Geodesic
Rosenthal's potential and a~discrete version of the Debreu--Gorman theorem
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 2, pp. 60-77.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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Nikolai S. Kukushkin. Rosenthal's potential and a~discrete version of the Debreu--Gorman theorem. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 2, pp. 60-77. http://geodesic.mathdoc.fr/item/MGTA_2014_6_2_a3/

[1] Bogomolnaia A., Jackson M. O., “The stability of hedonic coalition structures”, Games and Economic Behavior, 38 (2002), 201–230 | DOI | MR | Zbl

[2] Debreu G., “Topological methods in cardinal utility”, Mathematical Methods in Social Sciences, eds. Arrow K. J., Karlin S., Suppes P., Stanford University Press, Stanford, 1960, 16–26 | MR | Zbl

[3] Gorman W. M., “The structure of utility functions”, Review of Economic Studies, 35 (1968), 367–390 | DOI | Zbl

[4] Harks T., Klimm M., Möhring R. H., “Characterizing the existence of potential functions in weighted congestion games”, Theory of Computing Systems, 49 (2011), 46–70 | DOI | MR | Zbl

[5] Holzman R., Law-Yone N., “Strong equilibrium in congestion games”, Games and Economic Behavior, 21 (1997), 85–101 | DOI | MR | Zbl

[6] Konishi H., Le Breton M., Weber S., “Pure strategy Nash equilibrium in a group formation game with positive externalities”, Games and Economic Behavior, 21 (1997), 161–182 | DOI | MR | Zbl

[7] Kukushkin N. S., “Potential games: A purely ordinal approach”, Economics Letters, 64 (1999), 279–283 | DOI | MR | Zbl

[8] Kukushkin N. S., “Congestion games revisited”, International Journal of Game Theory, 36 (2007), 57–83 | DOI | MR | Zbl

[9] McLennan A., Monteiro P. K., Tourky R., “Games with discontinuous payoffs: a strengthening of Reny's existence theorem”, Econometrica, 79 (2011), 1643–1664 | DOI | MR | Zbl

[10] Milchtaich I., “Congestion games with player-specific payoff functions”, Games and Economic Behavior, 13 (1996), 111–124 | DOI | MR | Zbl

[11] Monderer D., Shapley L. S., “Potential games”, Games and Economic Behavior, 14 (1996), 124–143 | DOI | MR | Zbl

[12] Rosenthal R. W., “A class of games possessing pure-strategy Nash equilibria”, International Journal of Game Theory, 2 (1973), 65–67 | DOI | MR | Zbl

[13] Sandholm W. H., “Decompositions and potentials for normal form games”, Games and Economic Behavior, 70 (2010), 446–456 | DOI | MR | Zbl

[14] Wakker P. P., Additive Representations of Preferences, Kluwer Academic Publishers, Dordrecht, 1989 | MR | Zbl