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Weighted congestion games: Price of anarchy, universal worstcase examples, and tightness
 In Proceedings of the 18th Annual European Symposium on Algorithms (ESA
, 2010
"... Abstract. We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (co ..."
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Abstract. We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost functionindependent) worstcase examples. One noteworthy byproduct of our proofs is the fact that weighted congestion games are “tight”, which implies that the worstcase price of anarchy with respect to pure Nash, mixed Nash, correlated, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worstcase POA, at least for polynomial cost functions. We also prove a new result about unweighted congestion games: the worstcase price of anarchy in symmetric games is, as the number of players goes to infinity, as large as in their more general asymmetric counterparts. 1
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.
Social Context in Potential Games
"... Abstract. A prevalent assumption in game theory is that all players act in a purely selfish manner, but this assumption has been repeatedly questioned by economists and social scientists. In this paper, we study a model that allows to incorporate the social context of players into their decision mak ..."
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Cited by 4 (1 self)
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Abstract. A prevalent assumption in game theory is that all players act in a purely selfish manner, but this assumption has been repeatedly questioned by economists and social scientists. In this paper, we study a model that allows to incorporate the social context of players into their decision making. We consider the impact of otherregarding preferences in potential games, one of the most popular and central classes of games in algorithmic game theory. Our results concern the existence of pure Nash equilibria and potential functions in games with social context. The main finding is a tight characterization of the class of potential games that admit exact potential functions for any social context. In addition, we prove complexity results on deciding existence of pure Nash equilibria in numerous popular classes of potential games, such as different classes of load balancing, congestion, cost and market sharing games. 1
Restoring Pure Equilibria to Weighted Congestion Games
"... Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on s ..."
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Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on sharing costs proportional to players’ weights do not generally have purestrategy Nash equilibria. We propose a new way of assigning costs to players with weights in congestion games that recovers the important properties of the unweighted model. This method is derived from the Shapley value, and it always induces a game with a (weighted) potential function. For the special cases of weighted network costsharing and atomic selfish routing games (with Shapley valuebased cost shares), we prove tight bounds on the price of stability and price of anarchy, respectively.
Stochastic Congestion Games with RiskAverse Players?
"... Abstract. Congestion games ignore the stochastic nature of resource delays and the riskaverse attitude of the players to uncertainty. To take these aspects into account, we introduce two variants of atomic congestion games, one with stochastic players, where each player assigns load to her strate ..."
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Abstract. Congestion games ignore the stochastic nature of resource delays and the riskaverse attitude of the players to uncertainty. To take these aspects into account, we introduce two variants of atomic congestion games, one with stochastic players, where each player assigns load to her strategy independently with a given probability, and another with stochastic edges, where the latency functions are random. In both variants, the players are riskaverse, and their individual cost is a playerspecific quantile of their delay distribution. We focus on parallellink networks and investigate how the main properties of such games depend on the risk attitude and on the participation probabilities of the players. In a nutshell, we prove that stochastic congestion games on parallellinks admit an efficiently computable pure Nash equilibrium if the players have either the same risk attitude or the same participation probabilities, and also admit a potential function if the players have the same risk attitude. On the negative side, we present examples of stochastic games with players of different risk attitudes that do not admit a potential function. As for the inefficiency of equilibria, for parallellink networks with linear delays, we prove that the Price of Anarchy is Θ(n), where n is the number of stochastic players, and may be unbounded, in case of stochastic edges. 1
Collusion in Atomic Splittable Routing Games
"... We investigate how collusion affects the social cost in atomic splittable routing games. Suppose that players form coalitions and each coalition behaves as if it were a single player controlling all the flows of its participants. It may be tempting to conjecture that the social cost would be lower ..."
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We investigate how collusion affects the social cost in atomic splittable routing games. Suppose that players form coalitions and each coalition behaves as if it were a single player controlling all the flows of its participants. It may be tempting to conjecture that the social cost would be lower after collusion, since there would be more coordination among the players. We construct examples to show that this conjecture is not true. Even in very simple singlesourcesingledestination networks, the social cost of the postcollusion equilibrium can be higher than that of the precollusion equilibrium. This counterintuitive phenomenon of collusion prompts us to ask the question: under what conditions would the social cost of the postcollusion equilibrium be bounded by the social cost of the precollusion equilibrium? We show that if (i) the network is “welldesigned ” (satisfying a natural condition), and (ii) the delay functions are affine, then collusion is always beneficial for the social cost in the Nash equilibria. On the other hand, if either of the above conditions is unsatisfied, collusion can worsen the social cost. Our main technique is a novel flowaugmenting algorithm to build Nash equilibria. Our positive result for collusion is obtained by applying this algorithm simultaneously to two different flow value profiles of players and observing the difference in the derivatives of their social costs. Moreover, for a nontrivial subclass of selfish routing games, this algorithm finds the exact Nash equilibrium in polynomial time.
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"... Abstract. We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (c ..."
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Abstract. We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost functionindependent) worstcase examples. One noteworthy byproduct of our proofs is the fact that weighted congestion games are "tight", which implies that the worstcase price of anarchy with respect to pure Nash, mixed Nash, correlated, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worstcase POA, at least for polynomial cost functions. We also prove a new result about unweighted congestion games: the worstcase price of anarchy in symmetric games is, as the number of players goes to infinity, as large as in their more general asymmetric counterparts.
unknown title
"... The concavity of atomic splittable congestion games with nonlinear utility functions DARRELL HOY, Northwestern University Classical work in network congestion games assumes networks are deterministic and agents are riskneutral. In many settings, this is unrealistic and players have more complicate ..."
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The concavity of atomic splittable congestion games with nonlinear utility functions DARRELL HOY, Northwestern University Classical work in network congestion games assumes networks are deterministic and agents are riskneutral. In many settings, this is unrealistic and players have more complicated preferences. When driving to work in the morning, a commuter may prefer a safer route, rather than the faster but riskier route. A website sending out streaming video packets may not care about packets once they are late or derive much benefit from packets arriving much earlier, but would rather prefer a more consistent delivery model. We consider the atomicsplittable setting and model these preferences in two ways: when players have nonlinear preferences over (i) the delay on every path, and (ii) on the total delay they experience over all paths. We ask when are these games concave? In the riskneutral setting, the concavity of the setting underlies many results, including the existence of pure Nash equilibria. In setting (ii), when players have preferences over the total cost seen, the game is concave and pure Nash equilibria will always exist. In setting (i) however, we show that the game is no longer concave, and as a result we no longer know if pure Nash equilibria always exist. In both of these settings, we show that we can reduce questions about them in the stochastic setting to questions about them in the deterministic setting. 1.