Abstract
A global (cooperative) game describes the utility that the whole set of players generates depending on the coalition structure they form. These games were introduced by Gilboa and Lehrer (Int J Game Theory 20:129–147, 1991) who proposed and characterized a generalization of the Shapley value. We introduce two families of point valued solutions that contain the Gilboa–Lehrer value. We characterize each family by means of reasonable properties, which are related to the ones used by Gilboa and Lehrer.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Barrett, S.: Self-enforcing international environmental agreements. Oxf. Econ. Pap. 46, 878–894 (1994)
Carlsson, H., Van Damme, E.: Global games and equilibrium selection. Econometrica 61, 989–1018 (1993)
Caulier, J.-F., Mauleon, A., Vannetelbosch, V.: Allocation rules for coalitional network games. Math. Soc. Sci. 78, 80–88 (2015)
Chander, P., Tulkens, H.: A core-theoretic solution for the design of cooperative agreements on transfrontier pollution. In Public Goods, Environmental Externalities and Fiscal Competition, pp. 176–193. Springer (2006)
De Clippel, G., Serrano, R.: Marginal contributions and externalities in the value. Econometrica 76, 1413–1436 (2008)
Faigle, U., Grabisch, M.: Values for Markovian coalition processes. Econ. Theor. 51, 505–538 (2012). https://doi.org/10.1007/s00199-011-0617-7
Finus, M.: Game theoretic research on the design of international environmental agreements: insights, critical remarks, and future challenges. Int. Rev. Environ. Resour. Econ. 2, 29–67 (2008)
Gilboa, I., Lehrer, E.: Global games. Int. J. Game Theory 20, 129–147 (1991)
Hernandez-Lamoneda, L., Juarez, R., Sanchez-Sanchez, F.: Solutions without dummy axiom for TU cooperative games. Econ. Bull. 3, 1–9 (2008)
Kóczy, L.Á., et al.: Partition Function form Games. Springer (2018)
Myerson, R.: Values of games in partition function form. Int. J. Game Theory 6, 23–31 (1977)
Rossi, G.: Solutions of partition function-based TU games for cooperative communication networking. In: Future of Information and Communication Conference, pp. 645–666. Springer (2019)
Scafuri, A.J., Yannelis, N.C.: Non-symmetric cardinal value allocations. Econ. J. Econ. Soc. 52, 1365–1368 (1984)
Shafer, W.J.: On the existence and interpretation of value allocation. Econ. J. Econ. Soc. 48, 467–476 (1980)
Shapley, L.S.: A value for \(n\)-person games. In: Tucker, A.W. (ed.) Contributions to the Theory of Games II, pp. 307–317. Princeton University Press (1953)
Stanley, R.P.: Enumerative Combinatorics. Cambridge University Press, Cambridge (2011)
Thrall, R., Lucas, W.: n-person games in partition function form. Naval Res. Logist. Quart. 10, 281–298 (1963)
van den Brink, R.: Null or nullifying players: the difference between the Shapley value and equal division solutions. J. Econ. Theory 136, 767–775 (2007)
Acknowledgements
We are grateful to an anonymous reviewer and the associate editor for useful comments and suggestions. This work is part of the R+D+I project grants PID2020-113110GB-I00, PID2021-124030NB-C32, PID2021-124030NB-C33, and PID2022-138956NB-100 that were funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. This research was also funded by Grupos de Referencia Competitiva ED431C-2020/03 and ED431C-2021/24 from Consellería de Cultura, Educación e Universidades, Xunta de Galicia, by Generalitat de Catalunya through grant 2021-SGR-00306.
Funding
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Alonso-Meijide, J.M., Álvarez-Mozos, M., Fiestras-Janeiro, M.G. et al. Two families of values for global cooperative games. Econ Theory (2024). https://doi.org/10.1007/s00199-024-01567-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00199-024-01567-8