Probabilistic economics is based on the most well-known concept of economic theory, namely the concept of S&D. In its most general form, this concept is formulated in probabilistic economics as follows: all the main things that happen in the market depend on some specific balance of supply and demand, determined on the basis of decisions made and openly presented in the form of market orders or market quotations to buy or sell a certain amount of an asset at a certain price. And only what is determined in the market by supply and demand, expressed in this form, is the subject of the study of probabilistic economics. In this sense it can also be called S&D economic theory, and the S&D principle itself is the main element of its basis.

This is generally the most important concept, or paradigm, in respect of the markets. Here it is: every market consists of market agents, buyers and sellers, interacting quite intensively, and prone not only to competition, but also to mutually beneficial social cooperation. There are no other market forces in markets, except the forces of market agents’ interaction. All market results are a consequence of the market agents’ actions, even if their actions were strongly influenced by other factors: the state, institutions, etc. Everything that happens in markets is done by interacting market agents and therefore only agent-based models (agent action-based models or below simply action-based models) can provide a reasonable and reliable quantitative basis for any modern economic theory. And the actions of market agents in the market are exactly the issuing of bids or quotations to buy or sell, which was discussed above.

Markets are never completely closed or free. All market agents are constantly influenced not only by other agents, but also by numerous external forces and factors. These external forces and factors, playing the role of boundary conditions, give economic systems harmony, integrity and stability. The most important of these are, of course, institutions of various kinds, such as the state, trade unions, laws, innovations, etc. Just as important might be such forces and factors of the external environment as other markets and economies, including foreign ones, as well as natural and man-made processes, etc. The influences exerted by each of these forces and factors on the structure of market prices and on market behavior can be comparable to the effect of the market agents’ interaction. Moreover, the actions of strong external institutional and environmental factors can significantly both stimulate and impede effective operation of internal market mechanisms and even partially suppress effective functioning of the market as a whole. Thus, the influence of institutional and environmental factors should be adequately taken into account in models together with interaction between market agents.

Modern markets are complex non-linear nonequilibrium dynamic systems, since all market agents are in constant interaction with each other and external forces, in other words, in constant motion in search of profitable connections to buy or sell goods and services. Buyers seek to buy as low as possible, and sellers want the highest possible price. Mathematically, we can describe this time-dependent dynamic and evolutionary market process as a movement in some formal economic space of market agents acting according to objective economic laws. Therefore, this movement has a somewhat deterministic character, and the market movement itself, or the evolution of the market system, in time can be approximated by equations of motion similar to the equations of motion in physics, such as the Lagrange equations in classical mechanics or Schrödinger equations in quantum mechanics.