Non-Cooperative Rational Interactive Proofs
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to design protocols for computation outsourcing.
Existing interactive-proof games largely fall into two categories: either as games of cooperation such as multi-prover interactive proofs and cooperative rational proofs, where the provers work together as a team; or as games of conflict such as refereed games, where the provers directly compete with each other in a zero-sum game. Neither of these extremes truly capture the strategic nature of service providers in outsourcing applications. How to design and analyze non-cooperative interactive proofs is an important open problem.
In this paper, we introduce a mechanism-design approach to define a multi-prover interactive-proof model in which the provers are rational and non-cooperative - they act to maximize their expected utility given others' strategies. We define a strong notion of backwards induction as our solution concept to analyze the resulting extensive-form game with imperfect information.
We fully characterize the complexity of our proof system under different utility gap guarantees. (At a high level, a utility gap of u means that the protocol is robust against provers that may not care about a utility loss of 1/u.) We show, for example, that the power of non-cooperative rational interactive proofs with a polynomial utility gap is exactly equal to the complexity class P^{NEXP}.
non-cooperative game theory
extensive-form games with imperfect information
refined sequential equilibrium
rational proofs
interactive proofs
Theory of computation~Algorithmic game theory and mechanism design
Theory of computation~Interactive proof systems
Theory of computation~Computational complexity and cryptography
29:1-29:16
Regular Paper
This work has been partially supported by NSF CAREER Award CCF 1553385, CNS 1408695, CCF 1439084, IIS 1247726, IIS 1251137, CCF 1217708, by Sandia National Laboratories, by the European Research Council under the European Union’s 7th Framework Programme (FP7/2007-2013) / ERC grant agreement no. 614331, and a Zuckerman STEM Fellowship.
A full version of the paper is available at https://arxiv.org/abs/1708.00521.
Jing
Chen
Jing Chen
Stony Brook University, Stony Brook, NY 11794-4400, USA
Samuel
McCauley
Samuel McCauley
Williams College, Williamstown, MA 01267, USA
Shikha
Singh
Shikha Singh
Williams College, Williamstown, MA 01267, USA
10.4230/LIPIcs.ESA.2019.29
Pablo Daniel Azar and Silvio Micali. Rational proofs. In Proceedings of the Forty-Fourth Annual Symposium on Theory of Computing (STOC), pages 1017-1028, 2012.
Pablo Daniel Azar and Silvio Micali. Super-efficient rational proofs. In Proceedings of the Fourteenth Annual ACM conference on Electronic Commerce (EC), pages 29-30, 2013.
László Babai. Trading group theory for randomness. In Proceedings of the Seventeenth annual ACM symposium on Theory of Computing (STOC), pages 421-429, 1985.
László Babai, Lance Fortnow, and Carsten Lund. Non-deterministic exponential time has two-prover interactive protocols. Computational complexity, 1(1):3-40, 1991.
Jeffrey S Banks and Joel Sobel. Equilibrium selection in signaling games. Econometrica: Journal of the Econometric Society, pages 647-661, 1987.
Michael Ben-Or, Shafi Goldwasser, Joe Kilian, and Avi Wigderson. Multi-prover interactive proofs: How to remove intractability assumptions. In Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing (STOC), pages 113-131, 1988.
Nir Bitansky and Alessandro Chiesa. Succinct arguments from multi-prover interactive proofs and their efficiency benefits. In Advances in Cryptology-CRYPTO 2012, pages 255-272. Springer, 2012.
Andrew J Blumberg, Justin Thaler, Victor Vu, and Michael Walfish. Verifiable computation using multiple provers. IACR Cryptology ePrint Archive, 2014:846, 2014.
Benjamin Braun, Ariel J Feldman, Zuocheng Ren, Srinath Setty, Andrew J Blumberg, and Michael Walfish. Verifying computations with state. In Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles, pages 341-357, 2013.
Jin-yi Cai, Anne Condon, and Richard J Lipton. On games of incomplete information. Theoretical Computer Science, 103(1):25-38, 1992.
Matteo Campanelli and Rosario Gennaro. Sequentially Composable Rational Proofs. In International Conference on Decision and Game Theory for Security, pages 270-288, 2015.
Matteo Campanelli and Rosario Gennaro. Efficient Rational Proofs for Space Bounded Computations. In International Conference on Decision and Game Theory for Security, pages 53-73, 2017.
Ran Canetti, Ben Riva, and Guy N Rothblum. Practical delegation of computation using multiple servers. In Proceedings of the 18th ACM conference on Computer and communications security, pages 445-454, 2011.
Ran Canetti, Ben Riva, and Guy N Rothblum. Two 1-round protocols for delegation of computation. In International Conference on Information Theoretic Security, pages 37-61, 2012.
Ran Canetti, Ben Riva, and Guy N Rothblum. Refereed delegation of computation. Information and Computation, 226:16-36, 2013.
Ashok K Chandra and Larry J Stockmeyer. Alternation. In 17th Annual Symposium on Foundations of Computer Science (FOCS), pages 98-108, 1976.
