Fixed point theorems for nonconvex valued correspondences and applications in game theory

2013/04/02 by Monica Patriche, Patriche, Monica
Computer Science · Economics, Econometrics and Finance · Mathematics · #47H10 #91A47 #91A80 #Economic theories and models #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1304.0716

openalex publication_date 2013/04/02 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *--weakly convex graph and we prove some fixed point theorems for these kinds of correspondences. As a consequence, using a version of W. K. Kim's quasi-point theorem, we obtain the existence of equilibria for a quasi-game.

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