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Optimal design for redistributions among endogenous buyers and sellers

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The haves and have-notes

live on each other.

—Laotzu.

Abstract

Given a large market of individuals entitled to equal shares of a limited resource, each allowed to buy or sell the shares, we characterize the interim incentive-constrained Pareto frontier subject to market clearance and budget balance. At most two prices—partitioning the type space into at most three tiers and using rations only on the middle tier—are needed to attain any interim Pareto optimum. When the virtual surplus function satisfies a single crossing condition without having to be monotone, the optimal mechanism reduces to a single, posted price and requires neither rationing nor lump sum transfers. We find which types gain, and which types lose, when the social planner chooses a rationing mechanism over the single-price solution, as well as the welfare weight of which type is crucial to the choice. The finding suggests a market-like mechanism to distribute Covid vaccines optimally within the same priority group.

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References

  • Akbarpour, M., Budish,E., Dworczak, P., Kominers, S.D.: An economic framework for vaccine prioritization. Working Paper (2021)

  • Akbarpour, M., Dworczak, P., Kominers, S.D.: Redistributive allocation mechanisms. Working Paper (2020)

  • Bulow, J., Roberts, J.: The simple economics of optimal auctions. J. Polit. Econ. 97(5), 1060–1090 (1989)

    Article  Google Scholar 

  • Chien, H.-C.: Incentive Efficient Mechanism for Partnership. Mimeo, New York (2007)

    Google Scholar 

  • Cramton, P., Gibbons, R., Klemperer, P.: Dissolving a partnership efficiently. Econometrica 55(3), 615–632 (1987)

    Article  Google Scholar 

  • Dworczak, P., Kominers, S.D., Akbarpour, M.: Redistribution through markets. Econometrica 89(4), 1665–1698 (2021)

    Article  Google Scholar 

  • Gresik, T.: Incentive-efficient equilibria of two-party sealed-bid bargaining games. J. Econ. Theory 68, 26–48 (1996)

    Article  Google Scholar 

  • Holmström, B., Myerson, R.: Efficient and durable decision rules with incomplete information. Econometrica 51(6), 1799–1820 (1983)

    Article  Google Scholar 

  • Kamenica, E., Gentzkow, M.: Bayesian persuasion. Am. Econ. Rev. 101, 2590–2615 (2011)

    Article  Google Scholar 

  • Kang, M., Zheng, C.Z.: Pareto optimality of allocating the bad. Working Paper (2020). https://economics.uwo.ca/faculty/zheng/research/AllocatingTheBad.pdf

  • Kang, Z.Y.: Optimal public provision of private goods. Mimeo, Stanford USB, Stanford (2020)

    Book  Google Scholar 

  • Kittsteiner, T.: Partnerships and double auctions with interdependent valuations. Games Econ. Behav. 44, 54–76 (2003)

    Article  Google Scholar 

  • Laussel, D., Palfrey, T.: Efficient equilibria in the voluntary contributions mechanism with private information. J. Public Econ. Theory 5, 449–478 (2003)

    Article  Google Scholar 

  • Ledyard, J., Palfrey, T.: A characterization of interim efficiency with public goods. Econometrica 67, 435–448 (1999)

    Article  Google Scholar 

  • Ledyard, J., Palfrey, T.: A general characterization of interim efficient mechanisms for independent linear environments. J. Econ. Theory 133, 441–466 (2007)

    Article  Google Scholar 

  • Loertscher, S., Wasser, C.: Optimal structure and dissolution of partnerships. Theor. Econ. 14, 1063–1114 (2019)

    Article  Google Scholar 

  • Lu, H., Robert, J.: Optimal trading mechanisms with ex ante unidentifiable traders. J. Econ. Theory 97, 50–80 (2001)

    Article  Google Scholar 

  • Myerson, R.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)

    Article  Google Scholar 

  • Myerson, R., Satterthwaite, M.A.: Efficient mechanisms for bilateral trading. J. Econ. Theory 29, 265–281 (1983)

    Article  Google Scholar 

  • Mylovanov, T., Tröger, T.: Mechanism design by an informed principal: private values with transferable utility. Rev. Econ. Stud. 81, 1668–1707 (2014)

    Article  Google Scholar 

  • Pérez-Nievas, M.: Interim efficient allocation mechanisms. Working Paper 00-20, Departmento de Economia, Universidad Carlos III de Madrid (2000)

  • Reuter, M., Groh, C.-C.: Mechanism design for unequal societies. Discussion Paper No. 228 (2020)

  • Royden, H.L., Fitzpatrick, P.M.: Real Analysis, 4th edn. Pearson Education, Boston (2010)

    Google Scholar 

  • Segal, I., Whinston, M.: Property rights and the efficiency of bargaining. J. Eur. Econ. Assoc. 14, 1287–1328 (2016)

    Article  Google Scholar 

  • Sömet, T., Pathak, P.A., Ünever, U., Persad, G., Truog, R.D., White, D.B.: Categorized priority systems. Humanities: Vantage 159(3), 1294–1299 (2021)

    Google Scholar 

  • Wilson, R.: Incentive efficiency of double auctions. Econometrica 53, 1101–1105 (1985)

    Article  Google Scholar 

  • Yang, L., Debo, L., Gupta, V.: Trading time in a congested environment. Manag. Sci. 63, 2377–2395 (2017)

    Article  Google Scholar 

  • Yang, L., Wang, Z., Cui, S.: A model of queue scalping. Manag. Sci. (2021). https://doi.org/10.1287/mnsc.2020.3865

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Economics, Jinan University, Guangzhou, China

    Mingshi Kang

  2. Department of Economics, University of Western Ontario, London, ON, Canada

    Charles Z. Zheng

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  1. Mingshi Kang
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  2. Charles Z. Zheng
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Correspondence to Charles Z. Zheng.

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Previously titled “Pareto Optimal Hierarchies.” We thank Scott Kominers, two referees and the associate editor for comments and suggestions. Zheng acknowledges financial support from the Social Science and Humanities Research Council of Canada, Insight Grant R4809A04.

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Kang, M., Zheng, C.Z. Optimal design for redistributions among endogenous buyers and sellers. Econ Theory 75, 1141–1180 (2023). https://doi.org/10.1007/s00199-022-01442-4

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