Games and Decisions

Games and Decisions. Published in 1957 by R. Duncan Luce and Howard Raiffa, this seminal work provided the first comprehensive synthesis of game theory and decision theory. It systematically organized the field's developments from foundational works like John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior. The book became an essential text, bridging mathematical theory with applications in the social sciences.

Introduction to game theory

The book's introduction frames game theory as a formal study of strategic interaction among rational decision-makers. It builds upon the axiomatic foundation for utility theory established by von Neumann and Morgenstern, which provides a mathematical basis for modeling preferences. Luce and Raiffa carefully distinguish between games of strategy, where outcomes depend on the choices of multiple agents, and decisions under uncertainty, such as those against Nature. They credit early influences like Émile Borel and the pivotal work of John Nash on Nash equilibrium.

Types of games

A major contribution of Games and Decisions is its detailed taxonomy of strategic situations. It classifies games based on the number of players, such as two-person or n-person game models. A critical distinction is made between zero-sum games, epitomized by games like poker, and non-zero-sum games, which allow for mutual gain or loss. The text explores cooperative games, where binding agreements are possible, versus non-cooperative games, where they are not. It also analyzes structures like extensive-form games, represented by game trees, and normal-form games, represented by payoff matrices.

Solution concepts and equilibrium

The work rigorously examines various proposed solutions for predicting game outcomes. Central to its analysis is the Nash equilibrium, a state where no player can benefit by unilaterally changing strategy. It discusses refinements and related concepts like the minimax theorem for zero-sum games, proven by von Neumann. For cooperative games, it analyzes solution concepts such as the core, the Shapley value, and the von Neumann–Morgenstern stable set. The book also delves into dynamic solutions for sequential games and the challenges posed by games with multiple equilibria.

Applications in economics and social sciences

Luce and Raiffa championed the application of game-theoretic models to real-world problems in economics and political science. They explored its use in understanding oligopoly competition, akin to the Cournot competition model, and bargaining scenarios. In political science, the framework was applied to analyze voting systems, coalition formation in bodies like the United Nations Security Council, and arms race dynamics during the Cold War. The book suggested applications in sociology for studying social norms and in operations research for logistical planning.

Criticisms and extensions

The authors themselves provided a notable critical chapter, "Critique of the Theory," acknowledging limitations of the standard rational-actor model. They highlighted puzzles like the Prisoner's Dilemma, where individual rationality leads to collectively poor outcomes, and issues of indeterminacy in bargaining. These critiques paved the way for future extensions, including behavioral game theory, which incorporates findings from psychology, and evolutionary game theory, inspired by models in biology. Subsequent experimental work at institutions like the RAND Corporation tested the book's theoretical predictions, leading to new research in experimental economics. Category:Game theory books Category:1957 non-fiction books Category:John Wiley & Sons books