Stackelberg Strategies and Collusion in Network Games with Splittable Flow

Harks, Tobias

doi:10.1007/s00224-010-9269-4

Cited by 42 publications

(33 citation statements)

References 35 publications

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“…A celebrated result of Roughgarden [25], and Roughgarden and Tardos [30] gives tight bounds on the PoA for nonatomic routing games for the social welfare objective. Recently, similar results were obtained for the PoA in atomic splittable routing games [13,29].…”

Section: Related Worksupporting

confidence: 75%

Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions

Bhaskar

Ligett

Schulman

et al. 2014

2014 IEEE 55th Annual Symposium on Foundations of Computer Science

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The analysis of network routing games typically assumes, right at the onset, precise and detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as the equilibrium by suitably influencing player behavior in the routing game. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions.Our main result gives a crisp positive answer to this question. We show that, under fairly general settings, one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes candidate tolls as input and returns the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method. Our algorithm extends easily to many other settings, such as (i) when certain edges cannot be tolled or there is an upper bound on the total toll paid by a user, and (ii) general nonatomic congestion games. We obtain tighter bounds on the query complexity for series-parallel networks, and single-commodity routing games with linear latency functions, and complement these with a query-complexity lower bound. We also obtain strong positive results for Stackelberg routing to achieve target equilibria in series-parallel graphs.Our results build upon various new techniques that we develop pertaining to the computation of, and connections between, different notions of approximate equilibrium; properties of multicommodity flows and tolls in series-parallel graphs; and sensitivity of equilibrium flow with respect to tolls. Our results demonstrate that one can indeed circumvent the potentially-onerous task of modeling latency functions, and yet obtain meaningful results for the underlying routing game. *

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Section: Related Worksupporting

confidence: 75%

Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions

Bhaskar

Ligett

Schulman

et al. 2014

2014 IEEE 55th Annual Symposium on Foundations of Computer Science

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“…Very recently, Bonifaci et al [2010] showed that for general graphs, no Stackelberg strategy can reduce the price of anarchy to a constant depending only on α, for any α ∈ [0, 1), thus resolving one of the main questions left open by our work and Roughgarden [2004]. Finally, we note that Fotakis [2010] and Harks [2011] obtained some PoA bounds for Stackelberg strategies in atomic unsplittable congestion games, and atomic splittable routing games, respectively.…”

mentioning

confidence: 76%

“…Thus, in these settings, the PoA of the atomic splittable game is at most the PoA of the corresponding nonatomic game. Harks [2011] proved that the PoA with atomic splittable routing is at most m on a graph with m parallel links, and Bhaskar et al [2010] showed that this bound also holds for series-parallel graphs with m atomic players having the same source-sink pair. Awerbuch et al [2005] and Christodoulou and Koutsoupias [2005] provide PoA bounds for atomic, unsplittable routing games, and show that these can be worse than the PoA bounds in the nonatomic and atomic splittable setting.…”

mentioning

confidence: 94%

“…For atomic splittable routing, very recently, Cominetti et al [2009], Harks [2011], and Bhaskar et al [2010], all presented various bounds on the price of anarchy (with the latter two results appearing after the publication of the conference version of this article [Swamy 2007]). Cominetti et al [2009] showed that in a symmetric atomic game, that is, when all users control the same amount of flow and share the same source and sink, the cost of a Nash equilibrium is at most the cost of the Nash equilibrium in the corresponding nonatomic game.…”

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confidence: 98%

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The effectiveness of stackelberg strategies and tolls for network congestion games

Swamy

2012

ACM Trans. Algorithms

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It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this article, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, for example, network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy.For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs. (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled).(ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy. (iii) In parallellink graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most α + (1 − α) · ρ(L), where α is the fraction of flow controlled and ρ(L) is the PoA of class L (when α = 0).For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. This resolves a basic open question about the effectiveness of tolls for atomic splittable games. Furthermore, we give a complete characterization of flows that can be induced via tolls.

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“…For atomic splittable congestion games (cf. Bhaskar et al [5], Correa et al [14], Harks [24] and Schoppmann and Roughgarden [47]) it seems unclear whether or not similar results hold true.…”

Section: Discussionmentioning

confidence: 97%

Matroids Are Immune to Braess’ Paradox

Fujishige¹,

Goemans²,

Harks³

et al. 2017

Mathematics of OR

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The famous Braess paradox describes the counter-intuitive phenomenon in which, in certain settings, the increase of resources, like building a new road within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper, we consider general nonatomic congestion games and give a characterization of the combinatorial property of strategy spaces for which the Braess paradox does not occur. In short, matroid bases are precisely the required structure. We prove this characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest.

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Stackelberg Strategies and Collusion in Network Games with Splittable Flow

Cited by 42 publications

References 35 publications

Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions

Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions

The effectiveness of stackelberg strategies and tolls for network congestion games

Matroids Are Immune to Braess’ Paradox

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