Abstract
We consider the problem of developing and optimizing the rules of the spectrum auction. One-sided sealed-bid spectrum auctions are studied. Two types of pricing are compared theoretically: the first-price and the second-price. А game model of the auction with free riders is constructed. A free rider uses frequencies purchased by another such participant for free. All Nash equilibria of the obtained games are found and represented in an analytical form. The significant difference between games with all free riders and games with at least one ordinary player is shown. It is proved that when players eliminate their dominated strategies, the resulting auction price of the lot is determined by its value for ordinary players. In the case when all players are free riders, the price is equal to the minimal bid price. The influence of the information the participants have about their partners’ values of a lot on the outcome of the game is discussed. The theoretically obtained properties are in agreement with the results of the experiments presented for spectrum auctions in the scientific literature.
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REFERENCES
M. Jackson, “Mechanism theory,” in Optimization and Operations Research, Ed. by U. Derigs (EOLSS Publ., Oxford, 2003), vol. 3.
M. R. Davidson, Yu. V. Dogadushkina, E. M. Kreines, N. M. Novikova, A. V. Seleznev, Yu. A. Udal’tsov, and L. V. Shiryaeva, “Mathematical model of power system management in conditions of a competitive wholesale electric power (capacity) market in Russia,” J. Comput. Syst. Sci. Int. 48 (2), 243–253 (2009).
A. A. Vasin, Mathematical Models of Markets and Auctions (MAKS Press, Moscow, 2023) [in Russian].
K. I. Sonin, “Fundamentals of auction theory (Nobel Prize in economics 2020),” Vopr. Ekon. 1, 5–32 (2021).
Handbook of Spectrum Auction Design, Ed. by J. Bichler and J. Goeree (Cambridge University Press, Cambridge, 2017).
S. Hu and R. Shi, “Analysis of recent development of spectrum auction and forecast of future development,” in Third Int. Conf. on Economic Management and Cultural Industry (Atlantis Press, Guangzhou, 2021), Vol. 203, pp. 518–522.
X. Dong, Y. Zhang, Y. Guo, Y. Gong, Y. Shen, and J. Ma, “PRAM: A practical Sybil-proof auction mechanism for dynamic spectrum access with untruthful attackers,” IEEE Trans. Mobile Comput. 22, 1143–1156 (2021).
M. Devi, N. Sarma, and S. K. Deka, “Multi-winner spectrum allocation in cognitive radio networks: A single-sided auction theoretic modelling approach with sequential bidding,” Electronics 10, 602–626 (2021).
Y. Dang and Z. Li, “The analysis and discussion of spectrum auctions based on case study,” J. Educ., Humanit. Social Sci. 2, 181–185 (2022).
M. M. Bykowsky, M. Olson, and W. W. Sharkey, “Efficiency gains from using a market approach to spectrum management,” Inf. Econ. Policy 22, 73–90 (2010).
W. W. Sharkey, F. Beltran, and M. M. Bykowsky, “Comparing the ability of different auction mechanisms to efficiently designate spectrum between licensed and unlicensed use,” SSRN Electron. J., 2013. http://ssrn.com/abstract=14022. https://doi.org/10.2139/ssrn.2214022.
V. S. Kaplan, “The specifics and game-theoretic analysis of frequency allocation auctions,” in Abstracts of the Scientific Conference Tikhonov Readings (MAKS Press, Moscow, 2022), p. 85.
Yu. B. Germeier, Introduction to the Theory of Operational Research (Nauka, Moscow, 1971) [in Russian].
A. A. Vasin, P. S. Krasnoshchekov, and V. V. Morozov, Operational Research (Akademiya, Moscow, 2008) [in Russian].
H. Moulin, Théorie des jeux pour l’économie et la politique (Hermann, Paris, 1981; Mir, Moscow, 1985).
W. Vickrey, “Counterspeculation, auctions, and competitive sealed tenders,” J. Finance 16 (1), 8–37 (1961). https://doi.org/10.1111/j.1540-6261.1961.tb02789.x
N. Fookes and S. McKenzie, “Impact of budget constraints on the efficiency of multi-lot spectrum auctions,” in Handbook of Spectrum Auction Design, Ed. by M. Bichler and J. Goeree (Cambridge University Press, Cambridge, 2017), pp. 764–781.
B. Edelman, M. Ostrovsky, and M. Schwarz, “Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords,” Am. Econ. Rev. 97 (1), 242–259 (2007). https://doi.org/10.1257/aer.97.1.242
R. J. Weber, “Making more from less: Strategic demand reduction in the FCC spectrum auctions,” J. Econ. Manage. Strategy 6 (3), 529–548 (1997).
P. Cramton and J. A. Schwartz, “Collusive bidding: Lessons from the FCC spectrum auctions,” J. Regul. Econ. 17, 229–252 (2000).
P. Milgrom and I. Segal, “Designing the US incentive auction,” in Handbook of Spectrum Auction Design, Ed. by M. Bichler and J. Goeree (Cambridge University Press, Cambridge, 2017), pp. 803–815.
J. F. Nash, “Non cooperative games,” Ann. Math. 54 (2), 286–295 (1951).
E. Maskin, “Mechanism design for pandemics,” Rev. Econ. Des. 26 (3), 255–259 (2022).
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Kaplan, V.S., Novikova, N.M. & Pospelova, I.I. Game-Theoretic Specificity of a Competitive Allocation of the Frequency Spectrum. J. Comput. Syst. Sci. Int. 62, 1011–1024 (2023). https://doi.org/10.1134/S1064230723060059
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DOI: https://doi.org/10.1134/S1064230723060059