Keywords and Synonyms
Load balancing game ; Incentive compatible algorithms; Nashification ; Convergence of Nash dynamics
Problem Definition
This problem concerns the construction of pure Nash equilibria (PNE) in a special class of atomic congestion games, known as the Parallel Links Game (PLG). The purpose of this note is to gather recent advances in the existence and tractability of PNE in PLG.
The Pure Parallel Links Game. Let \( { N\equiv[n] } \) Footnote 1 be a set of (selfish) players, each of them willing to have her good served by a unique shared resource (link) of a system. Let \( { E=[m] } \) be the set of all these links. For each link \( { e\in E } \), and each player \( { i\in N } \),let \( { D_{i,e}(\cdot): \mathbb{R}_{\geq 0} \mapsto \mathbb{R}_{\geq 0} } \) be the charging mechanism according to which link e charges player i for using it. Each player \( { i\in[n] } \) comes with a service requirement (e. g. , traffic demand, or processing time) \( { W[i,e] > 0 } \), if...
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- 1.
\( { \forall k\in \mathbb{N},\:[k]\equiv\{1,2,\dots,k\} } \).
Recommended Reading
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Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence time to nash equilibria. In: Proc. of the 30th Int. Col. on Aut., Lang. and Progr. (ICALP '03). LNCS, pp. 502–513. Springer, Eindhoven (2003)
Even-Dar, E., Mansour, Y.: Fast convergence of selfish rerouting. In: Proc. of the 16th ACM-SIAM Symp. on Discr. Alg. (SODA '05), SIAM, pp. 772–781. SIAM, Vancouver (2005)
Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure nash equilibria. In: Proc. of the 36th ACM Symp. on Th. of Comp. (STOC '04). ACM, Chicago (2004)
Feldmann, R., Gairing, M., Lücking, T., Monien, B., Rode, M.: Nashification and the coordination ratio for a selfish routing game. In: Proc. of the 30th Int. Col. on Aut., Lang. and Progr. (ICALP '03). LNCS, pp. 514–526. Springer, Eindhoven (2003)
Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: The structure and complexity of nash equilibria for a selfish routing game. In: Proc. of the 29th Int. Col. on Aut., Lang. and Progr. (ICALP '02). LNCS, pp. 123–134. Springer, Málaga (2002)
Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish unsplittable flows. Theor. Comput. Sci. 348, 226–239 (2005) Special Issue dedicated to ICALP (2004) (TRACK-A)
Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic congestion games among coalitions. In: Proc. of the 33rd Int. Col. on Aut., Lang. and Progr. (ICALP '06). LNCS, vol. 4051, pp. 572–583. Springer, Venice (2006)
Gairing, M., Luecking, T., Mavronicolas, M., Monien, B.: The price of anarchy for restricted parallel links. Parallel Process. Lett. 16, 117–131 (2006) Preliminary version appeared in STOC 2004
Gairing, M., Monien, B., Tiemann, K.: Routing (un-)splittable flow in games with player specific linear latency functions. In: Proc. of the 33rd Int. Col. on Aut., Lang. and Progr. (ICALP '06). LNCS, pp. 501–512. Springer, Venice (2006)
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Kontogiannis, S. (2008). Computing Pure Equilibria in the Game of Parallel Links. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_87
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DOI: https://doi.org/10.1007/978-0-387-30162-4_87
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