TY - JOUR
T1 - Strong price of anarchy
AU - Andelman, Nir
AU - Feldman, Michal
AU - Mansour, Yishay
N1 - Funding Information:
Keywords: Strong equilibrium; Price of anarchy; Strong price of anarchy; Coalitions; Congestion games; Network formation; Job scheduling ✩ This work was supported in part by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778, by a Grant No. 1079/04 from the Israel Science Foundation, by a grant from BSF and an IBM faculty award. The second author is also supported by the Lady Davis Fellowship Trust. This publication only reflects the authors’ views. * Corresponding author. E-mail addresses: [email protected] (N. Andelman), [email protected] (M. Feldman), [email protected] (Y. Mansour). 1 The research was partially done when the author was at the School of Computer Science at the Hebrew University of Jerusalem.
PY - 2009/3
Y1 - 2009/3
N2 - A strong equilibrium is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy (SPoA) to be the ratio of the worst strong equilibrium to the social optimum. Differently from the Price of Anarchy (defined as the ratio of the worst Nash Equilibrium to the social optimum), it quantifies the loss incurred from the lack of a central designer in settings that allow for coordination. We study the SPoA in two settings, namely job scheduling and network creation. In the job scheduling game we show that for unrelated machines the SPoA can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the SPoA is at most 2. In both cases we show that a strong equilibrium always exists, except for a well defined subset of network creation games.
AB - A strong equilibrium is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy (SPoA) to be the ratio of the worst strong equilibrium to the social optimum. Differently from the Price of Anarchy (defined as the ratio of the worst Nash Equilibrium to the social optimum), it quantifies the loss incurred from the lack of a central designer in settings that allow for coordination. We study the SPoA in two settings, namely job scheduling and network creation. In the job scheduling game we show that for unrelated machines the SPoA can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the SPoA is at most 2. In both cases we show that a strong equilibrium always exists, except for a well defined subset of network creation games.
KW - Coalitions
KW - Congestion games
KW - Job scheduling
KW - Network formation
KW - Price of anarchy
KW - Strong equilibrium
KW - Strong price of anarchy
UR - http://www.scopus.com/inward/record.url?scp=59249097473&partnerID=8YFLogxK
U2 - 10.1016/j.geb.2008.03.005
DO - 10.1016/j.geb.2008.03.005
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AN - SCOPUS:59249097473
SN - 0899-8256
VL - 65
SP - 289
EP - 317
JO - Games and Economic Behavior
JF - Games and Economic Behavior
IS - 2
ER -