Article

The Price of Stochastic Anarchy

Authors:

Christine Chung,

Katrina Ligett,

Aaron RothAuthors Info & Claims

SAGT '08: Proceedings of the 1st International Symposium on Algorithmic Game Theory

Pages 303 - 314

https://doi.org/10.1007/978-3-540-79309-0_27

Published: 30 April 2008 Publication History

Abstract

We consider the solution concept of stochastic stability, and propose the <em>price of stochastic anarchy</em>as an alternative to the <em>price of (Nash) anarchy</em>for quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages that the set of stochastically stable states of a game avoid: unlike Nash equilibria, stochastically stable states are the result of natural dynamics of computationally bounded and decentralized agents, and are resilient to small perturbations from ideal play. The price of stochastic anarchy can be viewed as a smoothed analysis of the price of anarchy, distinguishing equilibria that are resilient to noise from those that are not. To illustrate the utility of stochastic stability, we study the load balancing game on unrelated machines. This game has an unboundedly large price of Nash anarchy even when restricted to two players and two machines. We show that in the two player case, the price of stochastic anarchy is 2, and that even in the general case, the price of stochastic anarchy is bounded. We conjecture that the price of stochastic anarchy is <em>O</em>(<em>m</em>), matching the price of strong Nash anarchy without requiring player coordination. We expect that stochastic stability will be useful in understanding the relative stability of Nash equilibria in other games where the worst equilibria seem to be inherently brittle.

References

[1]

Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: SODA 2007 (2007).

[2]

Awerbuch, B., Azar, Y., Richter, Y., Tsur, D.: Tradeoffs in worst-case equilibria. Theor. Comput. Sci. 361(2), 200-209 (2006).

[3]

Blum, A., Even-Dar, E., Ligett, K.: Routing without regret: On convergence to Nash equilibria of regret-minimizing algorithms in routing games. In: PODC 2006 (2006).

[4]

Blum, A., Hajiaghayi, M., Ligett, K., Roth, A.: Regret minimization and the price of total anarchy. In: STOC 2008 (2008).

[5]

Blume, L.E.: The statistical mechanics of best-response strategy revision. Games and Economic Behavior 11(2), 111-145 (1995).

[6]

Chen, X., Deng, X.: Settling the complexity of 2-player Nash-equilibrium. In: FOCS 2006 (2006).

[7]

Ellison, G.: Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution. Review of Economic Studies 67(1), 17-45 (2000).

[8]

Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence time to Nash equilibria. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, Springer, Heidelberg (2003).

[9]

Fabrikant, A., Papadimitriou, C.: The complexity of game dynamics: Bgp oscillations, sink equilibria, and beyond. In: SODA 2008 (2008).

[10]

Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure nash equilibria. In: STOC 2004 (2004).

[11]

Fiat, A., Kaplan, H., Levy, M., Olonetsky, S.: Strong price of anarchy for machine load balancing. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, Springer, Heidelberg (2007).

[12]

Fischer, S., Räcke, H., Vöcking, B.: Fast convergence to wardrop equilibria by adaptive sampling methods. In: STOC 2006 (2006).

[13]

Fischer, S., Vöcking, B.: On the evolution of selfish routing. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, Springer, Heidelberg (2004).

[14]

Foster, D., Young, P.: Stochastic evolutionary game dynamics. Theoret. Population Biol. 38, 229-232 (1990).

[15]

Goemans, M., Mirrokni, V., Vetta, A.: Sink equilibria and convergence. In: FOCS 2005 (2005).

[16]

Josephson, J., Matros, A.: Stochastic imitation in finite games. Games and Economic Behavior 49(2), 244-259 (2004).

[17]

Kandori, M., Mailath, G.J., Rob, R.: Learning, mutation, and long run equilibria in games. Econometrica 61(1), 29-56 (1993).

[18]

Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: 16th Annual Symposium on Theoretical Aspects of Computer Science, Trier, Germany, March 4-6, 1999, pp. 404-413 (1999).

[19]

Larry, S.: Stochastic stability in games with alternative best replies. Journal of Economic Theory 64(1), 35-65 (1994).

[20]

Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. (eds.): Algorithmic Game Theory. Cambridge University Press, Cambridge (2007).

[21]

Robson, A.J., Vega-Redondo, F.: Efficient equilibrium selection in evolutionary games with random matching. Journal of Economic Theory 70(1), 65-92 (1996).

[22]

Roughgarden, T., Tardos, É.: How bad is selfish routing. J. ACM 49(2), 236-259 (2002); In: FOCS 2000 (2000).

[23]

Suri, S.: Computational evolutionary game theory. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V., Vazirani, V.V. (eds.) Algorithmic Game Theory, Cambridge University Press, Cambridge (2007).

