the date of receipt and acceptance should be inserted later Abstract We present efficient algorithms for computing approximate Wardrop equilibria in a distributed and concurrent fashion. Our algorithms are exexuted by a finite number of agents each of which controls the flow of one commodity striving to balance the induced latency over all utilised paths. The set of allowed paths is represented by a DAG. Our algorithms are based on previous work on policies for infinite populations of agents. These policies achieve a convergence time which is independent of the underlying network and depends mildly on the latency functions. These policies can neither be applied to a finite set of agents nor can they be simulated directly due to the exponential number of paths. Our algorithms circumvent these problems by computing a randomised path decomposition in every communication round. Based on this decomposition, flow is shifted from overloaded to underloaded paths. This way, our algorithm can handle exponentially large path collections in polynomial time. Our algorithms are stateless, and the number of communication rounds depends polynomially on the approximation quality and is independent of the topology and size of the network.

It is known that the dynamics of best response in an environment of non-cooperative users may converge to a good solution when users play sequentially, but may cycle far away from the global optimum solution when users play concurrently. We introduce the notion of bounded best response where users react with best response subject to rules that are forced locally by the system. We investigate the problem of load balancing tasks on machines in a bipartite graph model and show that the dynamics of concurrent bounded best response converges to a near-optimum solution quickly, i.e., with poly-logarithmic number of rounds. This is in contrast to the concurrent best response dynamics which cycles far away from the optimum and to any sequential dynamics which requires at least a linear number of rounds to get to a reasonable solution. 1

Abstract. We study the efficiency of selfish routing problems in which traffic demands are revealed online. We go beyond the common Nash equilibrium concept in which possibly all players reroute their flow and form a new equilibrium upon arrival of a new demand. In our model, demands arrive in n sequential games. In each game, the new demands form a Nash equilibrium and their routings remain unchanged afterwards. We study the problem both with nonatomic and atomic player types and with continuous and nondecreasing latency functions on the edges. For polynomial latency functions, we give constant upper and lower bounds on the competitive ratio of the resulting online routing in terms of the maximum degree, the number of games and in the atomic setting the number of players. In particular, for nonatomic players and affine latency functions we show that the competitive ratio is at most 4n. Finally, we present improved upper bounds for the special n+2 case of two nodes connected by parallel arcs. 1

Abstract — The problem of channel allocation has been extensively studied in the context of cellular networks. There is a substantial amount of work in the field of dynamic frequency assignment for WLANs and mesh networks as well. The growing interest in the cognitive radio technology and its capability to offer more efficient spectrum usage brought this problem back as one of the most popular research topics nowadays. In this paper we present two quite simple to implement, distributed algorithms for selecting channels, in cognitive radio environment, so that the load is distributed (smoothed) over them. I.

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Computer systems increasingly involve the interaction of multiple self-interested agents. The designers of these systems have objectives they wish to optimize, but by allowing selfish agents to interact in the system, they lose the ability to directly control behavior. What is lost by this lack of centralized control? What are the likely outcomes of selfish behavior? In this work, we consider learning dynamics as a tool for better classifying and understanding outcomes of selfish behavior in games. In particular, when such learning algorithms exist and are efficient, we propose “regret-minimization” as a criterion for self-interested behavior and study the system-wide effects in broad classes of games when players achieve this criterion. In addition, we present a general transformation from offline approximation algorithms for linear optimization problems to online algorithms that achieve low regret.

Abstract—The rise of distributed services and user-driven networking concepts in recent years poses the critical question of stability. Can a system operating under non-cooperation and self-interest converge to a stable state? and how fast? The answers to these questions readily lend themselves to game theory analysis, and to the study of congestion games in particular. In the past, much work have been done on establishing the existence of pure Nash equilibria in congestion games, and has shown that finding a pure Nash equilibrium is PLS-complete [1] and hence convergence to a pure Nash equilibrium is very difficult (exponential time in worst case). Furthermore, much of the convergence analysis have been carried out on simple single-commodity game models. In this paper, we attempt to construct a more realistic multi-commodity congestion game model suited for distributed service and user-driven networking scenarios. We introduce the desirability of equilibrium concept that is helpful in determining whether a system state meets the quality requirements of the users and services. Desirability is an alternative concept to price of anarchy. In fact we show the desirability ratio is a special case of price of anarchy. We then define the α-threshold congestion game whose minimum potential state corresponds to a desirable equilibrium (if the system permits one) and we bound its convergence to polynomial time through game transformation. Finally, we present a mechanism for partial simultaneous moves. To the best of our knowledge, there has been no prior establishment of the desirability concept and no bound given on the convergence of asymmetric multi-commodity congestion games with exponential cost function. Index Terms—Game theory, stability, convergence I.