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Optimal, Truthful, and Private Securities Lending

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  • Emily Diana
  • Michael Kearns
  • Seth Neel
  • Aaron Roth

Abstract

We consider a fundamental dynamic allocation problem motivated by the problem of $\textit{securities lending}$ in financial markets, the mechanism underlying the short selling of stocks. A lender would like to distribute a finite number of identical copies of some scarce resource to $n$ clients, each of whom has a private demand that is unknown to the lender. The lender would like to maximize the usage of the resource $\mbox{---}$ avoiding allocating more to a client than her true demand $\mbox{---}$ but is constrained to sell the resource at a pre-specified price per unit, and thus cannot use prices to incentivize truthful reporting. We first show that the Bayesian optimal algorithm for the one-shot problem $\mbox{---}$ which maximizes the resource's expected usage according to the posterior expectation of demand, given reports $\mbox{---}$ actually incentivizes truthful reporting as a dominant strategy. Because true demands in the securities lending problem are often sensitive information that the client would like to hide from competitors, we then consider the problem under the additional desideratum of (joint) differential privacy. We give an algorithm, based on simple dynamics for computing market equilibria, that is simultaneously private, approximately optimal, and approximately dominant-strategy truthful. Finally, we leverage this private algorithm to construct an approximately truthful, optimal mechanism for the extensive form multi-round auction where the lender does not have access to the true joint distributions between clients' requests and demands.

Suggested Citation

  • Emily Diana & Michael Kearns & Seth Neel & Aaron Roth, 2019. "Optimal, Truthful, and Private Securities Lending," Papers 1912.06202, arXiv.org.
  • Handle: RePEc:arx:papers:1912.06202
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    References listed on IDEAS

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    1. repec:fip:fedcwp:13-12 is not listed on IDEAS
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    3. Mark Flood & Jonathan Katz & Stephen Ong & Adam Smith, 2013. "Cryptography and the Economics of Supervisory Information: Balancing Transparency and Confidentiality," Working Papers 13-11, Office of Financial Research, US Department of the Treasury.
    4. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    5. Michael Kearns & Mallesh M. Pai & Aaron Roth & Jonathan Ullman, 2014. "Mechanism Design in Large Games: Incentives and Privacy," American Economic Review, American Economic Association, vol. 104(5), pages 431-435, May.
    6. Ekkehart Boehmer & Juan (Julie) Wu, 2013. "Short Selling and the Price Discovery Process," The Review of Financial Studies, Society for Financial Studies, vol. 26(2), pages 287-322.
    7. Sun, Hanwen & Yin, Shuxing, 2017. "Information leakage in family firms: Evidence from short selling around insider sales," Journal of Corporate Finance, Elsevier, vol. 47(C), pages 72-87.
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