Jing Chen, Samuel McCauley, and Shikha Singh. Rational Proofs with Multiple Provers (Full Version). arXiv preprint arXiv:1504.08361, 2015. URL: http://arxiv.org/abs/1504.08361.
http://arxiv.org/abs/1504.08361
Jing Chen, Samuel McCauley, and Shikha Singh. Rational Proofs with Multiple Provers. In Proceedings of the Seventh Innovations in Theoretical Computer Science Conference (ITCS), pages 237-248, 2016.
Jing Chen, Samuel McCauley, and Shikha Singh. Efficient Rational Proofs with Strong Utility-Gap Guarantees. In International Symposium on Algorithmic Game Theory (SAGT), pages 150-162. Springer, 2018.
In-Koo Cho and David M Kreps. Signaling games and stable equilibria. The Quarterly Journal of Economics, 102(2):179-221, 1987.
John Duggan. An extensive form solution to the adverse selection problem in principal/multi-agent environments. Review of Economic Design, 3(2):167-191, 1998.
Uriel Feige and Joe Kilian. Making games short. In Proceedings of the Twenty-Ninth Annual ACM Symposium On Theory of Computing (STOC), pages 506-516, 1997.
Uriel Feige and László Lovász. Two-prover one-round proof systems: their power and their problems. In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing (STOC), pages 733-744, 1992.
Uriel Feige and Adi Shamir. Multi-oracle interactive protocols with constant space verifiers. Journal of Computer and System Sciences, 44(2):259-271, 1992.
Uriel Feige, Adi Shamir, and Moshe Tennenholtz. The noisy oracle problem. In Proceedings of the Tenth Annual Conference on Advances in Cryptology (CRYPTO), pages 284-296, 1990.
Joan Feigenbaum, Daphne Koller, and Peter Shor. A game-theoretic classification of interactive complexity classes. In Proceedings of Tenth Annual IEEE Structure in Complexity Theory Conference, pages 227-237, 1995.
Lance Fortnow, John Rompel, and Michael Sipser. On the power of multi-prover interactive protocols. Theoretical Computer Science, 134(2):545-557, 1994.
Jacob Glazer and Motty Perry. Virtual implementation in backwards induction. Games and Economic Behavior, 15(1):27-32, 1996.
S. Goldwasser, S. Micali, and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM J. Comput., 18(1), 1989.
Shafi Goldwasser, Yael Tauman Kalai, and Guy N Rothblum. Delegating computation: interactive proofs for muggles. In Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing (STOC), pages 113-122, 2008.
Siyao Guo, Pavel Hubáček, Alon Rosen, and Margarita Vald. Rational arguments: single round delegation with sublinear verification. In Proceedings of the Fifth Annual Conference on Innovations in Theoretical Computer Science (ITCS), pages 523-540, 2014.
Siyao Guo, Pavel Hubáček, Alon Rosen, and Margarita Vald. Rational sumchecks. In Theory of Cryptography Conference, pages 319-351, 2016.
Tsuyoshi Ito and Thomas Vidick. A multi-prover interactive proof for NEXP sound against entangled provers. In 53rd Annual Symposium on Foundations of Computer Science (FOCS), pages 243-252, 2012.
Gillat Kol and Ran Raz. Competing provers protocols for circuit evaluation. In Proceedings of the Fourth Annual Conference on Innovations in Theoretical Computer Science (ITCS), pages 473-484, 2013.
Daphne Koller and Nimrod Megiddo. The complexity of two-person zero-sum games in extensive form. Games and economic behavior, 4(4):528-552, 1992.
David M Kreps and Robert Wilson. Sequential equilibria. Econometrica: Journal of the Econometric Society, pages 863-894, 1982.
Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan. Algebraic methods for interactive proof systems. Journal of the ACM (JACM), 39(4):859-868, 1992.
Andrew McLennan. Justifiable beliefs in sequential equilibrium. Econometrica: Journal of the Econometric Society, pages 889-904, 1985.
Martin J Osborne and Ariel Rubinstein. A course in game theory. MIT press, 1994.
John H Reif. The complexity of two-player games of incomplete information. Journal of Computer and System Sciences, 29(2):274-301, 1984.
Guy N Rothblum, Salil Vadhan, and Avi Wigderson. Interactive proofs of proximity: delegating computation in sublinear time. In Proceedings of the forty-fifth annual ACM symposium on Theory of computing, pages 793-802, 2013.
Reinhard Selten. Reexamination of the perfectness concept for equilibrium points in extensive games. International journal of game theory, 4(1):25-55, 1975.
Adi Shamir. IP = PSPACE. J. ACM, 39(4):869-877, 1992.
Madhu Sudan. Probabilistically checkable proofs. Communications of the ACM, 52(3):76-84, 2009.
Justin Thaler, Mike Roberts, Michael Mitzenmacher, and Hanspeter Pfister. Verifiable Computation with Massively Parallel Interactive Proofs. In HotCloud, 2012.
Hannu Vartiainen. Subgame perfect implementation of voting rules via randomized mechanisms. Social Choice and Welfare, 29(3):353-367, 2007.
Michael Walfish and Andrew J Blumberg. Verifying computations without reexecuting them. Communications of the ACM, 58(2):74-84, 2015.
Jing Chen, Samuel McCauley, and Shikha Singh
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode