On best response dynamics in weighted congestion games with polynomial delays

Fanelli, Angelo; Moscardelli, Luca

doi:10.1007/s00446-011-0145-5

Cited by 16 publications

(20 citation statements)

References 26 publications

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“…Aland et al 1987;Bhawalkar et al 2010;Bilò 2012;Christodoulou and Koutsoupias 2005) and studying the best-response and approximate improvement dynamics (e.g. Awerbuch et al 2008;Caragiannis et al 2011;Chien and Sinclair 2007;Fanelli et al 2012;Fanelli and Moscardelli 2011) for congestion games.…”

Section: Related Workmentioning

confidence: 99%

On lookahead equilibria in congestion games

Bilò

Fanelli²,

Moscardelli

2015

Math. Struct. Comp. Sci.

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We investigate the issues of existence and efficiency of lookahead equilibria in congestion games. Lookahead equilibria, whose study has been initiated by Mirrokni et al. (2012), correspond to the natural extension of pure Nash equilibria in which the players, when making use of global information in order to predict subsequent reactions of the other ones, have computationally limited capabilities.

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Section: Related Workmentioning

confidence: 99%

On lookahead equilibria in congestion games

Bilò

Fanelli²,

Moscardelli

2015

Math. Struct. Comp. Sci.

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“…A similar, but independent, result by Bhalgat et al (2009) states that any approximate best-response dynamics converges in polynomial time to a constant approximation of the social optimum in congestion games whose resources have similar latency functions. Despite the negative result of Awerbuch et al (2008), Fanelli and Moscardelli (2011) show that, with some additional reasonable assumptions, best-response dynamics are guaranteed to converge in polynomial time to a constant approximation of the social optimum in weighted congestion games with polynomial latency functions. For the special case of congestion games with linear latency functions, Fanelli et al (2012) show that (n log log n) best-responses are necessary and sufficient to attain a constant approximation of the social optimum, where n is the number of players.…”

Section: Related Workmentioning

confidence: 91%

On the performance of mildly greedy players in cut games

Bilò

Paladini

2015

J Comb Optim

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We continue the study of the performance of mildly greedy players in cut games initiated by Christodoulou et al. (Theoret Comput Sci 438:13-27, 2012), where a mildly greedy player is a selfish agent who is willing to deviate from a certain strategy profile only if her payoff improves by a factor of more than 1 + , for some given ≥ 0. Hence, in presence of mildly greedy players, the classical concepts of pure Nash equilibria and best-responses generalize to those of (1 + )-approximate pure Nash equilibria and (1 + )-approximate best-responses, respectively. We first show that the -approximate price of anarchy, that is the price of anarchy of (1 + )-approximate pure Nash equilibria, is at least 1 2+ and that this bound is tight for any ≥ 0. Then, we evaluate the approximation ratio of the solutions achieved after a (1 + )-approximate one-round walk starting from any initial strategy profile, where a (1 + )-approximate one-round walk is a sequence of (1 + )-approximate bestresponses, one for each player. We improve the currently known lower bound on this ratio from min 1 4+2 , 4+2 up to min 1 2+ , 2 (1+ )(2+ ) and show that this is again tight for any ≥ 0. An interesting and quite surprising consequence of our results is that the worst-case performance guarantee of the very simple solutions generated after a (1 + )-approximate one-round walk is the same as that of (1 + )-approximate pure Nash equilibria when ≥ 1 and of that of subgame perfect equilibria (i.e., Nash equilibria for greedy players with farsighted, rather than myopic, rationality) when = 1.

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“…Other papers [Awerbuch et al 2008;Fanelli and Moscardelli 2011;Goemans et al 2005] consider the question of whether efficient states (in the sense that the total cost of the players, or social cost, is small compared to the optimum one) can be reached by best-response moves in linear weighted congestion games. In particular, Awerbuch et al [2008] show that using almost unrestricted sequences of (1 + )-improvement best-response moves, the players rapidly converge to efficient states.…”

Section: Introductionmentioning

confidence: 99%

Approximate Pure Nash Equilibria in Weighted Congestion Games

CaragiannisIoannis

Fanelli

GravinNick

et al. 2015

ACM Trans. Econ. Comput.

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We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of pure Nash equilibria is guaranteed by a potential function argument. Unfortunately, this proof of existence is inefficient and computing pure Nash equilibria in such games is a PLS-hard problem even when all players have unit weights. The situation gets worse when superlinear (e.g., quadratic) latency functions come into play; in this case, the Nash dynamics of the game may contain cycles and pure Nash equilibria may not even exist. Given these obstacles, we consider approximate pure Nash equilibria as alternative solution concepts. A ρ-approximate pure Nash equilibrium is a state of a (weighted congestion) game from which no player has any incentive to deviate in order to improve her cost by a multiplicative factor higher than ρ. Do such equilibria exist for small values of ρ? And if so, can we compute them efficiently?We provide positive answers to both questions for weighted congestion games with polynomial latency functions by exploiting an "approximation" of such games by a new class of potential games that we call -games. This allows us to show that these games have d!-approximate pure Nash equilibria, where d is the maximum degree of the latency functions. Our main technical contribution is an efficient algorithm for computing O(1)-approximate pure Nash equilibria when d is a constant. For games with linear latency functions, the approximation guarantee is 3+The running time is polynomial in the number of bits in the representation of the game and 1/γ . As a byproduct of our techniques, we also show the following interesting structural statement for weighted congestion games with polynomial latency functions of maximum degree d ≥ 2: polynomially-long sequences of best-response moves from any initial state to a d O(d 2 ) -approximate pure Nash equilibrium exist and can be efficiently identified in such games as long as d is a constant.To the best of our knowledge, these are the first positive algorithmic results for approximate pure Nash equilibria in weighted congestion games. Our techniques significantly extend our recent work on unweighted congestion games through the use of -games. The concept of approximating nonpotential games by potential ones is interesting in itself and might have further applications.

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On best response dynamics in weighted congestion games with polynomial delays

Cited by 16 publications

References 26 publications

On lookahead equilibria in congestion games

On lookahead equilibria in congestion games

On the performance of mildly greedy players in cut games

Approximate Pure Nash Equilibria in Weighted Congestion Games

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