"In what follows I have endeavored to reduce the complex phenomena of human economic activity to the simplest elements that can still be subjected to accurate observation, to apply to these elements the measure corresponding to their nature, and constantly adhering to this measure, to investigate the manner in which the more complex economic phenomena evolve from their elements according to definite principles".

Carl Menger [2007]

This chapter describes probabilistic economic theory in sufficient detail, starting from the formulation of the most general statement of the problem to the derivation of the fundamental formulas, using the simplest model of a two-agent economy as an example. To begin with and to avoid misunderstandings and ambiguities, let us repeat once again that, according to the ideology of the physical method, probabilistic economics is a theory that is developed using formal methods of theoretical physics or, in other words, by analogy with how theoretical physics is developed, but, fundamentally, it is an economic theory rather than a physical one, since it studies the structure and dynamics of the economic world, where rules are not in any way directly related to physical laws that describe the structure and dynamics of the natural world. This is already clear from the fact that the subjects of the economic world are people and their actions in the processes of exchange of goods and services, whereas the subjects of the physical world are particles and fields, in particular atoms. And, to be definite, let us also emphasize that this new economic theory was based on the classical concept of supply and demand, that was reinterpreted in the style of modern probabilistic scientific thinking.

There is no doubt that the modern real economy is a complex, nonequilibrium, dynamic system. Therefore, it is possible and necessary to actively study its structure and dynamics in different ways and from different points of view. Our point of view is that we look at the economy mainly as a set of a huge number of intelligently thinking and dynamically acting people, each of whom is "not only homo sapiens, but no less than homo agens" [Mises, 2005]. In order to solve problems and achieve goals, these "homo agens" or, more precisely, market agents, under the influence of constantly changing life and business circumstances, are forced almost continuously to make new important decisions related to the purchase and sale of goods and services, production, marketing, logistics, personnel control, etc. Being rational, these people try to make those decisions that will bring the greatest benefit and return on the efforts made. Such rational decisions can only be made on the basis of sufficient information available regarding the factors affecting their interests and decisions. This is why people are constantly in the process of searching for and processing new market information that is important to them. But the real world is such that we never fully have sufficient and reliable information about things of interest to us, primarily because of time constraints. Moreover, due to our limited mental and technical capabilities, we are not always able to correctly process and interpret even the information that we have at the right time and in the right place.

It is our deep conviction that human nature, as well as the nature of market economic systems, is such that all our knowledge of markets is only approximate, so all market decisions can only be approximately correct and optimal. Moreover, in practice we are Explicitly or implicitly aware of this fact and take it into account in our decision-making and evaluation of its consequences. Strictly speaking, our market decisions can only be probabilistic in nature. And since, according to our view of the market economy, all economic processes and phenomena are exclusively the result of the actions of all the economic agents, it inevitably follows from all of the above that all economic processes and phenomena in the market economy are also, to some extent, probabilistic in nature. Consequently, only one step remains to draw the fundamental conclusion that the market economy is not just a complex, dynamic, nonequilibrium system, but also a probabilistic one [von Neumann and Morgenstern, 1970; Kondratenko, 2005, 2015; Mises, 2005; Waltuch, 2008; Keynes, 1921; Farjoun, Machover, 1983; Ball, 2003]. Therefore, in order to present a sufficiently complete description of such complex probabilistic systems, the corresponding economic theory should also be largely probabilistic. For this, at least, it is necessary to incorporate the concept of uncertainty and probability into economic theory at a suitable mathematical level, i.e., to develop a dynamic probabilistic economic theory that is sufficiently adequate to economic reality. Our research is devoted mainly to achieving this goal.