The Purification Problem for Constrained Games with Incomplete Information

ISBN-13: 9783540184294 / Angielski / Miękka / 1987 / 127 str.

Helmut Meister

Opis

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.

Spis treści

§ 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.