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.
Contents: The Purification Problem in the Game-Theoretic Context.- A Market Game as a Game with Incomplete Information.- Some Applications to Statistical Decision Theory.- Appendix.- References.
Series: Lecture Notes in Economic and Mathematical Systems
Number Of Pages: 127
Published: December 1987
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99
Weight (kg): 0.24