Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem

Kukushkin, Nikolai S. (2014): Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem.

Abstract

The acyclicity of individual improvements in a generalized congestion game (where the sums of local utilities are replaced with arbitrary aggregation rules) can be established with a Rosenthal-style construction if aggregation rules of all players are "quasi-separable." Every universal separable ordering on a finite set can be represented as a combination of addition and lexicography.

• Item Type: MPRA Paper
• Language: English
• Keywords: Improvement dynamics; Acyclicity; Separable aggregation; Congestion game
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

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

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

Harks,~T., Klimm,~M., and R.H.~M\"ohring, 2011. Characterizing the existence of potential functions in weighted congestion games. Theory of Computing Systems 49, 46--70.

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. Pure strategy Nash equilibrium in a group formation game with positive externalities. Games and Economic Behavior 21, 161--182.

Kukushkin,~N.S., 1999. Potential games: A purely ordinal approach. Economics Letters 64, 279--283.

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

McLennan,~A., Monteiro,~P.K., and R.~Tourky, 2011. Games with discontinuous payoffs: a strengthening of Reny's existence theorem. Econometrica 79, 1643--1664.

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.

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

Sandholm,~W.H., 2010. Decompositions and potentials for normal form games. Games and Economic Behavior 70, 446--456.

Wakker,~P.P., 1989. Additive Representations of Preferences. Kluwer Academic Publishers, Dordrecht.