Open Access Journal Article

Bayesian-Nash equilibria for fuzzy value auctions

by Alexey S. Shvedov a,* orcid
a
Department of Applied Economics, National Research University Higher School of Economics, 20 Myasnitskaya ulitsa, Moscow, 101000, Russia
*
Author to whom correspondence should be addressed.
EAL  2024, 59; 3(2), 59; https://doi.org/10.58567/eal03020008
Received: 30 October 2023 / Accepted: 11 March 2024 / Published Online: 13 March 2024
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Abstract

This paper analyses a model of private value auctions with symmetric risk-neutral bidders, where bidders' private values of an indivisible good are fuzzy. The auction is studied as a game with incomplete information. Fuzzy random variables, their quantile functions, and expressions for expectations through quantile functions are used. An explicit expression for the solution is found. Also, expected bidders' payments are studied.

Keywords: Auction theory; Equilibrium strategy; Bidder's payment; Fuzzy random variable; Quantile function;
Copyright: © 2024 by Shvedov. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (Creative Commons Attribution 4.0 International License). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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ACS Style
Shvedov, A. S. Bayesian-Nash equilibria for fuzzy value auctions. Economic Analysis Letters, 2024, 3, 59. https://doi.org/10.58567/eal03020008
AMA Style
Shvedov A S. Bayesian-Nash equilibria for fuzzy value auctions. Economic Analysis Letters; 2024, 3(2):59. https://doi.org/10.58567/eal03020008
Chicago/Turabian Style
Shvedov, Alexey S. 2024. "Bayesian-Nash equilibria for fuzzy value auctions" Economic Analysis Letters 3, no.2:59. https://doi.org/10.58567/eal03020008
APA style
Shvedov, A. S. (2024). Bayesian-Nash equilibria for fuzzy value auctions. Economic Analysis Letters, 3(2), 59. https://doi.org/10.58567/eal03020008

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References

  1. Bhachu, K., Elkasrawy, A., and Venkatesh B. (2023) Fuzzy Optimization Model of an Incremental Capacity Auction Formulation with Greenhouse Gas Consideration. IET Smart Grid 6, 124-135. https://doi.org/10.1049/stg2.12065
  2. Cox, J., Smith, V., and Walker, J. (1984). Theory and Behavior of Multiple Unit Discriminative Auctions. Journal of Finance 39, 983-1010. https://doi.org/10.1111/j.1540-6261.1984.tb03888.x
  3. Fang, S., Nuttle, H., and Wang, D. (2004). Fuzzy Formulation of Auctions and Optimal Sequencing for Multiple Auctions. Fuzzy Sets and Systems 142, 421-441. https://doi.org/10.1016/S0165-0114(03)00127-1
  4. Gretscko, V., and Mass, H. (2024). Worst-Case Equilibria in First-Price Auctions. Theoretical Economics. 19, 61-93. https://doi.org/10.3982/TE4555
  5. Ignatius, J., Motlagh, S., Sepheri, M., Lai, Y., Mustafa, A. (2010). Fuzzy Prices in Combinatorial Auctions. In: L.C. Jain and C.P. Lim (Eds.): Handbook on Decision Making, ISRL 4, Berlin, Springer, 347-367. https://doi.org/10.1007/978-3-642-13639-9_14
  6. Kasberger, B., and Schlag, K. (2017). Robust Bidding in First-Price Auctions: How to Bid Without Knowing what Others are Doing. Vienna Economics Papers vie1707, University of Vienna, Department of Economics. https://papersecon.univie.ac.at/RePEc/vie/viennp/vie1707.pdf
  7. Kaur, P., Goyal, M., and Lu, J. (2017). A Comparison of Bidding Strategies for Online Auctions Using Fuzzy Reasoning and Negotiation Decision Functions. IEEE Transactions on Fuzzy Systems 25, 425-438. https://doi.org/10.1109/TFUZZ.2016.2598297
  8. Krishna, V. (2010). Auction Theory, 2nd ed., San Diego, Elsevier / Academic Press.
  9. Kwakernaak, H. (1978). Fuzzy Random Variables - I. Definitions and Theorems. Information Sciences 15, 1-29. https://doi.org/10.1016/0020-0255(78)90019-1
  10. Kwakernaak, H. (1979). Fuzzy Random Variables - II. Algorithms and Examples for the Discrete Case. Information Sciences 17, 153-178. https://doi.org/10.1016/0020-0255(79)90020-3
  11. Milgrom, P., and Weber R. (1982). A Theory of Auctions and Competitive Bidding. Econometrica 50, 1089-1122. https://doi.org/0012-9682(198209)50:5%3C1089:ATOAAC%3E2.0.CO;2-E
  12. Myerson, R. (1981). Optimal Auction Design. Mathematics of Operations Research 6, 58-73.
  13. Plum, M. (1992). Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information. International Journal of Game Theory 20, 393-418. https://doi.org/10.1007/BF01271133
  14. Puri, M. and, Ralescu D. (1986). Fuzzy Random Variables. Journal of Mathematical Analysis and Applications 114, 409-422. https://doi.org/10.1016/0022-247X(86)90093-4
  15. Riley, J., and Samuelson W. (1981). Optimal Auctions. American Economic Review 71, 381-392.
  16. Shvedov, A. (2016a). Estimating the Means and the Covariances of Fuzzy Random Variables. Applied Econometrics 42, 121-138. (In Russ.) http://pe.cemi.rssi.ru/pe_2016_42_121-138.pdf
  17. Shvedov, A. (2016b). Quantile Function of a Fuzzy Random Variable and an Expression for Expectations. Mathematical Notes 100, 477-481. https://doi.org/10.1134/S0001434616090157
  18. Shvedov, A. (2023). Cournot Equilibrium Under Fuzzy Random Yield. HSE Economic Journal 27, 435-448. (In Russ.) https://doi.org/10.17323/1813-8691-2023-27-3-435-448
  19. https://ej.hse.ru/data/2023/10/23/2049770577/Шведов.pdf
  20. Vickrey, W. (1961). Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance 16, 3-37. https://doi.org/10.1111/j.1540-6261.1961.tb02789.x
  21. Zhou, K., Ma, G., Wang, Y., Zhong, J., Wang, S., and Tang Y. (2021). Strategy Research of Used Cars in Online Sequential Auction Based on Fuzzy Theory. Journal of Intelligent and Fuzzy Systems 40, 4967-4977. https://doi.org/10.3233/JIFS-201719