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.

翻译：简单随机博弈（SSGs）由Anne Condon于1990年提出，作为随机博弈中最简单且尚无已知多项式时间算法的版本。Condon证明，随机博弈可多项式时间归约为SSGs，而SSGs又可多项式时间归约为停止博弈。SSGs是所有决策均为二元且每次移动具有已知概率分布的随机结果的博弈。停止博弈是保证会终止的SSGs。目前存在多种针对SSGs的算法，其中大多数在实践中运行迅速，但均缺乏多项式时间收敛的理论保证。寻求SSGs的多项式时间算法是当前活跃的研究领域。本文旨在通过简化SSGs图结构的研究来支持此类探索。我们的贡献包括：（1）一种停止博弈的生成算法；（2）证明该算法可生成任意博弈；（3）列出可施加于停止博弈的附加多项式时间归约；（4）一个开源生成器，用于生成完全约简的停止博弈实例，附带使用说明及完整文档；（5）一组此类实例的基准测试集；（6）分析两种主要算法类型在基准测试集上的性能表现。