We investigate the class of so-called

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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 that 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 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 PLS-completeness of network congestion games. In particular, we show that network congestion games are PLS-complete for directed and undirected networks even in case of linear latency functions.

We study the problem of traffic routing in noncooperative networks. In such networks, users may follow selfish strategies to optimize their own performance measure and therefore, their behavior does not have to lead to optimal performance of the entire network. In this article we investigate the worst-case coordination ratio, which is a game-theoretic measure aiming to reflect the price of selfish routing.Following a line of previous work, we focus on the most basic networks consisting of parallel links with linear latency functions. Our main result is that the worst-case coordination ratio on m parallel links of possibly different speeds is log m log log log m .In fact, we are able to give an exact description of the worst-case coordination ratio, depending on the number of links and ratio of speed of the fastest link over the speed of the slowest link. For example, for the special case in which all m parallel links have the same speed, we can prove that the worst-case coordination ratio is (−1) (m) + (1), with denoting the Gamma (factorial) function. Our bounds entirely resolve an open problem posed recently by Koutsoupias and Papadimitriou [1999].

This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multi-parameter agents. We focus on approximation algorithms for NP-hard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques.Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone FPTAS. This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for single-minded multi-unit auctions. The best previous result for such auctions was a 2-approximation. In addition, we present a monotone PTAS for the generalized assignment problem with any bounded number of parameters per agent.The most efficient way to solve packing integer programs (PIPs) is LP-based randomized rounding, which also is in general not monotone. We show that primal-dual greedy algorithms achieve almost the same approximation ratios for PIPs as randomized rounding. The advantage is that these algorithms are inherently monotone. This way, we can significantly improve the approximation ratios of truthful mechanisms for various fundamental mechanism design problems like single-minded combinatorial auctions (CAs), unsplittable flow routing and multicast routing. Our approximation algorithms can also be used for the winner determination in CAs with general bidders specifying their bids through an oracle. *