2 - One-Person Games

Abstract

This chapter focuses on the existence of one-person games in which a solitary decision maker is pitted against nature. Analyses of these games are based on ideas that crop up in the solution of more complicated games involving two or more decision maker. The superficially plausible principle of maximizing expected monetary value has been seen to lead to difficulties. The chapter presents the worst of these difficulties, which can be overcome through von Neumann and Morgenstern's utility theory. A method is outlined of assigning numerical utilities on an interval scale of measurement to games whose outcomes are essentially qualitative in character. Various suggested principles of solution—the principle of insufficient reason, maximax, maximin, and minimax regret—are discussed in the chapter and all are found to violate intuitive notions of common sense in certain cases, although the last two are found to have some merits.