论文标题
Tarski的固定点和超模型游戏的计算和复杂性
Computations and Complexities of Tarski's Fixed Points and Supermodular Games
论文作者
论文摘要
我们考虑了Tarski的订单保留函数F的两个模型与完整晶格中的固定点相关：Oracle函数模型和多项式函数模型。在这两个模型中，我们都找到了第一个用于查找Tarski固定点的多项式时间算法。此外，我们还提供了一个匹配的Oracle绑定，用于确定Oracle函数模型中的唯一性，并证明在多项式函数模型中它很难。 Tarski的固定点定理证明了超模块游戏中纯Nash平衡的存在。探索超模型游戏与塔斯基的固定点之间的区别，我们还开发了计算结果，以找到一个纯净的NASH平衡并确定超模型游戏中平衡的独特性。
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.
