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On the impact of combinatorial structure on congestion games
 in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS
"... We study the impact of combinatorial structure in congestion games on the complexity of computing pure Nash equilibria and the convergence time of best response sequences. In particular, we investigate which properties of the strategy spaces of individual players ensure a polynomial convergence time ..."
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We study the impact of combinatorial structure in congestion games on the complexity of computing pure Nash equilibria and the convergence time of best response sequences. In particular, we investigate which properties of the strategy spaces of individual players ensure a polynomial convergence time. We show, if the strategy space of each player consists of the bases of a matroid over the set of resources, then the lengths of all best response sequences are polynomially bounded in the number of players and resources. We can also prove that this result is tight, that is, the matroid property is a necessary and sufficient condition on the players ’ strategy spaces for guaranteeing polynomial time convergence to a Nash equilibrium. In addition, we present an approach that enables us to devise hardness proofs for various kinds of combinatorial games, including first results about the hardness of market sharing games and congestion games for overlay network design. Our approach also yields a short proof for the PLScompleteness of network congestion games. 1
On the Complexity of PureStrategy Nash Equilibria in Congestion and LocalEffect Games
 In Proc. of the 2nd Int. Workshop on Internet and Network Economics (WINE
, 2006
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Uncoordinated TwoSided Matching Markets
 EC'08
, 2008
"... Various economic interactions can be modeled as twosided markets. A central solution concept to these markets are stable matchings, introduced by Gale and Shapley. It is well known that stable matchings can be computed in polynomial time, but many reallife markets lack a central authority to match ..."
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Cited by 14 (0 self)
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Various economic interactions can be modeled as twosided markets. A central solution concept to these markets are stable matchings, introduced by Gale and Shapley. It is well known that stable matchings can be computed in polynomial time, but many reallife markets lack a central authority to match agents. In those markets, matchings are formed by actions of selfinterested agents. Knuth introduced uncoordinated twosided markets and showed that the uncoordinated better response dynamics may cycle. However, Roth and Vande Vate showed that the random better response dynamics converges to a stable matching with probability one, but did not address the question of convergence time. In this paper, we give an exponential lower bound for the convergence time of the random better response dynamics in twosided markets. We also extend the results for the better response dynamics to the best response dynamics, i.e., we present a cycle of best responses, and prove that the random best response dynamics converges to a stable matching with probability one, but its convergence time is exponential. Additionally, we identify the special class of correlated matroid twosided markets with reallife applications for which we prove that the random best response dynamics converges in expected polynomial time.
The robust price of anarchy of altruistic games
 In Proc. 7th Workshop on Internet and Network Economics (WINE
, 2011
"... We study the inefficiency of equilibria for several classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i’s perceived cost is a convex combination of 1−αi times his direct cost and αi times the social cost. Tuning the parameters αi allows sm ..."
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Cited by 14 (3 self)
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We study the inefficiency of equilibria for several classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i’s perceived cost is a convex combination of 1−αi times his direct cost and αi times the social cost. Tuning the parameters αi allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study altruistic extensions of costsharing games, utility games, and linear congestion games. Our main contribution is an adaptation of Roughgarden’s smoothness notion to altruistic extensions of games. We show that this extension captures the essential properties to determine the robust price of anarchy of these games, and use it to derive mostly tight bounds. For congestion games and costsharing games, the worstcase robust price of anarchy increases with increasing altruism, while for utility games, it remains constant and is not affected by altruism. However, the increase in the price of anarchy is not a universal phenomenon: for symmetric singleton linear congestion games, the pure price of anarchy decreases both under increasing uniform altruism and as the fraction of entirely altruistic individuals increases.
Strong nash equilibria in games with the lexicographical improvement property
 Internet and Network Economics
, 2009
"... Abstract. We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Le ..."
