The purification problems for constrained games with incomplete information
The monograph deals with N-person noncooperative games in which players' choice of strategies is restricted by some constraining relations and some parameters of the game are not known to some players. ``Purification'' is the procedure of replacing random strategies by payoff-equivalent pure strategies. The author presents an important purification lemma, deals with special classes of strategies, considers questions of the existence of equilibria, generally and specifically in pure strategies and, finally poses some approximation problems. The results are then applied in two separate chapters to problems of market games and statistical decision problems (minimax decisions and set-valued estimators). The book is written in a rigorous mathematical language. An appendix collects necessary tools from the areas of measure and measurability theory, (convex) analysis and fixed-point theory.
scientific article; zbMATH DE number 4053393