Noga Alon
Moshe Tennenholtz
ABSTRACT
We quantify the effect of Bayesian ignorance by comparing the social cost obtained in a Bayesian game by agents with local views to the expected social cost of agents having global views. Both benevolent agents, whose goal is to minimize the social cost, and selfish agents, aiming at minimizing their own individual costs, are considered. When dealing with selfish agents, we consider both best and worst equilibria outcomes. While our model is general, most of our results concern the setting of network cost sharing (NCS) games. We provide tight asymptotic results on the effect of Bayesian ignorance in directed and undirected NCS games with benevolent and selfish agents. Among our findings we expose the counter-intuitive phenomenon that "gnorance is bliss": Bayesian ignorance may substantially improve the social cost of selfish agents. We also prove that public random bits can replace the knowledge of the common prior in attempt to bound the effect of Bayesian ignorance in settings with benevolent agents. Together, our work initiates the study of the effects of local vs. global views on the social cost of agents in Bayesian contexts.
- S. Albers. On the Value of Coordination in Network Design. SIAM J. Comput. (SICOMP), 38(6):2273--2302, 2009. Google Scholar
Digital Library
- N. Alon and Y. Azar. On-line Steiner trees in the Euclidean plane. In Proc. of the 8th Symp. on Computational Geometry (SoCG), pages 337--343, 1992. Google ScholarDigital Library
- N. Andelman, M. Feldman, and Y. Mansour. Strong Price of Anarchy. In Proc. ACM-SIAM Symp. on Discrete Algorithms (SODA), 2007. Google ScholarDigital Library
- E. Anshelevich, A. Dasgupta, J. M. Kleinberg, É. Tardos, T. Wexler, and T. Roughgarden. The price of stability for network design with fair cost allocation. SIAM J. Comput. (SICOMP), 38(4):1602--1623, 2008. Google ScholarDigital Library
- I. Ashlagi, D. Monderer, and M. Tennenholtz. Two-Terminal Routing Games with Unknown Active Players. Artificial Intelligence Journal, 173(15):1441--1455, 2009. Google ScholarDigital Library
- H. L. Chen, and T. Roughgarden. Network design with weighted players. In Proc. ACM Symp. on Parallel Algorithms and Architecture (SPAA), pages 29--38, 2006. Google ScholarDigital Library
- J. Fakcharoenphol, S. Rao, and K. Talwar. A tight bound on approximating arbitrary metrics by tree metrics. J. Comput. Syst. Sci. (JCSS), 69(3):485--497, 2004. Google ScholarDigital Library
- I. Gilboa, and E. Lehrer. The Value of Information - An Axiomatic Approach. Journal of Mathematical Economics, 20: 443--459, 1991.Google ScholarCross Ref
- A. Gupta. Steiner points in tree metrics don't (really) help. In Proc. of the 12th ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 220--227, 2001. Google ScholarDigital Library
- R.A. Howard. Information value theory. IEEE Transactions on Systems Science and Cybernetics, 2: 22--26, 1996.Google ScholarCross Ref
- M. Imase and B. M. Waxman. Dynamic Steiner tree problem. SIAM J. Discrete Math. (SIDMA), 4(3):369--384, 1991.Google ScholarCross Ref
- E. Koutsoupias, and C. H. Papadimitriou. Worst-case equilibria. In Proc. 16th Symp. Theoretical Aspects of Computer Science (STACS), 1999. Google ScholarDigital Library
- C. H. Papadimitriou. Algorithms, games, and the Internet. In Proc. 33rd Symp. Theory of Computing (STOC), 749--753, 2001. Google ScholarDigital Library
- R. W. Rosenthal. The network equilibrium problem in integers. Networks, 3(1):53--59, 1973.Google ScholarCross Ref
Index Terms
- Bayesian ignorance
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