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Existence in Multidimensional Screening with General Nonlinear Preferences

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  • Kelvin Shuangjian Zhang

Abstract

We generalize the approach of Carlier (2001) and provide an existence proof for the multidimensional screening problem with general nonlinear preferences. We first formulate the principal's problem as a maximization problem with $G$-convexity constraints and then use $G$-convex analysis to prove existence.

Suggested Citation

  • Kelvin Shuangjian Zhang, 2017. "Existence in Multidimensional Screening with General Nonlinear Preferences," Papers 1710.08549, arXiv.org, revised Dec 2018.
  • Handle: RePEc:arx:papers:1710.08549
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    1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    3. Carlier, Guillaume, 2001. "A general existence result for the principal-agent problem with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 129-150, February.
    4. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    5. Monteiro, Paulo K. & Page Jr., Frank H., 1998. "Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 473-502, November.
    6. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    7. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    8. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, September.
    9. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    10. Spence, Michael, 1974. "Competitive and optimal responses to signals: An analysis of efficiency and distribution," Journal of Economic Theory, Elsevier, vol. 7(3), pages 296-332, March.
    11. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, September.
    12. A. Michael Spence, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 821-841.
    13. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, September.
    14. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, September.
    15. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    16. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    17. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    18. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    19. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, September.
    20. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, September.
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