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 maximum 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.

中文翻译：

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“价格合适”游戏中的最佳止损策略

受欢迎的电视节目“价格正确”是在竞争环境中为特定奖励建模策略行为的诱人来源。在这项研究中，表演的结构被用作几种游戏理论设置的基础。我们考虑了有限数量的玩家的非合作性最佳停止游戏。每个玩家通过观察单位间隔上均匀分布的独立随机变量的总和来赚取积分。在每个步骤中，玩家必须决定是停止还是继续游戏。获胜者是得分最高不超过1的玩家。如果所有玩家的分数都超过此限制，则获胜者是分数最低的玩家。我们使用有关先前玩家得分的完整信息来表征游戏的多步版本中玩家的最佳策略。我们还将比较具有完整信息和没有信息的玩家的最佳策略和收益。介绍了信息价格的概念。