Congestion games revisited

Kukushkin, Nikolai S.

doi:10.1007/s00182-007-0090-5

Cited by 16 publications

(26 citation statements)

References 15 publications

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“…The proof of the theorem, which is relegated to the Appendix, utilizes the ingenious idea of Rosenthal (1973) to show that our game of social interactions is a potential game studied in Monderer and Shapley (1996) (see also Kukushkin (2007)). Note that Assumption A1 is vacuous when X is a finite set.…”

Section: The Model and Resultsmentioning

confidence: 99%

Games of social interactions with local and global externalities

Breton

Weber

2011

Economics Letters

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Section: The Model and Resultsmentioning

confidence: 99%

Games of social interactions with local and global externalities

Breton

Weber

2011

Economics Letters

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“…An alternative, more transparent proof was given in Voorneveld et al (1999, Theorem 3.3). Kukushkin (2007) introduced games with structured utilities, in a sense, "dual" to congestion games; the players there do not choose which facilities to use, only how to use facilities from a fixed list. The idea of such a structure of utility functions can be traced back to Germeier and Vatel' (1974), although the local utilities in that paper were aggregated with the minimum function.…”

Section: Introductionmentioning

confidence: 99%

“…The idea of such a structure of utility functions can be traced back to Germeier and Vatel' (1974), although the local utilities in that paper were aggregated with the minimum function. Theorem 5 from Kukushkin (2007) showed that a strategic game admits an exact potential if and only if it can be represented as a game with structured utilities.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, two different classes of potential games were considered in Kukushkin (2007); one universal for finite potential games, the other for all of them. The possibility to combine both constructions was not discussed, actually, was overlooked altogether.…”

Section: Introductionmentioning

confidence: 99%

“…Actually, the necessity (in a sense) of addition was showed in Kukushkin (2007): If the players may aggregate local utilities with arbitrary (continuous and strictly increasing) functions, then the existence of an exact potential is ensured regardless of other characteristics of the game only if the players sum up local utilities; that statement remains valid when attention is restricted to congestion games (Theorem 2 of Kukushkin, 2007), or to games with structured utilities (Theorem 4).…”

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confidence: 99%

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A universal construction generating potential games

Kukushkin

2018

Games and Economic Behavior

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Strategic games are considered where each player's total utility is the sum of local utilities obtained from the use of certain "facilities." All players using a facility obtain the same utility therefrom, which may depend on the identities of users and on their behavior. If a regularity condition is satisfied by every facility, then the game admits an exact potential; both congestion games and games with structured utilities are included in the class and satisfy that condition. Under additional assumptions the potential attains its maximum, which is a Nash equilibrium of the game. MSC2010 Classification: 91A10; Journal of Economic Literature Classification: C 72.

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Generalizations of Weighted Matroid Congestion Games: Pure Nash Equilibrium, Sensitivity Analysis, and Discrete Convex Function

Takazawa

2019

Lecture Notes in Computer Science

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Congestion games offer a primary model in the study of pure Nash equilibria in non-cooperative games, and a number of generalized models have been proposed in the literature. One line of generalization includes weighted congestion games, in which the cost of a resource is a function of the total weight of the players choosing that resource. Another line includes congestion games with mixed costs, in which the cost imposed on a player is a convex combination of the total cost and the maximum cost of the resources in her strategy. This model is further generalized to that of congestion games with complementarities. For the above models, the existence of a pure Nash equilibrium is proved under some assumptions, including that the strategy space of each player is the base family of a matroid and that the cost functions have a certain kind of monotonicity. In this paper, we deal with common generalizations of these two lines, namely weighted matroid congestion games with complementarities, and its further generalization. Our main technical contribution is a proof of the existence of pure Nash equilibria in these generalized models under a simplified assumption on the monotonicity, which provide a common extension of the previous results. We also present some extensions on the existence of pure Nash equilibria in player-specific and weighted matroid congestion games with mixed costs.

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Congestion games revisited

Abstract: Nash equilibrium existence, Potential game, Congestion game, Additive aggregation,

Cited by 16 publications

References 15 publications

Games of social interactions with local and global externalities

Games of social interactions with local and global externalities

A universal construction generating potential games

Generalizations of Weighted Matroid Congestion Games: Pure Nash Equilibrium, Sensitivity Analysis, and Discrete Convex Function

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