偏序不动点理论下互替策略博弈比较静态分析

商业研究

偏序不动点理论下互替策略博弈比较静态分析

李兴昌，田仕芹

（常熟理工学院数学与统计学院，江苏常熟 215500）

收稿日期:2018-03-16 出版日期:2018-11-10
作者简介:李兴昌（1976-），男，山东日照人，常熟理工学院数学与统计学院副教授，理学博士，研究方向：非线性泛函分析、博弈论；田仕芹（1977-），女，山东日照人，常熟理工学院数学与统计学院讲师，教育学博士，研究方向：教育经济学、博弈论。
基金资助:
国家社会科学基金“序方法与一般经济均衡存在性问题的研究”，项目编号：13CJL006。

Comparative Static Analysis of Games with Strategic Substitute under Partial Order Fixed Point Theory

LI Xing-chang,TIAN Shi-qin

（School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500,China）

Received:2018-03-16 Online:2018-11-10

摘要/Abstract

摘要： 在互替策略博弈中，每个局中人对其他的局中人行为的最佳反应收益是递减的，增映射的塔尔斯基不动点定理对此问题已经无能为力，这给研究非合作互替策略博弈中 Nash均衡的比较静态分析带来了困难。本文通过引入锥确定偏序关系，利用锥理论研究了实 Banach 空间上一类减映射不动点比较静态分析问题，得到了映射在当前存在不动点条件下, 当参数增加时，仍会存在较大不动点，并且该结果降低了对空间凸性、紧性和格结构的要求。运用这一新方法，本文证明了非合作互替策略博弈中Nash均衡存在的比较静态分析，该问题对局中人的策略空间没有紧性和格序结构的要求。

关键词: 减映射, 互替策略博弈, Nash均衡, 锥

Abstract: In the cooperative game with strategic substitute,the best-response of each player is decreasing in actions of the other players. The famous Takisi fixed point theorem of the increasing mapping can do nothing about it. It brings difficulties to the study of comparative statics for Nash equilibrium in the cooperative games with strategic substitutes.The paper studies the comparative statics of a decreasing mapping by cone theory and some fixed point theorems are obtained.The result reduces the convexity, compactness and lattice structure of space. To demonstrate the applicability of our result, we apply it to study a problem of comparative statics for Nash equilibrium in the cooperative games with strategic substitutes. This result has no the requirement of convexity, compactness and lattice structure.

Key words: decreasing mapping, games with strategic substitutes, Nash equilibrium, Cone

李兴昌，田仕芹. 偏序不动点理论下互替策略博弈比较静态分析[J]. 商业研究.

LI Xing-chang,TIAN Shi-qin. Comparative Static Analysis of Games with Strategic Substitute under Partial Order Fixed Point Theory[J]. 商业研究.

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