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Cited by 11 (2 self)
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Abstract. We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Lexicographical Improvement Property (LIP) and show that it implies the existence of a generalized strong ordinal potential function. We use this characterization to derive existence, efficiency and fairness properties of strong Nash equilibria. We then study a class of games that generalizes congestion games with bottleneck objectives that we call bottleneck congestion games. We show that these games possess the LIP and thus the above mentioned properties. For bottleneck congestion games in networks, we identify cases in which the potential function associated with the LIP leads to polynomial time algorithms computing a strong Nash equilibrium. Finally, we investigate the LIP for infinite games. We show that the LIP does not imply the existence of a generalized strong ordinal potential, thus, the existence of SNE does not follow. Assuming that the function associated with the LIP is continuous, however, we prove existence of SNE. As a consequence, we prove that bottleneck congestion games with infinite strategy spaces and continuous cost functions possess a strong Nash equilibrium. 1
Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy
 Theory of Computing Systems
, 2010
"... 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 extensionparallel networks, an interesting class of netw ..."
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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 extensionparallel networks, an interesting class of networks with linearly independent paths, and establish two remarkable properties previously known only for parallellink games. More precisely, we show that for arbitrary (nonnegative and nondecreasing) 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 byproduct 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).
Characterizing the existence of potential functions in weighted congestion games
 Proc. 2nd Internat. Sympos. Algorithmic Game Theory, volume 5814 of LNCS, pages 97 – 108
, 2009
"... Abstract Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let C be an arbitrary set of locally bounded functions and let G(C) be the ..."
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Abstract Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let C be an arbitrary set of locally bounded functions and let G(C) be the set of weighted congestion games with cost functions in C. We show that every weighted congestion game G ∈ G(C) admits an exact potential if and only if C contains only affine functions. We also give a similar characterization for wpotentials with the difference that here C consists either of affine functions or of certain exponential functions. We finally extend our characterizations to weighted congestion games with facilitydependent demands and elastic demands, respectively.
Congestion games with loaddependent failures: identical resources
 In Proceedings of the 8th ACM Conference on Electronic Commerce (EC07
, 2007
"... We define a new class of games, congestion games with loaddependent failures (CGLFs), which generalizes the wellknown class of congestion games, by incorporating the issue of resource failures into congestion games. In a CGLF, agents share a common set of resources, where each resource has a cost a ..."
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Cited by 8 (6 self)
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We define a new class of games, congestion games with loaddependent failures (CGLFs), which generalizes the wellknown class of congestion games, by incorporating the issue of resource failures into congestion games. In a CGLF, agents share a common set of resources, where each resource has a cost and a probability of failure. Each agent chooses a subset of the resources for the execution of his task, in order to maximize his own utility. The utility of an agent is the difference between his benefit from successful task completion and the sum of the costs over the resources he uses. CGLFs possess two novel features. It is the first model to incorporate failures into congestion settings, which results in a strict generalization of congestion games. In addition, it is the first model to consider loaddependent failures in such framework, where the failure probability of each resource depends on the number of agents selecting this resource. Although, as we show, CGLFs do not admit a potential function, and in general do not have a pure strategy Nash equilibrium, our main theorem proves the existence of a pure strategy Nash equilibrium in every CGLF with identical resources and nondecreasing cost functions.
A Unified Approach to Congestion Games and TwoSided Markets
 In Proceedings of the 3nd International Workshop on Internet and Network Economics (WINE 2007
, 2007
"... Congestion games are a wellstudied model for resource sharing among uncoordinated selfish agents. Usually, one assumes that the resources in a congestion game do not have any preferences over the players that can allocate them. In typical load balancing applications, however, different jobs can hav ..."
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Cited by 8 (5 self)
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Congestion games are a wellstudied model for resource sharing among uncoordinated selfish agents. Usually, one assumes that the resources in a congestion game do not have any preferences over the players that can allocate them. In typical load balancing applications, however, different jobs can have different priorities, and jobs with higher priorities get, for example, larger shares of the processor time. We introduce a model in which each resource can assign priorities to the players and players with higher priorities can displace players with lower priorities. Our model does not only extend standard congestion games, but it can also be seen as a model of twosided markets with ties. We prove that singleton congestion games with priorities are potential games, and we show that every playerspecific singleton congestion game with priorities possesses a pure Nash equilibrium that can be found in polynomial time. Finally, we extend our results to matroid congestion games, in which the strategy space of each player consists of the bases of a matroid over the resources.
On the complexity of pure Nash equilibria in playerspecific network congestion games
 Internet and Network Economics, Lecture Notes in Computer Science
, 2007
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