What is the place of choice in equilibrium theory? Alfred Marshall and Leon Walras, who introduced competitive equilibrium theory, employed the theory of choice in terms of utility, analogously to the Austrian school. Enrico Barone and Karl Gustav Cassel (the latter introducing general equilibrium theory in the German speaking world. Walras-Cassel System) used demand and supply functions as starting data, disregarding the theory of choice. Pareto, on the one hand, argued that the two approaches are compatible. However, he discarded cardinal utility introducing the notion of preferences, i.e. ordinal utility, as sufficient foundations for the theory of choice, thus starting the modern analysis of choice. Pareto also suggested that these data can be derived directly from choices, so short-cutting the theory of choice (since choices are not to be explained) and anticipating the theory of revealed preferences. This theory is, perhaps, the point of maximal distance between equilibrium theory and the Austrian school. On the other hand, Pareto’s theory of economic efficiency, or Pareto-optimality, and all analysis connected with it (such as, for example, the theory of the core of an economy) requires at least individual preferences, an element which underlies choices and helps to explain them.
What was presented above is the present state of competitive equilibrium theory. Demand and supply functions are sufficient for determining prices and equilibrium allocations. These functions represent choices. In other words, theory of choice is not necessarily an integral element of competitive equilibrium theory, only a prerequisite. However, individual preferences and the theory of choice are required in order to define Pareto-optimal allocations and demonstrate the two theorems of welfare economics. Competitive equilibrium studies the compatibility of price-taking agents’ choices. Thus, it concerns choices without representing a theory about them. Nevertheless, such a theory is required if statements on Pareto-optimality and other relevant characteristics of competitive equilibrium are to be made.
In similar terms, the theory of choice is required by non-competitive equilibrium theory as well. For instance, game theory deeply analyzes strategic choices and in every non-competitive market equilibrium price-making agents’ choices have to be analyzed to a certain extent. However, this analysis differs from that given by the Austrian school. The difference lies in the aim of the two approaches. While the Austrian school is interested mainly in individual choices and their implications in as much as according to the famous Robbins’s definition, “economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses”, equilibrium theory, including game theory, is interested mainly in the compatibility of choices. That is, equilibrium theory is not so much a theory of intentional actions as a the theory of intentional interactions. The two approaches overlap but do not coincide, even if they share the same vision of society and main assumptions about the behavior of its components.
Maffeo Pantaleoni did not accept Pareto’s new theory of choice. He continued to follow the Jevons-Menger-Walras hedonistic approach to utility and he identified economic theory with the theory of subjective value. Probably, there was a courious change of position beteween Pantaleoni and Pareto about the political significance of economic theory. On the hand, Pareto was initially reluctant to accept Walras’s economic theory (introduced to him by Pantaleoni) because he was too liberal for sharing Walras’s socialism. In fact, he accepted Walras’s economic theory, not at all Walras’s political and philosophical view. On the other hand, Pantaleoni seems to have refuted Pareto’s new theory also because of its focus on equilibrium instead of individual choice. This would limit the liberal doctrine he envisaged strictly connected to economics as the theory of the individual choice.
For instance, let us take into consideration the theory of non-cooperative games. Its focus is on strategic interdependence, i.e. those situations in which each agent chooses their action knowing the result also depends on the actions of other individuals and that those actions as well generally depend on theirs. Individual action (for better clarity, plan of actions, or strategy) is not simply determined selecting the option that maximizes one’s utility from the set of actions available to each agent. The agent under consideration knows that other agents actions could prevent him from performing their optimal action and reaching the desired result. Individual equilibrium actions are determined simultaneously, i.e. we can generally determine the choice of an individual only by determining also the choices of all other individuals. Both the Austrian school and (competitive) equilibrium theory isolate the individual agent’s choice. However, while the Austrian school does not analyze the compatibility of the actions chosen by individuals (compatibility is presumed), competitive equilibrium theory analyzes interactions, although those among price-taking agents are rather weak. Interaction is predominant in strategic situations, where choices cannot be analyzed without taking interdependence explicitly into account.