
Existence and Complexity of Approximate Equilibria in Weighted Congestion Games
We study the existence of approximate pure Nash equilibria (αPNE) in we...
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Parametrized Nash Equilibria in Atomic Splittable Congestion Games via Weighted Block Laplacians
We consider atomic splittable congestion games with affine cost function...
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Nash Equilibrium in Smoothed Polynomial Time for Network Coordination Games
Extensive work in the last two decades has led to deep insights into the...
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Parallel computing as a congestion game
Gametheoretical approach to the analysis of parallel algorithms is prop...
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Smoothed Efficient Algorithms and Reductions for Network Coordination Games
Worstcase hardness results for most equilibrium computation problems ha...
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The Minimum Tollbooth Problem in Atomic Network Congestion Games with Unsplittable Flows
This work analyzes the minimum tollbooth problem in atomic network conge...
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Partial Altruism is Worse than Complete Selfishness in Nonatomic Congestion Games
We seek to understand the fundamental mathematics governing infrastructu...
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Node MaxCut and Computing Equilibria in Linear Weighted Congestion Games
Computing an equilibrium of a game is of central interest in Algorithmic Game Theory. We study the complexity of computing a PNE in Weighted Congestion Games with affine and linear delays, where O(1)approximate Nash equilibria can be computed in polynomial time and the only known PLShardness results follow from those for unweighted Congestion Games. We first show that it is PLScomplete to compute a PNE even in singlecommodity Weighted Network Congestion Games on seriesparallel networks with linear latencies, a result indicating that equilibrium computation for Weighted Congestion Games can be significantly more difficult than their unweighted counterparts. Note that for unweighted Congestion Games on singlecommodity series parallel networks with general latency functions, a PNE can be computed by a simple greedy algorithm. For that reduction, we use exponential coefficients on the linear latency functions. To investigate the impact of weighted players only, we restrict the game so that the linear latencies can only have polynomial coefficients. We show that it is PLScomplete to compute a PNE in Weighted Network Congestion Games with all edges having the identity function. For the latter, none of the known PLScomplete problems seems as a natural initial problem for the reduction. Hence, we consider the problem of finding a maximal cut in NodeMaxCut, a natural special case of MaxCut where the weights of the edges are the product of the weights of their endpoints. Via an involved reduction, we show that NodeMaxCut is PLScomplete, so that we can use it as our initial problem. The result and the reduction themselves are of independent interest and they may have more implications in proving other complexity results related to PLS.
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