Network topology and the efficiency of equilibrium

Milchtaich, Igal

doi:10.1016/j.geb.2005.09.005

Cited by 93 publications

(91 citation statements)

References 20 publications

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“…However, using the latter term would be potentially confusing, since the literature on congestion games (e.g., Milchtaich, 2006a;Correa et al, 2008) already assigns it several meanings that are substantially different from the meaning of separability in this paper and others.…”

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confidence: 80%

Weighted congestion games with separable preferences

Milchtaich

2009

Games and Economic Behavior

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Players in a congestion game may differ from one another in their intrinsic preferences (e.g., the benefit they get from using a specific resource), their contribution to congestion, or both. In many cases of interest, intrinsic preferences and the negative effect of congestion are (additively or multiplicatively) separable. This paper considers the implications of separability for the existence of pure-strategy Nash equilibrium and the prospects of spontaneous convergence to equilibrium. It is shown that these properties may or may not be guaranteed, depending on the exact nature of player heterogeneity.

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confidence: 80%

Weighted congestion games with separable preferences

Milchtaich

2009

Games and Economic Behavior

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“…Milchtaich [24] was the first to consider networks with linearly independent paths (under this name). Milchtaich proved that an undirected network has linearly independent paths if and only if it is extension-parallel.…”

Section: √ 3 23mentioning

confidence: 99%

“…Milchtaich [24,Proposition 5] proved that an undirected s − t network has linearly independent paths if and only if it is extension-parallel. Therefore, every (directed) extension-parallel network has linearly independent paths (see also [20,Theorem 1]).…”

Section: Model and Preliminariesmentioning

confidence: 99%

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Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

Fotakis¹

2008

Algorithmic Game Theory

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Abstract. We investigate the effect of linear independence in the strategies of congestion games on the convergence time of best improvement sequences and on the pure Price of Anarchy. In particular, we consider symmetric congestion games on extension-parallel networks, an interesting class of networks with linearly independent paths, and establish two remarkable properties previously known only for parallel-link games. More precisely, we show that for arbitrary (non-negative and non-decreasing) latency functions, any best improvement sequence reaches a pure Nash equilibrium in at most as many steps as the number of players, and that for latency functions in class D, the pure Price of Anarchy is at most ρ(D). As a by-product of our analysis, we obtain that for symmetric congestion games on general networks with latency functions in class D, the Price of Stability is at most ρ(D).

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“…By contrast, the Pareto efficiency of the equilibria in nonatomic congestion games strongly depends on the topology. For a twoterminal network G, the equilibria are always Pareto efficient if and only if G has linearly independent routes, meaning that each route has an edge that is not in any other route [18]. In a sense, equilibria that are not Pareto efficient may occur in only three known two-terminal "forbidden" networks, which are the minimal ones without linearly independent routes.…”

Section: Introductionmentioning

confidence: 99%

The Equilibrium Existence Problem in Finite Network Congestion Games

Milchtaich

2006

Lecture Notes in Computer Science

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Abstract. An open problem is presented regarding the existence of pure strategy Nash equilibrium (PNE) in network congestion games with a finite number of non-identical players, in which the strategy set of each player is the collection of all paths in a given network that link the player's origin and destination vertices, and congestion increases the costs of edges. A network congestion game in which the players differ only in their origin-destination pairs is a potential game, which implies that, regardless of the exact functional form of the cost functions, it has a PNE. A PNE does not necessarily exist if (i) the dependence of the cost of each edge on the number of users is player-as well as edgespecific or (ii) the (possibly, edge-specific) cost is the same for all players but it is a function (not of the number but) of the total weight of the players using the edge, with each player i having a different weight w i . In a parallel two-terminal network, in which the origin and the destination are the only vertices different edges have in common, a PNE always exists even if the players differ in either their cost functions or weights, but not in both. However, for general twoterminal networks this is not so. The problem is to characterize the class of all two-terminal network topologies for which the existence of a PNE is guaranteed even with player-specific costs, and the corresponding class for player-specific weights. Some progress in solving this problem is reported.

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Network topology and the efficiency of equilibrium

Cited by 93 publications

References 20 publications

Weighted congestion games with separable preferences

Weighted congestion games with separable preferences

Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

The Equilibrium Existence Problem in Finite Network Congestion Games

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