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On convexity in cooperative games with externalities

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Abstract

We introduce new notions of superadditivity and convexity for games with coalitional externalities. We show parallel results to the classic ones for transferable utility games without externalities. In superadditive games the grand coalition is the most efficient organization of agents. The convexity of a game is equivalent to having non decreasing contributions to larger embedded coalitions. We also see that convex games can only have negative externalities.

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References

  • Abe, T.: Efficiency and the core in games with positive and negative externalities. Technical report, WINPEC Working Paper Series (2016)

  • Abe, T.: Population monotonic allocation schemes for games with externalities. Int. J. Game Theory 49, 97–117 (2020)

    Article  Google Scholar 

  • Alonso-Meijide, J.M., Álvarez-Mozos, M., Fiestras-Janeiro, M.G., Jiménez-Losada, A.: Some structural properties of a lattice of embedded coalitions. Int. J. Gen. Syst. 46, 123–143 (2017)

    Article  Google Scholar 

  • Alonso-Meijide, J.M., Álvarez-Mozos, M., Fiestras-Janeiro, M.G., Jiménez-Losada, A.: Complete null agent for games with externalities. Expert Syst. Appl. 135, 1–11 (2019)

    Article  Google Scholar 

  • Ambec, S., Ehlers, L.: Sharing a river among satiable agents. Games Econ. Behav. 64, 35–50 (2008)

    Article  Google Scholar 

  • Ambec, S., Sprumont, Y.: Sharing a river. J. Econ. Theory 107, 453–462 (2002)

    Article  Google Scholar 

  • Bloch, F., van den Nouweland, A.: Expectation formation rules and the core of partition function games. Games Econ. Behav. 88, 339–353 (2014)

    Article  Google Scholar 

  • de Clippel, G., Serrano, R.: Marginal contributions and externalities in the value. Econometrica 76, 1413–1436 (2008)

    Article  Google Scholar 

  • Diamantoudi, E., Macho-Stadler, I., Pérez-Castrillo, D., Xue, L.: Sharing the surplus in games with externalities within and across issues. Econ. Theor. 60, 315–343 (2015)

    Article  Google Scholar 

  • Dutta, B., Ehlers, L., Kar, A.: Externalities, potential, value and consistency. J. Econ. Theory 145, 2380–2411 (2010)

    Article  Google Scholar 

  • Futagami, K., Nakabo, Y.: Capital accumulation game with quasi-geometric discounting and consumption externalities. Econ. Theor. 71, 251–281 (2019)

    Article  Google Scholar 

  • Graziano, M.G., Meo, C., Yannelis, N.C.: Shapley and Scarf housing markets with consumption externalities. J. Public Econ. Theory 22, 1481–1514 (2020)

    Article  Google Scholar 

  • Hafalir, I.: Efficiency in coalition games with externalities. Games Econ. Behav. 61, 242–258 (2007)

    Article  Google Scholar 

  • Hart, S., Kurz, M.: Endogenous formation of coalitions. Econometrica 51, 1047–1064 (1983)

    Article  Google Scholar 

  • Hervés-Beloso, C., Moreno-García, E.: Revisiting the Coase theorem. Econ. Theor. (2021). https://link.springer.com/article/10.1007/s00199-020-01330-9

  • Jelnov, A., Tauman, Y.: The private value of a patent: a cooperative approach. Math. Soc. Sci. 58, 84–97 (2009)

    Article  Google Scholar 

  • Kóczy, L.Á.: A recursive core for partition function form games. Theor. Decis. 63, 41–51 (2007)

    Article  Google Scholar 

  • Liu, X., Lindroos, M., Sandal, L.: Sharing a fish stock when distribution and harvest costs are density dependent. Environ. Resour. Econ. 63, 665–686 (2016)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Maskin, E.: Bargaining, coalitions, and externalities. Presidential address to the econometric society. Institute for Advanced Study, Princeton (2003)

    Google Scholar 

  • Maskin, E.: How can cooperative game theory be made more relevant to economics? An open problem. In Open Problems in Mathematics, pp. 347–350. Springer (2016)

  • McQuillin, B.: The extended and generalized Shapley value. Simultaneous consideration of coalitional externalities and coalition structure. J. Econ. Theory 144, 696–721 (2009)

  • Milgrom, P., Shannon, C.: Generalized convex games. Technical report, Berkley University (1996)

  • Ray, D., Vohra, R.: A theory of endogenous coalition structures. Games Econ. Behav. 2, 286–336 (1999)

    Article  Google Scholar 

  • Shapley, L.S.: Cores of convex games. Int. J. Game Theory 1, 11–26 (1971)

    Article  Google Scholar 

  • Thrall, R., Lucas, W.: n-person games in partition function form. Naval Res. Logist. Q. 10, 281–298 (1963)

    Article  Google Scholar 

  • Topkis, D.: Supermodularity and Complementarity. Frontiers of Economic Research. Princeton University Press, Princeton (1998)

    Google Scholar 

  • van den Brink, R., van der Laan, G., Moes, N.: Fair agreements for sharing international rivers with multiple springs and externalities. J. Environ. Econ. Manag. 63, 388–403 (2012)

    Article  Google Scholar 

  • Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    Google Scholar 

Download references

Acknowledgements

This work has been supported by the European Regional Development Fund (ERDF) and Ministerio de Economía, Industria y Competitividad through grants ECO2017-86481-P, MTM2017-83455-P, MTM2017-87197-C3-2-P, MTM2017-87197-C3-3-P, by the Generalitat de Catalunya through grant 2017-SGR-778, by the Junta de Andalucía through grant FQM237, and by the Xunta de Galicia through the European Regional Development Fund (Grupos de Referencia Competitiva ED431C-2016-040 and ED431C-2017/38).

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Correspondence to M. Álvarez-Mozos.

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Alonso-Meijide, J.M., Álvarez-Mozos, M., Fiestras-Janeiro, M.G. et al. On convexity in cooperative games with externalities. Econ Theory 74, 265–292 (2022). https://doi.org/10.1007/s00199-021-01371-8

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