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)
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)
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)
Ambec, S., Ehlers, L.: Sharing a river among satiable agents. Games Econ. Behav. 64, 35–50 (2008)
Ambec, S., Sprumont, Y.: Sharing a river. J. Econ. Theory 107, 453–462 (2002)
Bloch, F., van den Nouweland, A.: Expectation formation rules and the core of partition function games. Games Econ. Behav. 88, 339–353 (2014)
de Clippel, G., Serrano, R.: Marginal contributions and externalities in the value. Econometrica 76, 1413–1436 (2008)
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)
Dutta, B., Ehlers, L., Kar, A.: Externalities, potential, value and consistency. J. Econ. Theory 145, 2380–2411 (2010)
Futagami, K., Nakabo, Y.: Capital accumulation game with quasi-geometric discounting and consumption externalities. Econ. Theor. 71, 251–281 (2019)
Graziano, M.G., Meo, C., Yannelis, N.C.: Shapley and Scarf housing markets with consumption externalities. J. Public Econ. Theory 22, 1481–1514 (2020)
Hafalir, I.: Efficiency in coalition games with externalities. Games Econ. Behav. 61, 242–258 (2007)
Hart, S., Kurz, M.: Endogenous formation of coalitions. Econometrica 51, 1047–1064 (1983)
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)
Kóczy, L.Á.: A recursive core for partition function form games. Theor. Decis. 63, 41–51 (2007)
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)
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)
Maskin, E.: Bargaining, coalitions, and externalities. Presidential address to the econometric society. Institute for Advanced Study, Princeton (2003)
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)
Shapley, L.S.: Cores of convex games. Int. J. Game Theory 1, 11–26 (1971)
Thrall, R., Lucas, W.: n-person games in partition function form. Naval Res. Logist. Q. 10, 281–298 (1963)
Topkis, D.: Supermodularity and Complementarity. Frontiers of Economic Research. Princeton University Press, Princeton (1998)
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)
Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
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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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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DOI: https://doi.org/10.1007/s00199-021-01371-8