Congestion Games with Player-Specific Payoff Functions

Milchtaich, Igal

doi:10.1006/game.1996.0027

Cited by 565 publications

(534 citation statements)

References 11 publications

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“…This also holds for nonincreasing cost functions as proven by Rozenfeld and Tennenholtz [36]. Allowing for player-specific cost functions, Milchtaich [25] showed that unweighted singleton congestion games with player-specific cost functions possess at least one PNE. He also presented an instance with weighted players and player-specific cost functions without a PNE.…”

Section: Related Workmentioning

confidence: 78%

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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We study the existence of pure Nash equilibria in weighted congestion games. Let denote a set of cost functions. We say that is consistent if every weighted congestion game with cost functions in possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of continuous cost functions. We prove that a set of continuous functions is consistent for two-player games if and only if contains only monotonic functions and for all nonconstant functions c 1 c 2 ∈ , there are constants a b ∈ such that c 1 x = a c 2 x + b for all x ∈ ≥0 . For games with at least three players, we prove that is consistent if and only if exactly one of the following cases holds: (a) contains only affine functions; (b) contains only exponential functions such that c x = a c e x + b c for some a c b c ∈ , where a c and b c may depend on c, while must be equal for every c ∈ . The latter characterization is even valid for three-player games. Finally, we derive several characterizations of consistency of cost functions for games with restricted strategy spaces, such as weighted network congestion games or weighted congestion games with singleton strategies.

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Section: Related Workmentioning

confidence: 78%

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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“…An important subclass of congestion games is the class of singleton congestion games (also known as parallel-link games) in which every player's strategy consists of a single resource [1,11,13,15,16,21,29].…”

Section: Congestion Models and Gamesmentioning

confidence: 99%

“…Note that capacitated congestion games follow the original congestion model of Rosenthal [32] when the resources are not overcrowded. When the capacity of a resource is exceeded, the game shares similarities with the player-specific model of Milchtaich [29] and with its generalization in [1]. However congestion games with capacitated resources are neither a refinement nor an extension of player-specific congestion games (this is discussed in detail in Appendix 1).…”

Section: Congestion Games With Capacitated Resourcesmentioning

confidence: 99%

Congestion Games with Capacitated Resources

Gourvès

Monnot

Moretti

et al. 2012

Algorithmic Game Theory

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Abstract. The players of a congestion game interact by allocating bundles of resources from a common pool. This type of games leads to well studied models for analyzing strategic situations, including networks operated by uncoordinated selfish users. Congestion games constitute a subclass of potential games, meaning that a pure Nash equilibrium emerges from a myopic process where the players iteratively react by switching to a strategy that diminishes their individual cost. With the aim of covering more applications, for instance in communication networks, we extend congestion games to the setting where every resource is endowed with a capacity which possibly limits its number of users. From the negative side, we show that a pure Nash equilibrium is not guaranteed to exist in any case and we prove that deciding whether a game possesses a pure Nash equilibrium is NP-complete. Our positive results state that congestion games with capacities are potential games in the well studied singleton case. Polynomial algorithms that compute these equilibria are also provided.

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“…There is one common resource, every player can request an arbitrary part of this resource and the payoff of every player depends on the moves of all players. Note that this game bears some similarity with congestion games [23] but it does not fit into the class of congestion games or weighted congestion games (See for example [23,16,15,9]). In the one-shot game the cost cannot be a timeout since there is only one round.…”

Section: Window-games With Non-aimd Flowsmentioning

confidence: 99%

Window-Games between TCP Flows

Efraimidis

Tsavlidis

2008

Algorithmic Game Theory

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Abstract. We consider network congestion problems between TCP flows and define a new game, the Window-game, which models the problem of network congestion caused by the competing flows. Analytical and experimental results show the relevance of the Window-game to the real TCP game and provide interesting insight on Nash equilibria of the respective network games. Furthermore, we propose a new algorithmic queue mechanism, called Prince, which at congestion makes a scapegoat of the most greedy flow. Preliminary evidence shows that Prince achieves efficient Nash equilibria while requiring only limited computational resources.

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Congestion Games with Player-Specific Payoff Functions

Cited by 565 publications

References 11 publications

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Congestion Games with Capacitated Resources

Window-Games between TCP Flows

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