We present a game-theoretic analysis of optimal solutions for interactions between censors and censorship resistance systems (CRSs) by focusing on the data channel used by the CRS to smuggle clients’ data past the censors. This analysis leverages the inherent errors (false positives and negatives) made by the censor when trying to classify traffic as either non-circumvention traffic or as CRS traffic, as well as the underlying rate of CRS traffic. We identify Nash equilibrium solutions for several simple censorship scenarios and then extend those findings to more complex scenarios where we find that the deployment of a censorship apparatus does not qualitatively change the equilibrium solutions, but rather only affects the amount of traffic a CRS can support before being blocked. By leveraging these findings, we describe a general framework for exploring and identifying optimal strategies for the censorship circumventor, in order to maximize the amount of CRS traffic not blocked by the censor. We use this framework to analyze several scenarios with multiple data-channel protocols used as cover for the CRS. We show that it is possible to gain insights through this framework even without perfect knowledge of the censor’s (secret) values for the parameters in their utility function.
 T. Alpcan and T. Ba¸sar. Network Security: A Decision and Game-Theoretic Approach. Cambridge University Press, 2010.
 R. Anderson and T. Moore. The Economics of Information Security. Science, 314(5799):610-613, 2006.
 R. Anderson, T. Moore, S. Nagaraja, and A. Ozment. Incentives and Information Security. Algorithmic Game Theory, pages 633-649, 2007.
 R. J. Aumann. Acceptable Points in General Cooperative n-Person Games. Contributions to the Theory of Games, 4:287-324, 1959.
 D. Blackwell. Discounted dynamic programming. The Annals of Mathematical Statistics, 36(1):226-235, 1965.
 F. Brandt, T. Sandholm, and Y. Shoham. Spiteful bidding in sealed-bid auctions. In Proceedings of the 20th International Joint Conference on Artifical Intelligence, IJCAI’07, pages 1207-1214, San Francisco, CA, USA, 2007. Morgan Kaufmann Publishers Inc.
 C. Brubaker, A. Houmansadr, and V. Shmatikov. CloudTransport: Using Cloud Storage for Censorship-Resistant Networking. In Proceedings of 14th Privacy Enhancing Technologies Symposium. Springer, 2014.
 J. R. Crandall, D. Zinn, M. Byrd, E. T. Barr, and R. East. ConceptDoppler: A Weather Tracker for Internet Censorship. In Proceedings of the 14th ACM SIGSAC Conference on Computer and Communications Security, pages 352-365, 2007.
 G. Danezis. An anomaly-based censorship detection system for Tor. Technical Report 2011-09-001, The Tor Project, 2011. https://research.torproject.org/techreports/detector-2011-09-09.pdf.
 G. Danezis and R. Anderson. The Economics of Censorship Resistance. Proceedings of the 3rd Annual Workship on Economics and Information Security, 2004.
 R. Dingledine. Obfsproxy: The Next Step in the Censorship Arms Race. Tor Blog, https://blog.torproject.org/blog/obfsproxy-next-step-censorship-arms-race, February 2012. Retrieved May 2015.
 R. Dingledine, N. Mathewson, and P. Syverson. Tor: The Second-Generation Onion Router. In Proceedings of the 13th conference on USENIX Security Symposium-Volume 13, pages 303-320. USENIX Association, 2004.
 K. P. Dyer, S. E. Coull, T. Ristenpart, and T. Shrimpton. Protocol Misidentification Made Easy with Format-Transforming Encryption. In Proceedings of the 20th ACM conference on Computer and Communications Security, November 2013.
 F. Fang, P. Stone, and M. Tambe. Defender strategies in domains involving frequent adversary interaction. In Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, pages 1663-1664. International Foundation for Autonomous Agents and Multiagent Systems, 2015.
 D. Fifield, C. Lan, R. Hynes, P. Wegmann, and V. Paxson. Blocking-resistant Communication through Domain Fronting. Proceedings on Privacy Enhancing Technologies, 2015(2):46-64, June 2015.
 A. Filasto and J. Applebaum. OONI: Open Observatory of Network Interference. In Proceedings of the USENIX Workshop on Free and Open Communications on the Internet. USENIX, 2012.
 D. Fudenberg and E. Maskin. The folk theorem in repeated games with discounting or with incomplete information. Econometrica, 54(3):533-554, 1986.
 J. Geddes, M. Schuchard, and N. Hopper. Cover Your ACKs: Pitfalls of Covert Channel Censorship Circumvention. In Proceedings of the 20th ACM conference on Computer and Communications Security, 2013.
