The purification problems for constrained games with incomplete information
type: Item
instance of: scholarly article
title: The purification problems for constrained games with incomplete information
zbMATH Open document ID: 0645.90101
author: Helmut Meister
published in: Lecture Notes in Economics and Mathematical Systems
publication date: 1987-01-01T00:00:00Z
review text: The monograph deals with N-person noncooperative games in which players' choice of strategies is restricted by some constraining relations and some parameters of the game are not known to some players. ``Purification'' is the procedure of replacing random strategies by payoff-equivalent pure strategies. The author presents an important purification lemma, deals with special classes of strategies, considers questions of the existence of equilibria, generally and specifically in pure strategies and, finally poses some approximation problems. The results are then applied in two separate chapters to problems of market games and statistical decision problems (minimax decisions and set-valued estimators). The book is written in a rigorous mathematical language. An appendix collects necessary tools from the areas of measure and measurability theory, (convex) analysis and fixed-point theory.
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 91A35
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91A80
zbMATH DE Number: 4053393
zbMATH Keywords: constrained games
zbMATH Keywords: incomplete information
zbMATH Keywords: N-person noncooperative games
zbMATH Keywords: Purification
zbMATH Keywords: existence of equilibria
zbMATH Keywords: market games
zbMATH Keywords: statistical decision problems
zbMATH Keywords: minimax decisions
zbMATH Keywords: set-valued estimators
zbMATH Keywords: measurability theory
zbMATH Keywords: fixed-point theory
reviewed by: Andrzej Wieczorek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4053393