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The Purification Problem for Constrained Games with Incomplete Information

  • Book
  • © 1987

Overview

Authors:
  1. Helmut Meister

    1. Fachbereich Mathematik und Informatik, Fernuniversität Hagen, Hagen 1, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 295)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-X
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  2. The Purification Problem in the Game-Theoretic Context

    • Helmut Meister
    Pages 1-58

  3. A Market Game as a Game with Incomplete Information

    • Helmut Meister
    Pages 59-81

  4. Some Applications to Statistical Decision Theory

    • Helmut Meister
    Pages 82-124

  5. Back Matter

    Pages 125-127
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Keywords

About this book

The approach presented in this book combines two aspects of generalizations of the noncooperative game as developed by Nash. First, players choose their acts dependent on certain information variables, and second there are constraints on the sets of decisions for players. After the derivation of a general (Nash)equilibrium existence theorem, some results from purification theory are used to prove the existence of an approximate equilibrium in pure strategies, that is in nonrandomized decision functions. For some types of payoff-functions and constraints, these games prove to have an (exact) equilibrium in pure strategies. The reason for considering constrained games with incomplete information is that, apart from their game-theoretic importance, they have rather widespread application. Market games with a continuum of traders as well as some statistical decision problems are covered with this approach.

Authors and Affiliations

  • Fachbereich Mathematik und Informatik, Fernuniversität Hagen, Hagen 1, Germany

    Helmut Meister

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