3.1 - Subjective Probability and the Theory of Games

Summary

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.

…“Probability has often been visualized as a subjective concept more or less in the nature of an estimation. Since we propose to use it in constructing an individual, numerical estimation of utility, the above view of probability would not serve our purpose. The simplest procedure is, therefore, to insist upon the alternative, perfectly well founded interpretation of probability as frequency in the long run.”

von Neumann and Morgenstern [50. p. 19

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]).