简单随机停止博弈：一个生成器与基准库
Simple Stochastic Stopping Games: A Generator and Benchmark Library
AI总结：
本文提出一个停止博弈生成算法及其开源实现，证明其能生成任意博弈，并提供基准集与分析，以支持简单随机博弈多项式时间算法的研究。
摘要：
简单随机博弈（SSGs）由Anne Condon于1990年提出，是随机博弈中最简单的版本，目前尚无已知的多项式时间算法。Condon证明了随机博弈可在多项式时间内归约为SSGs，而SSGs又可在多项式时间内归约为停止博弈。SSGs是所有决策均为二元且每一步移动都有已知概率分布的随机结果的博弈。停止博弈是保证终止的SSGs。针对SSGs有许多算法，其中大多数在实践中运行速度很快，但它们都缺乏多项式时间收敛的理论保证。寻找SSGs的多项式时间算法是一个活跃的研究领域。本文旨在通过使研究SSGs的图结构更加容易来支持此类研究。我们的贡献包括：（1）一个用于生成停止博弈的生成算法；（2）证明该算法可以生成任何博弈；（3）一系列可应用于停止博弈的额外多项式时间归约；（4）一个用于生成完全归约的停止博弈实例的开源生成器，附带说明并具有完整文档；（5）一组此类实例的基准集；（6）以及关于两种主要算法类型在我们基准集上表现的分析。
英文摘要：
Simple Stochastic Games (SSGs) were introduced by Anne Condon in 1990, as the simplest version of Stochastic Games for which there is no known polynomial-time algorithm. Condon showed that Stochastic Games are polynomial-time reducible to SSGs, which in turn are polynomial-time reducible to Stopping Games. SSGs are games where all decisions are binary and every move has a random outcome with a known probability distribution. Stopping Games are SSGs that are guaranteed to terminate. There are many algorithms for SSGs, most of which are fast in practice, but they all lack theoretical guarantees for polynomial-time convergence. The pursuit of a polynomial-time algorithm for SSGs is an active area of research. This paper is intended to support such research by making it easier to study the graphical structure of SSGs. Our contributions are: (1) a generating algorithm for Stopping Games, (2) a proof that the algorithm can generate any game, (3) a list of additional polynomial-time reductions that can be made to Stopping Games, (4) an open source generator for generating fully reduced instances of Stopping Games that comes with instructions and is fully documented, (5) a benchmark set of such instances, (6) and an analysis of how two main algorithm types perform on our benchmark set.
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