Strong equilibrium in games with common and complementary local utilities

Kukushkin, Nikolai S. (2014): Strong equilibrium in games with common and complementary local utilities.

Abstract

A rather general class of strategic games is described where the coalition improvements are acyclic and hence strong equilibria exist: The players derive their utilities from the use of certain "facilities"; all players using a facility extract the same amount of "local utility" therefrom, which amount depends both on the set of users and on their actions, and is decreasing in the set of users; the "ultimate" utility of each player is the minimum of the local utilities at all relevant facilities. Two important subclasses are "games with structured utilities," basic properties of which were discovered in 1970s and 1980s, and "bottleneck congestion games," which attracted researchers' attention quite recently. The former games are representative in the sense that every game from the whole class is isomorphic to one of them. The necessity of the minimum aggregation for the "persistent" existence of strong equilibria, actually, just Pareto optimal Nash equilibria, is established.

• Item Type: MPRA Paper
• Language: English
• Keywords: Strong equilibrium; Weakest-link aggregation; Coalition improvement path; Congestion game; Game with structured utilities
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

d'Aspremont,~C., and L.~Gevers, 1977. Equity and the informational basis of collective choice. Review of Economic Studies 44, 199--209.

Debreu,~G., 1960. Topological methods in cardinal utility. In: Arrow,~K.J., S.~Karlin, and P.~Suppes, (Eds.) Mathematical Methods in Social Sciences. Stanford University Press, Stanford, 16--26.

Deschamps,~R., and L.~Gevers, 1978. Leximin and utilitarian rules: A joint characterization. Journal of Economic Theory 17, 143--163.

Fotakis,~D, S.~Kontogiannis, and P.~Spirakis, 2008. Atomic congestion games among coalitions. ACM Transactions on Algorithms 4(4), Art. 52.

Galbraith,~G.K., 1958. The Affluent Society. The New American Library, New York and Toronto.

Germeier,~Yu.B., and I.A.~Vatel', 1974. On games with a hierarchical vector of interests. Izvestiya Akademii Nauk SSSR, Tekhnicheskaya Kibernetika, 3, 54--69 (in Russian; English translation in Engineering Cybernetics 12(3), 25--40 (1974)).

Gillies,~D.B., 1959. Solutions to general non-zero-sum games. In: Tucker,~A.W., and R.D.~Luce (Eds.) Contributions to the Theory of Games 4 (Annals of Mathematical Studies 40). Princeton University Press, 47--85.

Gorman,~W.M., 1968. The structure of utility functions. Review of Economic Studies 35, 367--390.

Harks,~T., M.~Klimm, and R.H.~Mohring, 2013. Strong equilibria in games with the lexicographical improvement property. International Journal of Game Theory 42, 461--482.

Holzman,~R., and N.~Law-Yone, 1997. Strong equilibrium in congestion games. Games and Economic Behavior 21, 85--101.

Konishi,~H., M.~Le~Breton, and S.~Weber, 1997. Equilibria in a model with partial rivalry. Journal of Economic Theory 72, 225--237.

Kukushkin,~N.S., 1992. On existence of stable and efficient outcomes in games with public and private objectives. International Journal of Game Theory 20, 295--303.

Kukushkin,~N.S., 2004. Acyclicity of Improvements in Games with Common Intermediate Objectives. Russian Academy of Sciences, Dorodnicyn Computing Center, Moscow.

Kukushkin,~N.S., 2007. Congestion games revisited. International Journal of Game Theory 36, 57--83.

Kukushkin,~N.S., 2008. Maximizing an interval order on compact subsets of its domain. Mathematical Social Sciences 56, 195--206.

Kukushkin,~N.S., 2010. Improvement Paths in Strategic Games: A Topological Approach. Russian Academy of Sciences, Dorodnicyn Computing Center, Moscow.

Kukushkin,~N.S., 2011. Nash equilibrium in compact-continuous games with a potential. International Journal of Game Theory 40, 387--392.

Kukushkin,~N.S., I.S.~Men'shikov, O.R.~Men'shikova, and N.N.~Moiseev, 1985. Stable compromises in games with structured payoffs. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki 25, 1761--1776 (in Russian; English translation in USSR Computational Mathematics and Mathematical Physics 25, 108--116).

Milchtaich,~I., 1996. Congestion games with player-specific payoff functions. Games and Economic Behavior 13, 111--124.

Monderer,~D., and L.S.~Shapley, 1996. Potential games. Games and Economic Behavior 14, 124--143.

Moulin,~H., 1982. Game Theory for the Social Sciences. New York University Press, New York.

Moulin,~H., 1988. Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge--New York--Sydney.

Rosenthal,~R.W., 1973. A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65--67.

Smith,~T.E., 1974. On the existence of most-preferred alternatives. International Economic Review 15, 184--194.