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Multidimensional Monotonicity and Economic Applications

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  • Frank Yang
  • Kai Hao Yang

Abstract

We characterize the extreme points of multidimensional monotone functions from $[0,1]^n$ to $[0,1]$, as well as the extreme points of the set of one-dimensional marginals of these functions. These characterizations lead to new results for various mechanism design and information design problems, including public good provision with interdependent values; interim efficient bilateral trade mechanisms; mechanism (anti) equivalence; asymmetric reduced form auctions; and optimal private private information structure.

Suggested Citation

  • Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Papers 2502.18876, arXiv.org, revised Aug 2025.
    • Handle: RePEc:arx:papers:2502.18876
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    References listed on IDEAS

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    1. Ian Ball, 2023. "Bauer's Maximum Principle for Quasiconvex Functions," Papers 2305.04893, arXiv.org.
    2. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    3. Werner Güth & Martin Hellwig, 1986. "The private supply of a public good," Journal of Economics, Springer, vol. 5(1), pages 121-159, December.
    4. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 267-289.
    5. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann & Yamashita, Takuro, 2023. "Optimal persuasion via bi-pooling," Theoretical Economics, Econometric Society, vol. 18(1), January.
    6. A. Dawid & M. DeGroot & J. Mortera & R. Cooke & S. French & C. Genest & M. Schervish & D. Lindley & K. McConway & R. Winkler, 1995. "Coherent combination of experts' opinions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 263-313, December.
    7. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2021. "A Theory of Auctions with Endogenous Valuations," Journal of Political Economy, University of Chicago Press, vol. 129(4), pages 1011-1051.
    8. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2021. "Feasible Joint Posterior Beliefs," Journal of Political Economy, University of Chicago Press, vol. 129(9), pages 2546-2594.
    9. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    10. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    11. John O. Ledyard & Thomas R. Palfrey, 1999. "A Characterization of Interim Efficiency with Public Goods," Econometrica, Econometric Society, vol. 67(2), pages 435-448, March.
    12. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    13. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    14. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    15. Manelli, Alejandro M. & Vincent, Daniel R., 2012. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly. A corrigendum," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2492-2493.
    16. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    17. Gerhard Winkler, 1988. "Extreme Points of Moment Sets," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 581-587, November.
    18. Loertscher, Simon & Wasser, Cédric, 2019. "Optimal structure and dissolution of partnerships," Theoretical Economics, Econometric Society, vol. 14(3), July.
    19. Yi‐Chun Chen & Wei He & Jiangtao Li & Yeneng Sun, 2019. "Equivalence of Stochastic and Deterministic Mechanisms," Econometrica, Econometric Society, vol. 87(4), pages 1367-1390, July.
    20. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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