Theory of Games and Economic Behavior

[Title Page and Chapter I Introduction]: Title page and introductory remarks for Chapter I, establishing the book's purpose to apply the mathematical theory of games of strategy to fundamental economic problems such as utility and profit maximization. [Difficulties of the Application of the Mathematical Method]: The authors discuss the historical and conceptual hurdles to applying mathematics in economics, drawing parallels to the evolution of physics. They argue that the lack of success in mathematical economics stems from vague problem formulation and inadequate empirical data rather than inherent qualities of human behavior or a lack of measurement tools. [Necessary Limitations and Concluding Remarks on Method]: Von Neumann and Morgenstern advocate for a modest approach to economic theory, focusing on precisely defined, limited problems rather than universal systems. They outline the progression of a mathematized science from heuristic analysis to rigorous theory and, eventually, genuine prediction. [Qualitative Discussion of Rational Behavior]: This section analyzes the concept of rational behavior, contrasting the 'Robinson Crusoe' isolated economy with a social exchange economy. The authors argue that while Crusoe faces a simple maximum problem, social participants face a 'disconcerting mixture' of conflicting maximum problems where they do not control all variables, necessitating a game-theoretic approach. [Variables, Participants, and Free Competition]: The authors examine how the number of participants changes the nature of economic problems, noting that combinatorial complexity increases tremendously with each additional player. They critique the Lausanne School and traditional theories of free competition, arguing that the formation of coalitions is a decisive factor that must be understood through small-number participant models before addressing large-scale competition. [The Notion of Utility and Principles of Measurement]: A detailed defense of treating utility as a numerically measurable quantity. The authors argue that if an individual can express preferences between combinations of events with stated probabilities, a numerical utility scale can be constructed. They provide an axiomatic framework (completeness, transitivity, and combining) to show that utility is a number unique up to a linear transformation, similar to temperature in physics. [Marginal Utility and Complete Information]: The authors address the role of marginal utility and the assumption of 'complete information.' They argue that many social phenomena usually attributed to 'incomplete information' actually arise from stable standards of behavior within a system of complete information, and they suggest that marginal utility's role in social exchange is more subtle than in a Crusoe economy. [Structure of the Theory: Solutions and Standards of Behavior]: This section defines the 'solution' to a game as a set of imputations representing a stable 'standard of behavior.' Because the relationship of 'domination' between imputations is intransitive, a solution must be a system of imputations that is internally consistent (no imputation in the set dominates another) and externally stable (any imputation outside the set is dominated by one inside). The authors conclude by distinguishing their static theory from potential dynamic theories and emphasizing the shift toward combinatorics and set theory in social science modeling.