Tarski不动点和超模对策的计算与复杂性
Computations and Complexities of Tarski's Fixed Points and Supermodular Games
摘要：
我们考虑了与完备格中不动点有关的Tarski保序函数f的两种计算模型：预言函数模型和多项式函数模型。在这两个模型中，我们找到了第一个多项式时间算法，找到一个塔斯基的不动点。此外，我们还给出了一个在预言机函数模型中判定唯一性的匹配预言机界，并证明了它在多项式函数模型中是Co-NP困难的。利用Tarski不动点定理证明了超模对策中纯纳什均衡的存在性。探讨了超模对策与Tarski不动点之间的区别，给出了超模对策中纯纳什均衡的计算结果，并证明了该均衡的唯一性.
英文摘要：
We consider two models of computation for Tarski's order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. In both models, we find the first polynomial time algorithm for finding a Tarski's fixed point. In addition, we provide a matching oracle bound for determining the uniqueness in the oracle function model and prove it is Co-NP hard in the polynomial function model. The existence of the pure Nash equilibrium in supermodular games is proved by Tarski's fixed point theorem. Exploring the difference between supermodular games and Tarski's fixed point, we also develop the computational results for finding one pure Nash equilibrium and determining the uniqueness of the equilibrium in supermodular games.
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