The Purification Problem for Constrained Games with Incomplete Information

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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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.

• decision theory
• equilibrium
• incomplete information
• strategy

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

  Helmut Meister

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