[24]

Peyton Young, H.: The evolution of conventions. Econometrica 61(1), 57-84 (1993).

[25]

Peyton Young, H.: Individual Strategy and Social Structure. Princeton University Press, Princeton (1998).

Cited By

Scherrer SPerrig ASchmid S(2020)The Value of Information in Selfish RoutingStructural Information and Communication Complexity10.1007/978-3-030-54921-3_21(366-384)Online publication date: 29-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-54921-3_21
Chen CPenna PXu Y(2017)Selfish Jobs with Favorite Machines: Price of Anarchy vs. Strong Price of AnarchyCombinatorial Optimization and Applications10.1007/978-3-319-71147-8_16(226-240)Online publication date: 16-Dec-2017
https://dl.acm.org/doi/10.1007/978-3-319-71147-8_16
Panageas IPiliouras GConitzer VBergemann DChen Y(2016)Average Case Performance of Replicator Dynamics in Potential Games via Computing Regions of AttractionProceedings of the 2016 ACM Conference on Economics and Computation10.1145/2940716.2940784(703-720)Online publication date: 21-Jul-2016
https://dl.acm.org/doi/10.1145/2940716.2940784
Show More Cited By

The Price of Stochastic Anarchy

Recommendations

Price of anarchy for auction revenue
EC '14: Proceedings of the fifteenth ACM conference on Economics and computation

This paper develops tools for welfare and revenue analyses of Bayes-Nash equilibria in asymmetric auctions with single-dimensional agents. We employ these tools to derive price of anarchy results for social welfare and revenue. Our approach separates ...
Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions

We study the price of anarchy (PoA) of simultaneous first-price auctions (FPAs) for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian price of anarchy (BPoA) of these auctions are e/(e − 1) [Syrgkanis and ...
Liquid Price of Anarchy
Algorithmic Game Theory
Abstract
Incorporating budget constraints into the analysis of auctions has become increasingly important, as they model practical settings more accurately. The social welfare function, which is the standard measure of efficiency in auctions, is inadequate ...

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

SAGT '08: Proceedings of the 1st International Symposium on Algorithmic Game Theory

April 2008

361 pages

ISBN:9783540793083

Editors:
Burkhard Monien
Institut für Informatik, Universität Paderborn, Paderborn, Germany 33102
,
Ulf-Peter Schroeder
Institut für Informatik, Universität Paderborn, Paderborn, Germany 33102

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 30 April 2008

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 08 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Scherrer SPerrig ASchmid S(2020)The Value of Information in Selfish RoutingStructural Information and Communication Complexity10.1007/978-3-030-54921-3_21(366-384)Online publication date: 29-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-54921-3_21
Chen CPenna PXu Y(2017)Selfish Jobs with Favorite Machines: Price of Anarchy vs. Strong Price of AnarchyCombinatorial Optimization and Applications10.1007/978-3-319-71147-8_16(226-240)Online publication date: 16-Dec-2017
https://dl.acm.org/doi/10.1007/978-3-319-71147-8_16
Panageas IPiliouras GConitzer VBergemann DChen Y(2016)Average Case Performance of Replicator Dynamics in Potential Games via Computing Regions of AttractionProceedings of the 2016 ACM Conference on Economics and Computation10.1145/2940716.2940784(703-720)Online publication date: 21-Jul-2016
https://dl.acm.org/doi/10.1145/2940716.2940784
Leme RSyrgkanis VTardos ÉGoldwasser S(2012)The curse of simultaneityProceedings of the 3rd Innovations in Theoretical Computer Science Conference10.1145/2090236.2090242(60-67)Online publication date: 8-Jan-2012
https://dl.acm.org/doi/10.1145/2090236.2090242
Hoefer MSouza A(2010)Tradeoffs and Average-Case Equilibria in Selfish RoutingACM Transactions on Computation Theory (TOCT)10.1145/1867719.18677212:1(1-25)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1145/1867719.1867721
Asadpour ASaberi A(2009)On the Inefficiency Ratio of Stable Equilibria in Congestion GamesProceedings of the 5th International Workshop on Internet and Network Economics10.1007/978-3-642-10841-9_54(545-552)Online publication date: 9-Dec-2009
https://dl.acm.org/doi/10.1007/978-3-642-10841-9_54
Chung CPyrga E(2009)Stochastic Stability in Internet Router Congestion GamesProceedings of the 2nd International Symposium on Algorithmic Game Theory10.1007/978-3-642-04645-2_17(183-195)Online publication date: 13-Oct-2009
https://dl.acm.org/doi/10.1007/978-3-642-04645-2_17

View Options

View options

Figures

Tables

Media

View Table of Conten