The Purification Problem for Constrained Games with Incomplete Information

Name: The Purification Problem for Constrained Games with Incomplete Information
Author: Helmut Meister

Specificaties

Paperback, 127 blz. | Engels

Springer Berlin Heidelberg | 0e druk, 1987

ISBN13: 9783540184294

Rubricering

Juridisch :

Springer Berlin Heidelberg 0e druk, 1987 9783540184294

Onderdeel van serie Lecture Notes in Economics and Mathematical Systems

€ 60,99

In winkelwagen

Levertijd ongeveer 9 werkdagen

Gratis verzonden

Samenvatting

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.

Specificaties

ISBN13:9783540184294

Taal:Engels

Bindwijze:paperback

Aantal pagina's:127

Uitgever:Springer Berlin Heidelberg

Druk:0

Hoofdrubriek:Economie

Serie:Lecture Notes in Economics and Mathematical Systems

Inhoudsopgave

§ 1 The Purification Problem in the Game-Theoretic Context.- 1.1 A constrained game with incomplete information.- 1.2 The purification problem.- 1.3 On existence of approximate purifications.- 1.4 Some topological properties of the set of strategies concentrated on a correspondence.- 1.5 Theorems on existence of an equilibrium.- 1.6 On existence of pure strategy equilibrium.- 1.7 Determining approximately payoff-equivalent pure strategies.- § 2 A Market Game as a Game with Incomplete Information.- 2.1 A model of a market game with a continuum of traders.- 2.2 On the connection between core, r-core and the set of r-Walras allocations.- § 3 Some Applications to Statistical Decision Theory.- 3.1 Minimax decision rules.- 3.2 Set-valued minimax estimators.- Appensdix.- References.