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Optimal coordination mechanisms for multijob scheduling games
 IN 22ND ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2014
"... We consider the unrelated machine scheduling game in which players control subsets of jobs. Each player’s objective is to minimize the weighted sum of completion time of her jobs, while the social cost is the sum of players ’ costs. The goal is to design simple processing policies in the machines ..."
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We consider the unrelated machine scheduling game in which players control subsets of jobs. Each player’s objective is to minimize the weighted sum of completion time of her jobs, while the social cost is the sum of players ’ costs. The goal is to design simple processing policies in the machines with small coordination ratio, i.e., the implied equilibria are within a small factor of the optimal schedule. We work with a weaker equilibrium concept that includes that of Nash. We first prove that if machines order jobs according to their processing time to weight ratio, a.k.a. Smithrule, then the coordination ratio is at most 4, moreover this is best possible among nonpreemptive policies. Then we establish our main result. We design a preemptive policy, externality, that extends Smithrule by adding extra delays on the jobs accounting for the negative externality they impose on other players. For this policy we prove that the coordination ratio is 1 +φ ≈ 2.618, and complement this result by proving that this ratio is best possible even if we allow for randomization or full information. Finally, we establish that this externality policy induces a potential game and that an εequilibrium can be found in polynomial time. An interesting consequence of our results is that an ε−local optima of R  ∑wjCj for the jump (a.k.a. move) neighborhood can be found in polynomial time and are within a factor of 2.618 of the optimal solution. The latter constitutes the first direct application of purely gametheoretic ideas to the analysis of a well studied local search heuristic.
Altruism and Its Impact on the Price of Anarchy
, 2014
"... We study the inefficiency of equilibria for congestion 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 int ..."
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We study the inefficiency of equilibria for congestion 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 primarily altruistic extensions of (atomic and nonatomic) congestion games, but also obtain some results on fair costsharing games and valid utility games. We derive (tight) bounds on the price of anarchy of these games for several solution concepts. Thereto, we suitably adapt the smoothness notion introduced by Roughgarden and show that it captures the essential properties to determine the robust price of anarchy of these games. Our bounds show that for atomic congestion games and costsharing games, the robust price of anarchy gets worse with increasing altruism, while for valid 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 general nonatomic congestion games with uniform altruism, the price of anarchy improves with increasing altruism. For atomic and nonatomic symmetric singleton congestion games, we derive bounds on the pure price of anarchy that improve as the average level of altruism increases. (For atomic games, we only derive such bounds when cost