Abstract
We study game-theoretically secure protocols for the classical ordinal assignment problem (aka matching with one-sided preference), in which each player has a total preference order on items. To achieve the fairness notion of equal treatment of equals, conventionally the randomness necessary to resolve conflicts between players is assumed to be generated by some trusted authority. However, in a distributed setting, the mutually untrusted players are responsible for generating the randomness themselves.
In addition to standard desirable properties such as fairness and Pareto-efficiency, we investigate the game-theoretic notion of maximin security, which guarantees that an honest player following a protocol will not be harmed even if corrupted players deviate from the protocol. Our main contribution is an impossibility result that shows no maximin secure protocol can achieve both fairness and ordinal efficiency. Specifically, this implies that the well-known probabilistic serial (PS) mechanism by Bogomolnaia and Moulin cannot be realized by any maximin secure protocol.
On the other hand, we give a maximin secure protocol that achieves fairness and stability (aka ex-post Pareto-efficiency). Moreover, inspired by the PS mechanism, we show that a variant known as the OnlinePSVar (varying rates) protocol can achieve fairness, stability and uniform dominance, which means that an honest player is guaranteed to receive an item distribution that is at least as good as a uniformly random item. In some sense, this is the best one can hope for in the case when all players have the same preference order.
This work was partially supported by the Hong Kong RGC grants 17203122, 17202121 and 17201220.
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Notes
- 1.
A bistochastic matrix is one with non-negative real elements such that the sum of every row and the sum of every column is equal to 1.
- 2.
A convex hull of \(S\subset \textsf{R}^n\) refers to the minimum convex set that contains S.
- 3.
In probability theory, a coupling between two probability spaces \((\varOmega _1, \Pr _1)\) and \((\varOmega _2, \Pr _2)\) is a joint space \((\varOmega _1 \times \varOmega _2, \Pr )\), whose projections into \(\varOmega _1\) and \(\varOmega _2\) equal to \((\varOmega _1, \Pr _1)\) and \((\varOmega _2, \Pr _2)\), respectively.
References
Abdulkadiroglu, A., Sönmez, T.: Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica 66(3), 689–702 (1998). https://EconPapers.repec.org/RePEc:ecm:emetrp:v:66:y:1998:i:3:p:689-702
Badertscher, C., Maurer, U., Tschudi, D., Zikas, V.: Bitcoin as a transaction ledger: a composable treatment. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 324–356. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_11
Blum, M.: How to exchange (secret) keys. ACM Trans. Comput. Syst. 1(2), 175–193 (1983)
Bogomolnaia, A., Moulin, H.: A new solution to the random assignment problem. J. Econ. Theory 100(2), 295–328 (2001)
Chung, K.-M., Chan, T.-H.H., Wen, T., Shi, E.: Game-theoretic fairness meets multi-party protocols: the case of leader election. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 3–32. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84245-1_1
Chung, K.-M., Guo, Y., Lin, W.-K., Pass, R., Shi, E.: Game theoretic notions of fairness in multi-party coin toss. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 563–596. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_21
Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: STOC, pp. 364–369. ACM (1986)
Echenique, F., Immorlica, N., Vazirani, V.V.: Online and Matching-Based Market Design. Cambridge University Press, London (2021)
Gardenfors, P.: Assignment problem based on ordinal preferences. Manag. Sci. 20(3), 331–340 (1973). https://EconPapers.repec.org/RePEc:inm:ormnsc:v:20:y:1973:i:3:p:331-340
Hylland, A., Zeckhauser, R.: The efficient allocation of individuals to positions. J. Political Econ. 87(2), 293–314 (1979). https://EconPapers.repec.org/RePEc:ucp:jpolec:v:87:y:1979:i:2:p:293-314
Lin, H., Pass, R.: Constant-round nonmalleable commitments from any one-way function. J. ACM 62(1), 1–30 (2015)
Micali, S., Rabin, M.O., Vadhan, S.P.: Verifiable random functions. In: FOCS, pp. 120–130. IEEE Computer Society (1999)
Miller, A., Bentov, I.: Zero-collateral lotteries in bitcoin and ethereum. In: EuroS &P Workshops, pp. 4–13. IEEE (2017)
Nakamoto, S.: Bitcoin: A peer-to-peer electronic cash system (2009). http://www.bitcoin.org/bitcoin.pdf
Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: STOC, pp. 232–241. ACM (2004)
Saban, D., Sethuraman, J.: The complexity of computing the random priority allocation matrix. Math. Oper. Res. 40(4), 1005–1014 (2015). https://EconPapers.repec.org/RePEc:inm:ormoor:v:40:y:2015:i:4:p:1005-1014
Zhou, L.: On a conjecture by gale about one-sided matching problems. J. Econ. Theory 52, 123–135 (1990). https://doi.org/10.1016/0022-0531(90)90070-Z
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Chan, TH.H., Wen, T., Xie, H., Xue, Q. (2023). Game-Theoretically Secure Protocols for the Ordinal Random Assignment Problem. In: Tibouchi, M., Wang, X. (eds) Applied Cryptography and Network Security. ACNS 2023. Lecture Notes in Computer Science, vol 13906. Springer, Cham. https://doi.org/10.1007/978-3-031-33491-7_22
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