AI 中文总结
研究问答竞赛游戏中确定回答问题最优顺序的问题，考虑主持人分配奖金预算的博弈论版本，给出三个变体，对第一个变体给出闭式解，第二个变体简化求解，第三个变体通过分析一般游戏获部分结果。
AI 中文摘要
我们考虑一种问答竞赛游戏，参赛者会面对一系列问题。每次正确回答问题就能获得奖品并进入下一题，回答问题正确的概率已知。若回答错误，获得安慰奖且游戏结束。确定已知固定参数下回答问题的最优顺序是经典问题，已有基于索引的简单解法。我们考虑博弈论版本，即游戏节目主持人可选择如何分配固定奖金预算。我们的模型受国家安全中涉及侦察任务和检查核浓缩证据的行动搜索问题以及某些调度问题启发。研究了游戏的三个变体，对应主持人分配奖金的不同方式。对于第一个变体，给出了完整的闭式解，包括均衡策略和游戏价值。将第二个变体简化为文献中已解决的游戏。对于第三个变体，通过分析具有几何结构的更一般游戏获得了部分结果。
英文摘要
We consider a quiz show game in which a contestant is presented with a sequence of questions. Each time the contestant answers a question correctly, she receives a prize and proceeds to the next question; the probability of answering each question correctly is given. If the contestant answers a question incorrectly, she receives a consolation prize and the game ends. The contestant's problem of determining the optimal order in which to answer questions, for known fixed parameters, is a classic one studied in Kadane (1969), and admits a simple index-based solution. We consider game-theoretic versions of this problem in which a game show host can choose how to allocate a fixed prize budget. Our models are motivated by operational search problems in national security involving reconnaissance missions and inspecting for evidence of nuclear enrichment, as well as certain scheduling problems. We study three variants of the game, corresponding to different ways in which the host can distribute the prize money. For the first variant, we provide complete closed-form solutions, including equilibrium strategies and the value of the game. We reduce the second variant to a game solved in the literature. For the third variant, we obtain partial results by analyzing a more general game with a geometric structure.
