Rethinking the Foundations of Statistics

ABSTRACT

This chapter explores some or the consequences of adopting a modern subjective view of probability for game theory. The consequences are substantial. The subjective view of probability clarifies the important distinction between normative and positive theorizing about behavior in games, a distinction that is often lost in the search for “solution concepts” which largely characterizes game-theory since the work of von Neumann and Morgenstern. Many of the distinctions that appear important in conventional game theory (two-person versus n-person, zero-sum versus variable sum) appear unimportant in the subjective formulation. Other distinctions, such as single play versus repetitive-play games, appear to be more important in the subjective formulation than in the conventional formulation.

The Theory of Games and Economic Behavior (von Neumann and Morgenstern, [50]) has directly and indirectly spawned an enormous body of work. Theories of games are found in several disciplines including mathematics (Lucas [26]), statistics (Blackwell and Girshick [6]), economics (Schotter and Schwodiauer [42]), political science (Riker and Ordeshook [36]) and social psychology (Miller and Steinfatt [29]).