Oskar Morgenstern, On Some Criticisms of Game Theory (1964)

Morgenstern’s address defends mathematical analysis of conflict and cooperation by distinguishing constructive criticism from objections founded on misunderstanding. His argument acknowledges substantial limitations: game theory supplies a selective representation of strategic interaction, not an exhaustive account of decision-making. The central methodological question is how to assess an incomplete theory without either exaggerating its powers or dismissing its achievements.

Morgenstern distinguishes game theory’s normative task—identifying optimal conduct—from its descriptive use in representing social situations. Descriptive adequacy requires both resemblance to reality and mathematical manageability.

If game theory is to be thought of in the latter sense, then it is really a model, and like all models must be looked upon as such.

This qualification governs the defense. Some decisions lie outside the theory’s scope; their existence does not invalidate its treatment of other situations. Criticism should identify the consequences of particular assumptions and omissions rather than demand that one model encompass every human consideration.

Constructive criticism, accordingly, opens problems to systematic investigation.

As for constructive criticisms: in the original work, only finite numbers of strategies were considered.

Morgenstern surveys developments involving infinite strategy spaces, communication costs, large numbers of players, alternative solution concepts, opponents’ mistakes, transferable utility, and subjective probabilities. These examples distinguish restrictions that subsequent research has relaxed from difficulties that remain unresolved. He questions whether the conventional opposition between “static” and “dynamic” adequately describes games whose extensive forms already represent sequential interaction. He also acknowledges the absence of a general existence proof for solutions to arbitrarily large n-person zero-sum games, distinguishing the proof that solutions exist from a procedure for finding them.

Experiments provide another route to development. Axiomatic utility theory offers a basis for controlled economic investigation, but responses to numbers and differently described uncertainties complicate interpretation. Experimental games remain preliminary: neither apparent confirmation nor apparent refutation justifies an immediate verdict on the theory. Experimental design and interpretation are themselves scientific problems, not transparent tests applied from outside.

The conceptual center of the rebuttal concerns rationality. Morgenstern rejects the view that game theory simply assumes rational behavior as an established psychological fact. Rather, strategic interdependence makes rationality something the theory must clarify. An actor’s outcome depends on others pursuing their own aims, while their outcomes likewise depend on that actor’s conduct. The problem is therefore to give precise meaning to rational action under mutual dependence. He similarly rejects the claim that game theory excludes non-zero-sum interaction, emphasizing its treatment of cooperation, threats, coalitions, and variable sums.

His polemic against critics also targets the use of intuition as an unexplained alternative to formal analysis.

Instead, recourse is had to exhortations, to appeal to "intuition", "experience", "judgement" etc.

Morgenstern does not deny intuition a role in inquiry. His objection is that invoking it supplies no explicit method for managing the complications a model leaves out. In two-person zero-sum theory, a major achievement is precisely to avoid making success depend on deciphering an opponent’s intentions. He likewise resists attributing immorality to the theory itself.

Looking forward, Morgenstern distinguishes current inability from demonstrated impossibility. Unsolved problems may demand new concepts; claims that they are permanently inaccessible require justification. Conversely, insisting on unique solutions may impose an unsuitable expectation on social reality. Cooperative games can admit multiple solutions containing multiple imputations. Such multiplicity may express features of social relations rather than merely expose mathematical inadequacy.

The concluding military discussion gives these methodological distinctions practical urgency. Game theory cannot furnish a decisive solution to war, but analysis of catastrophic consequences may clarify adversaries’ common interest in avoiding mutual destruction. Morgenstern’s defense remains conditional: acknowledge genuine deficiencies, pursue tractable extensions, and require proposed alternatives to explain how their judgments are reached. Formal analysis is valuable not because it abolishes uncertainty, but because it makes assumptions and reasoning available for criticism.