Crowding games are sequentially solvable
International Journal of Game Theory
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Performance Guarantees of Local Search for Multiprocessor Scheduling
INFORMS Journal on Computing
Strong equilibrium in cost sharing connection games
Proceedings of the 8th ACM conference on Electronic commerce
Network formation games with local coalitions
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the value of coordination in network design
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Approximate strong equilibrium in job scheduling games
Journal of Artificial Intelligence Research
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the price of anarchy and stability of correlated equilibria of linear congestion games,,
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Strong price of anarchy for machine load balancing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Pareto efficiency and approximate pareto efficiency in routing and load balancing games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Theoretical Computer Science
Future Generation Computer Systems
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A Nash Equilibriun (NE) is a strategy profile that is resilientto unilateral deviations, and is predominantly used in analysis ofcompetitive games. A downside of NE is that it is not necessarilystable against deviations by coalitions. Yet, as we show in thispaper, in some cases, NE does exhibit stability against coalitionaldeviations, in that the benefits from a joint deviation arebounded. In this sense, NE approximates strong equilibrium(SE) [6].We provide a framework for quantifying the stability and theperformance of various assignment policies and solution concept inthe face of coalitional deviations. Within this framework weevaluate a given configuration according to three measurements: (i)IRmin: the maximal number α,such that there exists a coalition in which the minimum improvementratio among the coalition members is α(ii) IRmax: the maximum improvement ratio among thecoalition's members. (iii) DRmax: themaximum possible damage ratio of an agent outside thecoalition.This framework can be used to study the proximity betweendifferent solution concepts, as well as to study the existence ofapproximate SE in settings that do not possess any suchequilibrium. We analyze these measurements in job scheduling gameson identical machines. In particular, we provide upper and lowerbounds for the above three measurements for both NE and thewell-known assignment rule Longest Processing Time(LPT)(which is known to yield a NE). Most of our bounds are tight forany number of machines, while some are tight only for threemachines. We show that both NE and LPT configurations yield smallconstant bounds for IRminand DRmax. As for IRmax, itcan be arbitrarily large for NE configurations, while a small boundis guaranteed for LPT configurations. For all three measurements,LPT performs strictly better than NE.With respect to computational complexity aspects, we show thatgiven a NE on m≥ 3 identical machines and a coalition,it is NP-hard to determine whether the coalition can deviate suchthat every member decreases its cost. For the unrelated machinessettings, the above hardness result holds already for m≥2 machines.