The price of stability in selfish scheduling games

Article type: Research Article

Authors: Agussurja, Lucas | Lau, Hoong Chuin^;

Affiliations: The Logistics Institute – Asia Pacific, National University of Singapore, 21 Heng Mui Keng Terrace #04-01, Singapore 119613 | School of Information Systems, Singapore Management University, 80 Stamford Road, Singapore 178902

Note: [] Corresponding author. E-mail: [email protected]

Abstract: Game theory has gained popularity as an approach to analysing and understanding distributed systems with self-interested agents. Central to game theory is the concept of Nash equilibrium as a stable state (solution) of the system, which comes with a price − the loss in efficiency. The quantification of the efficiency loss is one of the main research concerns. In this paper, we study the quality and computational characteristics of the best Nash equilibrium in two selfish scheduling models: the congestion model and the sequencing model. In particular, we present the following results: (1) In the congestion model: first, the best Nash equilibrium is socially optimum and consequently, computing the best Nash is NP-hard; second, any ε-approximation algorithm for finding the optimum can be transformed into an ε-approximation algorithm for the best Nash. (2) In sequencing model: for identical machines, we show that the best Nash is no better than the worst Nash and it is easy to compute; for related machines, we show that there is a gap between the worst and the best Nash equilibrium, and leave the analytical bound of this gap for future work.

Keywords: Price of stability, scheduling games

DOI: 10.3233/WIA-2009-0171

Journal: Web Intelligence and Agent Systems: An International Journal, vol. 7, no. 4, pp. 321-332, 2009