The theory of games provides a set of mathematical techniques for analyzing situations in which each agent’s utility depends not only on his own actions but also on the actions of others; and all of the agents take these interdependencies into account when deciding their actions. Von Neumann and Morgenstern explained the difference between a game-theoretic problem and an optimization problem of the sort more traditionally solved in economic theory, such as a single consumer’s maximization problem:
Consider now a participant in a social exchange economy. His problem has, of course, many elements in common with a maximum problem. But it also contains some, very essential, elements of an entirely different nature. He too tries to obtain an optimum result. But in order to achieve this, he must enter into relations of exchange with others. If two or more persons exchange goods with each other, then the result for each one will depend in general not merely upon his own actions but on those of the others as well. Thus each participant attempts to maximize a function (his above-mentioned “result”) of which he does not control all variables. This is certainly no maximum problem, but a peculiar and disconcerting mixture of several conflicting maximum problems. Every participant is guided by another principle and neither determines all variables which affect his interest. This kind of problem is nowhere dealt with in classical mathematics [159, pp. 10–11].