Abstract
We explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions.
The full version of this paper is available at https://arxiv.org/abs/1502.04052.
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Notes
- 1.
Our formal proofs, along with code for the \(\textsf {HOARe}^2\) tool, are available online: https://github.com/ejgallego/HOARe2/tree/master/examples/bic.
References
Barrett, C., Sebastini, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of satisfiability, vol. 185. IOS press (2009)
Barthe, G., Grégoire, B., Heraud, S., Béguelin, S.Z.: Computer-aided security proofs for the working cryptographer. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 71–90. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22792-9_5
Barthe, G., Dupressoir, F., Grégoire, B., Kunz, C., Schmidt, B., Strub, P.-Y.: EasyCrypt: a tutorial. In: Aldini, A., Lopez, J., Martinelli, F. (eds.) FOSAD 2012-2013. LNCS, vol. 8604, pp. 146–166. Springer, Heidelberg (2014). doi:10.1007/978-3-319-10082-1_6
Barthe, G., Gaboardi, M., Gallego Arias, E.J., Hsu, J., Roth, A., Strub, P.-Y.: Higher-order approximate relational refinement types for mechanism design and differential privacy. In: ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), Mumbai, India, pp. 55–68 (2015). http://arxiv.org/abs/1407.6845
Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006). doi:10.1007/11761679_25
Brânzei, S., Procaccia, A.D.: Verifiably truthful mechanisms. In: ACM SIGACT Innovations in Theoretical Computer Science (ITCS), Princeton, New Jersey (2014)
Caminati, M.B., Kerber, M., Lange, C., Rowat, C.: Sound auction specification and implementation. In: ACM SIGecom Conference on Economics and Computation (EC), Portland, Oregon, pp. 547–564 (2015). http://doi.acm.org/10.1145/2764468.2764511
Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: ACM SIGACT Symposium on Theory of Computing (STOC), Baltimore, Maryland, pp. 67–73. ACM (2005). http://dl.acm.org/citation.cfm?id=1060600
Clarke, E.H.: Multipart pricing of public goods. Public Choice 11(1), 17–33 (1971)
Conitzer, V.: Computational aspects of preference aggregation. PhD thesis, IBM (2006)
Conitzer, V., Sandholm, T.: Complexity of mechanism design. In: Conference on Uncertainty in Artificial Intelligence (UAI), Edmonton, Alberta, pp. 103–110. Morgan Kaufmann Publishers Inc. (2002)
Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(1), 195–259 (2009)
Goldberg, A.V., Hartline, J.D., Karlin, A.R., Saks, M., Wright, A.: Competitive auctions. Games Econ. Behav. 55(2), 242–269 (2006)
Groves, T.: Incentives in teams. Econ. J. Econ. Soc. 41(4), 617–631 (1973)
Halevi, S.: A plausible approach to computer-aided cryptographic proofs. Cryptology ePrint Archive, Report 2005/181 (2005). https://eprint.iacr.org/2005/181.pdf
Hart, S., Mansour, Y.: The communication complexity of uncoupled Nash equilibrium procedures. In: ACM SIGACT Symposium on Theory of Computing (STOC), San Diego, California, pp. 345–353. ACM (2007)
Hartline, J.D., Kleinberg, R., Malekian, A.: Bayesian incentive compatibility via matchings. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), San Francisco, California, pp. 734–747. SIAM (2011)
Kerber, M., Lange, C., Rowat, C.: An introduction to mechanized reasoning. CoRR, abs/1603.02478, 2016. http://arxiv.org/abs/1603.02478
Li, S.: Obviously strategy-proof mechanisms. SSRN Electron. J. http://dx.doi.org/10.2139/ssrn.2560028
Milgrom, P., Segal, I.: Deferred acceptance auctions and radio spectrum reallocation (2014). http://www.as.huji.ac.il/sites/default/files/DA%20Heuristic%20Auctions%20June-2014.pdf
Mu’alem, A.: A note on testing truthfulness. In: Electronic Colloquium on Computational Complexity (ECCC), No. 130 (2005)
Roughgarden, T.: Selfish Routing and the Price of Anarchy, vol. 174. MIT Press, Cambridge (2005)
Sandholm, T.: Automated mechanism design: a new application area for search algorithms. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 19–36. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45193-8_2
Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finan. 16(1), 8–37 (1961)
Acknowledgments
We thank the anonymous reviewers for their careful reading; their suggestions have significantly improved this work. This work was partially supported by NSF grants TWC-1513694, CNS-1237235, CNS-1565365 and a grant from the Simons Foundation (\(\#360368\) to Justin Hsu).
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Barthe, G., Gaboardi, M., Arias, E.J.G., Hsu, J., Roth, A., Strub, PY. (2016). Computer-Aided Verification for Mechanism Design. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_20
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