Abstract
We consider network cost-sharing games with nonanonymous cost functions, where the cost of each edge is a submodular function of its users, and this cost is shared using the Shapley value. Nonanonymous cost functions model asymmetries between the players, which can arise from different bandwidth requirements, durations of use, services needed, and so on.
These games can possess multiple Nash equilibria of wildly varying quality. The goal of this article is to identify well-motivated equilibrium refinements that admit good worst-case approximation bounds. Our primary results are tight bounds on the cost of strong Nash equilibria and potential function minimizers in network cost-sharing games with nonanonymous cost functions, parameterized by the set C of allowable submodular cost functions.
These two worst-case bounds coincide for every set C, and equal the summability parameter introduced in Roughgarden and Sundararajan [2009] to characterize efficiency loss in a family of cost-sharing mechanisms. Thus, a single parameter simultaneously governs the worst-case inefficiency of network cost-sharing games (in two incomparable senses) and cost-sharing mechanisms. This parameter is always at most the kth Harmonic number Hk ≈ ln k, where k is the number of players, and is constant for many function classes of interest.
- S. Albers. 2009. On the value of coordination in network design. SIAM Journal on Computing 38, 6 (2009), 2273--2302. Google ScholarDigital Library
- E. Anshelevich, A. Dasgupta, J. Kleinberg, E. Tardos, T. Wexler, and T. Roughgarden. 2008a. The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38, 4 (2008), 1602--1623. Google ScholarDigital Library
- E. Anshelevich, A. Dasgupta, E. Tardos, and T. Wexler. 2008b. Near-optimal network design with selfish agents. Theory of Computing 4, 1 (2008), 77--109.Google ScholarCross Ref
- A. Asadpour and A. Saberi. 2009. On the inefficiency ratio of stable equilibria in congestion games. In Internet and Network Economics, Stefano Leonardi (Ed.). Springer, 545--552. Google ScholarDigital Library
- R. J. Aumann. 1959. Acceptable points in general cooperative n-person games. Contributions to the Theory of Games 4 (1959), 287--324.Google Scholar
- Y. Bachrach, V. Syrgkanis, É. Tardos, and M. Vojnovi. 2014. Strong price of anarchy, utility games and coalitional dynamics. In Algorithmic Game Theory, Ron Lavi (Ed.). Lecture Notes in Computer Science, Vol. 8768. Springer, Berlin, 218--230.Google Scholar
- V. Bilò and R. Bove. 2011. Bounds on the price of stability of undirected network design games with three players. Journal of Interconnection Networks 12, 01-02 (2011), 1--17.Google ScholarCross Ref
- V. Bilò, I. Caragiannis, A. Fanelli, and G. Monaco. 2013. Improved lower bounds on the price of stability of undirected network design games. Theory of Computing Systems 52, 4 (2013), 668--686. Google ScholarDigital Library
- V. Bilò, M. Flammini, G. Monaco, and L. Moscardelli. 2013. Some anomalies of farsighted strategic behavior. In Approximation and Online Algorithms. Vol. 7846. Springer, Berlin, 229--241.Google Scholar
- V. Bilò, M. Flammini, and L. Moscardelli. 2014. The price of stability for undirected broadcast network design with fair cost allocation is constant. Games and Economic Behavior (2014).Google Scholar
- L. E. Blume. 1993. The statistical mechanics of strategic interaction. Games and Economic Behavior 5, 3 (1993), 387--424.Google ScholarCross Ref
- M. Charikar, H. Karloff, C. Mathieu, J. Naor, and M. Saks. 2008. Online multicast with egalitarian cost sharing. In Parallelism in Algorithms and Architectures. ACM, 70--76. Google ScholarDigital Library
- C. Chekuri, J. Chuzhoy, L. Lewin-Eytan, J. Naor, and A. Orda. 2007. Non-cooperative multicast and facility location games. IEEE Journal on Selected Areas in Communications 25, 6 (2007), 1193--1206. Google ScholarDigital Library
- H. Chen and T. Roughgarden. 2009. Network design with weighted players. Theory of Computing Systems 45, 2 (2009), 302--324. Google ScholarDigital Library
- H. Chen, T. Roughgarden, and G. Valiant. 2010. Designing network protocols for good equilibria. SIAM Journal on Computing 39, 5 (2010), 1799--1832. Google ScholarDigital Library
- R. Chen and Y. Chen. 2011. The potential of social identity for equilibrium selection. American Economic Review 101, 6 (2011), 2562--2589.Google ScholarCross Ref
- S. Chien and A. Sinclair. 2009. Strong and Pareto price of anarchy in congestion games. In Automata, Languages and Programming. Springer, 279--291. Google ScholarDigital Library
- G. Christodoulou, C. Chung, K. Ligett, E. Pyrga, and R. van Stee. 2010. On the price of stability for undirected network design. In Approximation and Online Algorithms. Springer, 86--97. Google ScholarDigital Library
