Colell, A.: Potential, value and consistency. Econometrica 57, 589–614 (1989)CrossRefGoogle Scholar
  11. Macho-Stadler, I., Pérez-Castrillo, D., Wettstein, D.: Efficient bidding with externalities. Games Econ. Behav. 57, 304–320 (2006)CrossRefGoogle Scholar
  12. Macho-Stadler, I., Pérez-Castrillo, D., Wettstein, D.: Sharing the surplus: an extension of the Shapley value for environments with externalities. J. Econ. Theory 135, 339–356 (2007)CrossRefGoogle Scholar
  13. Maskin, E.: Bargaining, coalitions and externalities. In: Presidential Address to the Econometric Society. Institute for Advanced Study, Princeton (2003)Google Scholar
  14. McQuillin, B.: The extended and generalized Shapley value: simultaneous consideration of coalitional externalities and coalitional structure. J. Econ. Theory 144, 696–721 (2009)CrossRefGoogle Scholar
  15. Myerson, R.B.: Game Theory: Analysis of Conflict. Harvard University Press, Cambridge (1991)Google Scholar
  16. Myerson, R.B.: Values of games in partition function form. Int. J. Game Theory 6, 23–31 (1977)CrossRefGoogle Scholar
  17. Nax, H.H.: A note on the core of TU-cooperative games with multiple membership externalities. Games 5, 191–203 (2014)CrossRefGoogle Scholar
  18. Pham Do, K.H., Norde, H.: The Shapley value for partition function form games. Int. Game Theory Rev. 9, 353–360 (2007)CrossRefGoogle Scholar
  19. Shapley, L.S.: A value for \(n\)-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games II, pp. 307–317 (1953)Google Scholar
  20. Thrall, R.M., Lucas, W.F.: \(n\)-Person games in partition function form. Nav. Res. Logist. Q. 10, 281–298 (1963)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Effrosyni Diamantoudi
    • 1
  • Inés Macho-Stadler
    • 2
  • David Pérez-Castrillo
    • 2
    Email author
  • Licun Xue
    • 3
  1. 1.CIREQ and Department of EconomicsConcordia UniversityMontrealCanada
  2. 2.Dept. Economía e Hist. EconómicaUniversitat Autonoma de Barcelona, Barcelona GSEBellaterraSpain
  3. 3.CIREQ and Department of EconomicsMcGill UniversityMontrealCanada

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