 B. Hahn, R. Nithyanand, P. Gill, and R. Johnson. Games Without Frontiers: Investigating Video Games as a Covert Channel. http://arxiv.org/pdf/1503.05904v2.pdf, 2015. Retrieved May 2015.
 A. Houmansadr, T. Riedl, N. Borisov, and A. Singer. IP over Voice-over-IP for Censorship Circumvention. arXiv preprint arXiv:1207.2683, 2012.
 S. Khattak, T. Elahi, L. Simon, C. M. Swanson, S. J. Murdoch, and I. Goldberg. SoK: Making Sense of Censorship Resistance Systems. Proceedings on Privacy Enhancing Technologies, 2016(4), 2016.
 A. Lewman. Iran Partially Blocks Encrypted Network Traffic. Tor Blog, https://blog.torproject.org/blog/iran-partially-blocksencrypted-network-traffic, February 2012. Retrieved May 2015.
 K. Leyton-Brown and Y. Shoham. Essentials of Game Theory: A Concise Multidisciplinary Introduction. Synthesis Lectures on Artificial Intelligence and Machine Learning, 2(1):1-88, 2008.
 S. Li, M. Schliep, and N. Hopper. Facet: Streaming over Videoconferencing for Censorship Circumvention. In Proceedings of the Workshop on Privacy in the Electronic Society, November 2014.
 M. H. Manshaei, Q. Zhu, T. Alpcan, T. Bac¸sar, and J.-P. Hubaux. Game Theory meets Network Security and Privacy. ACM Computing Surveys, 45(3):25, 2013.
 H. Mohajeri Moghaddam, B. Li, M. Derakhshani, and I. Goldberg. SkypeMorph: Protocol Obfuscation for Tor Bridges. In Proceedings of the 19th ACM conference on Computer and Communications Security, October 2012.
 J. Morgan, K. Steiglitz, and G. Reis. The spite motive and equilibrium behavior in auctions. Contributions in Economic Analysis & Policy, 2(1), 2003.
 M. J. Osborne. An introduction to game theory. Oxford University Press New York, 2003.
 J. Pita, M. Jain, J. Marecki, F. Ordóñez, C. Portway, M. Tambe, C. Western, P. Paruchuri, and S. Kraus. Deployed ARMOR Protection: The Application of a Game Theoretic Model for Security at the Los Angeles International Airport. In Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems: Industrial Track, pages 125-132. International Foundation for Autonomous Agents and Multiagent Systems, 2008.
 Psiphon Inc. Psiphon. https://psiphon.ca. Retrieved May 2015.
 S. Roy, C. Ellis, S. Shiva, D. Dasgupta, V. Shandilya, and Q. Wu. A Survey of Game Theory as Applied to Network Security. In 2010 43rd Hawaii International Conference on System Sciences, pages 1-10. IEEE, 2010.
 Sandvine. Global Internet Phenomena Report - Spotlight encrypted Internet traffic. https://www.sandvine.com/downloads/general/globalinternet-phenomena/2016/global-internet-phenomenaspotlight-encrypted-internet-traffic.pdf.
 Y. Shoham and K. Leyton-Brown. Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2008.
 T. Tor Project. Tor Mertics Portal: Bridge users by country. https://metrics.torproject.org/userstats-bridge-country.html, 2016. Retrieved May 2016.
 M. C. Tschantz, S. Afroz, V. Paxson, and J. Tygar. On Modeling the Costs of Censorship. arXiv preprint arXiv:1409.3211, 2014.
 P. Vines and T. Kohno. Rook: Using Video Games as a Low- Bandwidth Censorship Resistant Communication Platform. http://homes.cs.washington.edu/~yoshi/papers/tech-reportrook.pdf, 2015. Retrieved May 2015.
 Q. Wang, X. Gong, G. T. K. Nguyen, A. Houmansadr, and N. Borisov. CensorSpoofer: Asymmetric Communication using IP Spoofing for Censorship-Resistant Web Browsing. In Proceedings of the 19th ACM conference on Computer and Communications Security, October 2012.
 Z. Weinberg, J. Wang, V. Yegneswaran, L. Briesemeister, S. Cheung, F. Wang, and D. Boneh. StegoTorus: A Camouflage Proxy for the Tor Anonymity System. In Proceedings of the 19th ACM conference on Computer and Communications Security, October 2012.
 J. Wright, A. Darer, and O. Farnan. Detecting Internet Filtering from Geographic Time Series. http://arxiv.org/pdf/1507.05819v1.pdf, July 2015. Retrieved August 2015.