@MISC{Jong_thesequential, author = {Jasper De Jong and Marc Uetz}, title = {The Sequential Price Of Anarchy for Atomic Congestion Games}, year = {} }

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Abstract

Abstract. In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, we consider games where players choose their actions sequentially. The sequential price of anarchy, recently introduced by Paes Leme, Syrgkanis, and Tardos Model and Notation We consider atomic congestion games with affine cost functions. The input of an instance I ∈ I consists of a finite set of resources R, a finite set of players N = {1, . . . , n}, and for each player i ∈ N a collection A i of possible actions A i ⊆ R. We say a resource r ∈ R is chosen by player i if r ∈ A i , where A i is the action chosen by player i. By A = (A i ) i∈N we denote a possible outcome, that is, a complete profile of actions chosen by all players i ∈ N . Each resource r ∈ R has a constant activation cost d r ≥ 0 and a variable cost or weight w r ≥ 0 that expresses the fact that the resource gets more congested the more players choose it. The total cost of resource r ∈ R, for outcome A, is then f r (A) = d r +w r ·n r (A), where n r (A) denotes the number of players choosing resource r in A. Given outcome A, the total cost of all resources chosen by player i is cost i (A) = r∈Ai f r (A). Players aim to minimize their costs. The total cost over all players of an outcome A is denoted by cost(A) = i∈N cost i (A). Note that this class of problems includes as a special case the celebrated network routing games as studied e.g. in Research supported by CTIT (www.ctit.nl) and 3TU.AMI (www.3tu.nl), project "Mechanisms for Decentralized Service Systems".