Abstract
The objective of this paper is three-fold. First, we specify what it means for a fixed point of a stabilizing distributed system to be a Nash equilibrium. Second, we present methods that can be used to verify whether or not a given fixed point of a given stabilizing distributed system is a Nash equilibrium. Third, we argue that in a stabilizing distributed system, whose fixed points are all Nash equilibria, no process has an incentive to perturb its local state, after the system reaches one fixed point, in order to force the system to reach another fixed point where the perturbing process achieves a better gain. If the fixed points of a stabilizing distributed system are all Nash equilibria, then we refer to the system as perturbation-proof. Otherwise, we refer to the system as perturbation-prone. We identify four natural classes of perturbation-(proof/prone) systems. We present system examples for three of these classes of systems, and show that the fourth class is empty.
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Nash, J.F.: Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 36, 48–49 (1950)
Flood, M.M.: Some experimental games. Management Science 5, 5–26 (1958)
Bhattacharya, A., Ghosh, S.: Self-optimizing peer-to-peer networks with selfish processes. In: Proceedings of the First International Conference on Self-Adaptive and Self-Organizing Systems, pp. 340–343 (2007)
Cohen, J., Dasgupta, A., Ghosh, S., Tixeuil, S.: An exercise in selfish stabilization. ACM Trans. Auton. Adapt. Syst. 3, 1–12 (2008)
Arora, A., Gouda, M.: Closure and convergence: A foundation for fault-tolerant computing. IEEE Transactions on Computers 19, 1015–1027 (1993)
Abraham, I., Dolev, D., Gonen, R., Halpern, J.: Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In: Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing, pp. 53–62. ACM, New York (2006)
Abraham, I., Dolev, D., Halpern, J.: Lower bounds on implementing robust and resilient mediators. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 302–319. Springer, Heidelberg (2008)
Halpern, J.Y.: Beyond nash equilibrium: Solution concepts for the 21st century. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, p. 1. Springer, Heidelberg (2008)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17, 643–644 (1974)
Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)
Gouda, M.G.: The triumph and tribulation of system stabilization. In: Helary, J.-M., Raynal, M. (eds.) WDAG 1995. LNCS, vol. 972, pp. 1–18. Springer, Heidelberg (1995)
Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks. In: Proceedings of the 17th International Symposium on Parallel and Distributed Processing, Washington, DC, USA, p. 162.2. IEEE Computer Society, Los Alamitos (2003)
Huang, S.T., Hung, S.S., Tzeng, C.H.: Self-stabilizing coloration in anonymous planar networks. Information Processing Letters 95, 307–312 (2005)
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Gouda, M.G., Acharya, H.B. (2009). Nash Equilibria in Stabilizing Systems. In: Guerraoui, R., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2009. Lecture Notes in Computer Science, vol 5873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05118-0_22
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DOI: https://doi.org/10.1007/978-3-642-05118-0_22
Publisher Name: Springer, Berlin, Heidelberg
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