T.V. Seregina, A.A. Ivashko, V.V. Mazalov. Optimal stopping strategies in the game “The Price Is Right” ... P. 217-231

The popular TV show “The Price Is Right” is an attractive source of modeling the strategic behavior in a competitive environment for a specific reward. In this study, the structure of the show is used as a basis for several game-theoretic settings. We consider a noncooperative optimal stopping game for a finite number of players. Each player earns points by observing the sums of independent random variables uniformly distributed on the unit interval. At each step, the player must decide whether to stop or continue the game. The winner is the player with the maximal score not exceeding unity. If the scores of all players exceed this limit, the winner is the player with the lowest score. We characterize the optimal strategies of the players in the multi-step version of the game with complete information about the scores of the previous players. We also compare the optimal strategies and payoffs of the players in the games with complete information and with no information. The notion of information price is introduced.

Keywords: optimal stopping, n-person game, Nash equilibrium, threshold strategy, complete information, Showcase Showdown

Received August 6, 2019

Revised August 15, 2019

Accepted August 19, 2019

Funding Agency: This work was supported by the Shandong Province “Double-Hundred Talent Plan” (No. WST2017009).

Tatiana Valerievna Seregina, PhD in Computer Science and Automation, $\acute{\mathrm E}$cole Nationale de l’Aviation Civile - Universit$\acute{\mathrm e}$ de Toulouse, 31055 Toulouse Cedex 4, France, Toulouse Business School - Universit$\acute{\mathrm e}$ Toulouse I, 31068 Toulouse Cedex 7, France, e-mail: ts.tseregina@gmail.com

Anna Antonovna Ivashko, Cand. Phys.-Math. Sci., Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, Petrozavodsk, 185910 Russia; Petrozavodsk State University, Petrozavodsk, 185910 Russia, e-mail: aivashko@krc.karelia.ru

Vladimir Viktorovich Mazalov, Dr. Phys.-Math. Sci., Prof., School of Mathematics and Statistics, Qingdao University, Institute of Applied Mathematics, Qingdao, 266071, China; Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, Petrozavodsk, 185910 Russia, e-mail: vmazalov@krc.karelia.ru

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Cite this article as: T.V. Seregina, A.A. Ivashko, V.V. Mazalov. Optimal stopping strategies in the game “The Price Is Right”, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 217–231.