- G. Christodoulou and E. Koutsoupias. 2005. On the price of anarchy and stability of correlated equilibria of linear congestion games. In ESA, Lecture Notes in Computer Science, Vol. 3669, Springer, Berlin, 59--70. Google ScholarDigital Library
- A. Epstein, M. Feldman, and Y. Mansour. 2009. Strong equilibrium in cost sharing connection games. Games and Economic Behavior 67, 1 (2009), 51--68.Google ScholarCross Ref
- A. Fabrikant, A. Luthra, E. Maneva, C. Papadimitriou, and S. Shenker. 2003. On a network creation game. In Principles of Distributed Computing. ACM, 347--351. Google ScholarDigital Library
- A. Fiat, H. Kaplan, M. Levy, S. Olonetsky, and R. Shabo. 2006. On the price of stability for designing undirected networks with fair cost allocations. In Automata, Languages and Programming. Springer, 608--618. Google ScholarDigital Library
- R. Gopalakrishnan, J. R. Marden, and A. Wierman. 2013. Potential games are necessary to ensure pure Nash equilibria in cost sharing games. In Proceedings of the 14th ACM Conference on Electronic Commerce. ACM, 563--564. Google ScholarDigital Library
- S. Hart and A. Mas-Colell. 1989. Potential, value, and consistency. Econometrica: Journal of the Econometric Society (1989), 589--614.Google Scholar
- R. Holzman and N. Law-Yone. 1997. Strong equilibrium in congestion games. Games and Economic Behavior 21, 1 (1997), 85--101.Google ScholarCross Ref
- M. O. Jackson. 2008. Social and Economic Networks. Princeton. Google ScholarDigital Library
- K. Jain and M. Mahdian. 2007. Cost sharing. Algorithmic Game Theory (2007), 385--410.Google Scholar
- E. Kalai and D. Samet. 1987. On weighted Shapley values. International Journal of Game Theory 16, 3 (1987), 205--222. Google ScholarDigital Library
- Y. Kawase and K. Makino. 2013. Nash equilibria with minimum potential in undirected broadcast games. Theoretical Computer Science 482 (April 2013), 33--47.Google Scholar
- K. Kollias and T. Roughgarden. 2015. Restoring pure equilibria to weighted congestion games. ACM Transactions on Economics and Computation 3, 4, Article 21 (July 2015), 24 pages. Google ScholarDigital Library
- E. Lee and K. Ligett. 2013. Improved bounds on the price of stability in network cost sharing games. In Proceedings of the 14th ACM Conference on Electronic Commerce. ACM, 607--620. Google ScholarDigital Library
- J. Li. 2009. An upper bound on the price of stability for undirected Shapley network design games. Information Processing Letters 109, 15 (2009), 876--878. Google ScholarDigital Library
- D. Monderer and L. S. Shapley. 1996. Potential games. Games and Economic Behavior 14, 1 (1996), 124--143.Google ScholarCross Ref
- D. Moreno and J. Wooders. 1996. Coalition-proof equilibrium. Games and Economic Behavior 17, 1 (1996), 80--112.Google ScholarCross Ref
- H. Moulin. 1999. Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare 16, 2 (1999), 279--320.Google ScholarCross Ref
- H. Moulin and S. Shenker. 2001. Strategyproof sharing of submodular costs: Budget balance versus efficiency. Economic Theory 18, 3 (2001), 511--533.Google ScholarCross Ref
- R. Paes Leme, V. Syrgkanis, and E. Tardos. 2012. The curse of simultaneity. In Innovations in Theoretical Computer Science. ACM, 60--67. Google ScholarDigital Library
- T. Roughgarden and M. Sundararajan. 2009. Quantifying inefficiency in cost-sharing mechanisms. Journal of the ACM 56, 4 (2009), 23. Google ScholarDigital Library
- O. Rozenfeld and M. Tennenholtz. 2006. Strong and correlated strong equilibria in monotone congestion games. In Internet and Network Economics. Springer, 74--86. Google ScholarDigital Library
- L. S. Shapley. 1953. Additive and Non-Additive Set Functions. Ph.D. dissertation. Department of Mathematics, Princeton University.Google Scholar
- M. E. Slade. 1994. What does an oligopoly maximize? Journal of Industrial Economics 42 (1994), 45--61.Google ScholarCross Ref
- V. Syrgkanis. 2010. The complexity of equilibria in cost sharing games. In Internet and Network Economics. Springer, 366--377. Google ScholarDigital Library
- É. Tardos and T. Wexler. 2007. Network formation games and the potential function method. In Algorithmic Game Theory. Cambridge University Press, Chapter 19, 487--516.Google Scholar
- P. von Falkenhausen and T. Harks. 2013. Optimal cost sharing for resource selection games. Mathematics of Operations Research 38, 1 (2013), 184--208. Google ScholarDigital Library
Index Terms
- Network Cost-Sharing without Anonymity
Recommendations
Equilibrium refinement in finite action evidence games
AbstractEvidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (Am Econ Rev 107:690-713, 2017) propose to ...
How egalitarian are Nash equilibria in network cost-sharing games?
We consider the egalitarian social cost, which is the maximum individual cost (instead of the sum), when analyzing Nash equilibria in fair network cost-sharing games. Intuitively, the egalitarian price of anarchy reflects how uneven cost is distributed ...
Comments