Oskar Morgenstern, The Theory of Games (1949)

Oskar Morgenstern’s magazine article introduces game theory as a mathematical approach to economic and social behavior, moving from two-person contests to coalitions and competing social arrangements. Its central claim is stronger than an analogy between business and games: many economic interactions have the same logical structure as games of strategy. Their outcomes depend on several participants’ decisions, expectations, and efforts to conceal intentions. Rational behavior therefore cannot be understood simply as an individual maximizing a return under fixed conditions.

No single person has control of all the variables, but only of a few.

This observation grounds Morgenstern’s criticism of classical economics. Its isolated individual confronts given prices and controls the actions determining his own return; actual employers, unions, and competing firms confront other decision-makers who can frustrate their purposes. Wage negotiations involve bargaining, bluffing, and attempts to discover an opponent’s strategy. Monopoly and markets dominated by a few participants are consequently central cases, not peripheral complications. Morgenstern argues that mechanics, with its familiar notions of equilibrium and stability, supplies an inadequate model for these mutually dependent choices.

The article first develops this alternative through two-person zero-sum games, where one participant’s gain equals the other’s loss. Each seeks the greatest advantage compatible with the opponent’s attempts to prevent it: the minimax problem. Some games possess a safe pure strategy, represented mathematically by a saddle point. Discovering that strategy does not enable an opponent to defeat it. Morgenstern distinguishes the existence of such a solution from the practical ability to calculate it: chess has a pure strategy, but its enormous range of possible positions places that strategy beyond available computation.

Games such as matching pennies and poker require another conceptual move. When a predictable course can be exploited, rationality demands a probability distribution over possible actions rather than consistent adherence to one action. Morgenstern attributes the mathematical foundation of this result to von Neumann’s minimax proof.

Since the player's chief aim must be to prevent any leakage of information from himself to the other player, the best way to accomplish this is not to have the information oneself.

Randomization is thus purposeful protection, not a failure to decide. The player selects probabilities while leaving the eventual action uncertain even to himself until the decisive moment. Matching pennies illustrates the simplest case; competing manufacturers show how the same reasoning can govern sales strategies. The Holmes–Moriarty pursuit makes a further distinction between success on one occasion and the security of a strategy. Holmes’s successful escape in the story does not establish that his reasoning offers reliable protection against a strategically capable pursuer. The assigned payoffs and repeated-play calculation, rather than narrative triumph, determine the assessment.

With three or more participants, the article turns from opposing individual strategies to coalition formation. An “essential” game permits participants to gain more by combining than by acting separately. This creates questions of admission, compensation, bargaining, and the distribution of collective gains. Morgenstern interprets unions, cartels, and trusts through this structure, treating the tendency toward monopoly as a fundamental feature of economic life.

Now the important characteristic of this type of game is that there is no single "best" solution for any individual player.

In the three-person example, any pair can profit at the remaining player’s expense. A solution must therefore comprise several possible distributions rather than one uniquely optimal outcome. Morgenstern introduces “imputations,” or payment distributions, and “domination”: one distribution dominates another when it improves the position of every member of a coalition able to secure it. Distributions within a solution do not dominate one another, while every distribution outside it is dominated by one within it. Crucially, an individual distribution inside the solution can still be threatened from outside; its protection depends on the other possibilities belonging to the solution. Stability is collective and relational, not the invulnerability of a single allocation. The article acknowledges that establishing solutions for arbitrarily many players remains mathematically difficult.

This multiplicity of solutions may be interpreted as a mathematical formulation of the undisputed fact that on the same physical background of economic and social culture utterly different types of society can be established.

This is the article’s broadest interpretive move. Different solutions correspond to different standards of social behavior, while different distributions within one solution represent variations in income and privilege under a shared standard. Morgenstern extends the argument to exclusion and discrimination: coalitions may deny an outsider participation without eliminating his income entirely. Conversely, privileges formally guaranteed by the rules may become economically untenable when they conflict with accepted behavior. Game theory promises to explain such arrangements through strategic relations rather than through formal rules alone.

The conclusion tempers this ambition with computational and theoretical limits. Even radically simplified poker produces a large strategy matrix; realistic industrial competition and larger coalitions pose still greater difficulties. Military operations and selected economic problems offer promising applications, but Morgenstern does not present a finished science of economic policy.

But we must first obtain precision and mastery in a limited field, and then proceed to increasingly greater problems. There are no short cuts in economics.

The article’s relevance lies in this combination of conceptual reconstruction and methodological restraint. It relocates economic rationality within conflict, secrecy, cooperation, and negotiated distribution, while insisting that a general theory must emerge from exact analysis of tractable cases rather than sweeping philosophical claims.