连续位置收益
Continuous Positional Payoffs
AI总结：
本文研究有限有向图上确定性双人对抗性博弈中连续收益的位置确定性，证明其等价于前缀单调性，并运用归纳、不动点和策略改进三种技术给出证明，深化了对该收益结构的理解并得出算法结果。
摘要：
对于有限有向图上的确定性双人对抗性博弈，哪些收益是位置确定的？本文针对连续收益研究该问题。连续位置确定收益受关注的主要原因是它们包含多折扣收益。我们证明对于连续收益，位置确定性等价于一个称为前缀单调性的简单性质。我们使用归纳技术、不动点技术和策略改进技术这三种建立位置确定性的主要技术，给出了三个证明。这些方法的结合使我们更好地理解了连续位置确定收益的结构，并获得了一些算法结果。
英文摘要：
What payoffs are positionally determined for deterministic two-player antagonistic games on finite directed graphs? In this paper we study this question for payoffs that are continuous. The main reason why continuous positionally determined payoffs are interesting is that they include the multi-discounted payoffs. We show that for continuous payoffs, positional determinacy is equivalent to a simple property called prefix-monotonicity. We provide three proofs of it, using three major techniques of establishing positional determinacy -- inductive technique, fixed point technique and strategy improvement technique. A combination of these approaches provides us with better understanding of the structure of continuous positionally determined payoffs as well as with some algorithmic results.
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