Oskar Morgenstern, Game Theory

Oskar Morgenstern’s encyclopedia entry “Game Theory,” originally published in 1973 and supplied here in a republication of undocumented date, presents strategic interaction as the basis for a distinctive mathematical science of human decisions. Its nine sections move from decision-making and historical antecedents through utility, modeling, rationality, and the relation between prescription and description to technical concepts, applications, and philosophical implications. The central argument is that interdependent choices require concepts fundamentally different from those appropriate to an isolated individual maximizing a quantity under his own control.

The historical survey distinguishes the analysis of chance from the analysis of strategy. Probability theory arose from gambling, but uncertainty about an impersonal outcome differs from uncertainty generated by independent agents pursuing their own purposes. Morgenstern traces scattered anticipations through Leibniz, Waldegrave, and others before identifying von Neumann’s 1928 minimax theorem and their joint Theory of Games and Economic Behavior (1944) as decisive developments. This history emphasizes the distance between recognizing that life resembles a game and constructing a rigorous theory of that resemblance.

Utility supplies the numerical medium needed to compare outcomes that cannot simply be measured in money. Combining ordered preferences with probabilities yields utility defined up to a positive linear transformation. Morgenstern separates this construction from the additional assumption that an individual seeks to maximize utility, and distinguishes it from older economic utility theories and philosophical utilitarianism. Experimental tests matter because the axioms and their treatment of risk invite empirical investigation.

The modeling argument rests on the structure of interaction rather than a loose analogy with recreation:

It is the entirety of the actions of the players—and of chance if nature intervenes—which determines the outcome and the equilibria (which the theory is to determine).

Unlike physical bodies, agents cooperate, conceal information, bluff, and oppose one another’s purposes. Morgenstern therefore challenges the borrowing of mathematical forms from mechanics. His criticism of competitive economics is particularly sharp: replacing strategically consequential participants with innumerable individually powerless agents removes the interaction requiring explanation. Oligopolies, political parties, and states instead make the small-number problem unavoidable.

This distinction changes the meaning of rationality. Maximization under complete control cannot simply be transferred to situations in which another person controls some of the decisive variables.

Rational behavior is not an assumption of that theory; rather, its identification is one of its outcomes.

The theory assumes a preference for greater advantage, but must establish which conduct realizes that preference under strategic dependence. It consequently has both normative and descriptive uses: it recommends strategies while explaining patterns that may already have emerged through experience. Its dissemination also changes its subject matter. People can alter their conduct after learning the theory, producing feedback between social knowledge and social events.

The longest section develops games through rules, players, payoffs, information, and strategies understood as complete plans of action. In two-person zero-sum games, a saddle point permits optimal pure strategies; without one, disclosing a definite choice can expose a player to exploitation. Mixed strategies answer this difficulty by assigning probabilities to available pure strategies. The minimax theorem establishes an optimal randomized strategy protecting the player’s expected payoff against the opponent.

In games of chance the task is to determine and then to evaluate probabilities inherent in the game; in games of strategy we introduce probability in order to obtain the optimal choice of strategy.

Randomness here is an instrument of rational conduct, not merely an external disturbance. Morgenstern also distinguishes proof of an optimal strategy’s existence from the practical ability to compute it.

Coalition formation introduces a different kind of indeterminacy. Agreements and side payments make the distribution of collective gains itself contested. Rather than identifying one universally superior allocation, Morgenstern explains stable sets of “imputations”: allocations that do not dominate one another but collectively dominate allocations outside the set. Stability belongs to this pattern of proposals and counterproposals, not to an isolated settlement resembling a physical equilibrium. Multiple stable sets may exist; Lucas’s example of a game without a solution further qualifies their availability. Morgenstern treats nonuniqueness as a substantive feature of social organization, not simply a theoretical failure, and regards Pareto optimality as insufficient to capture it.

The applications section surveys statistics, economics, voting, negotiation, military conflict, ethics, and biology. It distinguishes games that model interacting agents from uses of game-theoretic mathematics as a technique through formal correspondence. Throughout, computational obstacles, problems of quantification, and developing concepts temper the claims of practical usefulness.

The philosophical conclusion joins mathematical ambition to resistance against a final blueprint for society:

Every social theory must therefore be dynamic, proceeding from one formalism to another.

People invent new games and institutions, while coalitions can transform formally equal opportunities into unequal arrangements. Morgenstern’s concluding claim is therefore that rigorous axiomatization must coexist with conceptual revision. Game theory’s relevance lies in making rationality, information, cooperation, and uncertainty more precise without promising either a uniquely best social order or a complete formalization of human affairs.