Probabilistic Economic Theory

2. The Agent Distinction Axiom.

All market agents are distinguished. The second axiom works when the first axiom fails. Thus, it defines those areas and aspects of the agents’ behavior on the markets that are the subject of the studies of other sciences of more applied nature, such as marketing, behavioral science, managerial economics, psychology, policy, etc. In other words, these social sciences are concerned with the specific nuances and peculiarities in the behavior of concrete people, agents and communities in different markets and situations, etc.

Let us stress that in economics we do not study real people, but rather the real actions of these people on markets. The people can be different but market decisions and actions of these people can be the same, depending primarily on their supplies and demands on markets. It is this fact that lies in the background of the agent identity axiom.

Hence, we will sum up everything we have stated above in the form of the five general principles of physical economics and probabilistic economic theory as follows:

1. The Cooperation-Oriented Agent Principle.

The most important concept concerning markets is as follows: every market consists of market agents, buyers and sellers, all strongly interacting with each other. There are never any mysterious forces in markets. Everything that markets do, the cooperation-oriented market agents do, and therefore only the cooperation-oriented, agent-based models can provide the reasonable and justified foundation for any modern economic theory.

2. The Institutional and Environmental Principle.

Markets are never completely closed and free; all the market agents are under continuous influences and under such external institutional and environmental forces and factors as states, institutions, other markets and economies, natural and technogenic phenomena, etc. The influences, exerted by each of these forces and factors on the structure of market prices and on the market behavior, can be completely compared with the effect from inter-agent interactions. Moreover, the action of strong external institutional and environmental factors can significantly hamper the effective work of market mechanisms and even practically suppress it in a way that results in the breakdown of the market’s invisible hand concept, well-known in classical economics. Therefore, the influence of institutional, environmental and other external factors must be adequately taken into account in the models, as well as simultaneously with the inter-agent interactions.

3. The Dynamic and Evolutionary Principle.

Markets are complex dynamic systems; all the market agents are in perpetual motion in search of profitable deals with each other for the sale or purchase of goods. Buyers tend to buy as cheaply as possible, and sellers want to obtain the highest possible prices. Mathematically, we can describe this time-dependent dynamic and evolutionary market process as motion in the price – quantity economic space of market agents acting in accordance with objective economic laws. Therefore, this motion has a deterministic character to some extent. This motion can and must be approximately described with the help of equations of motion;

4. The Market-Based Trade Maximization Principle.

On relatively free markets, the buyers and sellers consciously and deliberately enter into transactions of buying and selling with each other, since they make deals only under conditions in which they obtain the portion of profit that suits each of them. It is in no way compulsory that they aspire to maximize their profit in each concluded transaction, since they understand that the transactions can only be mutually beneficial. But they do attempt to increase their profit via the conclusion of a maximally possible quantity of such mutually beneficial transactions. Thus, it is possible to assert that the market as a whole strives for the largest possible volume of trade during the specific period of time. Consequently, we can make the conclusion that market dynamics can approximately be described and even approximate equations of motion for the market agents can be derived in turn by means of applying the market-based trade maximization principle to the whole economic system (more exactly, this principle is system-based).

5. The Uncertainty and Probability Principle.

Uncertainty and probability are essential parts of human action in markets. This is caused by the nature of human reasoning, as well as the fundamental human inability to accurately predict a future state of the markets. Furthermore, market outcome is the result of the actions of multiple agents, and no market is ever completely closed and free. For these reasons, all market processes are probabilistic by nature too, and an adequate description of all the market processes needs to apply probabilistic approaches and models in the economic price – quantity space. The uncertainty law results from this principle.

We assume that, from one side, these five general principles are capable of sufficiently and adequately describing the basic structural and dynamic properties of market economic systems and the market processes within them. From other side, they can be regarded as the basic pillars of physical economics, which carry on constructing step-by-step the bodies or frameworks of our physical economic models. These principles and their substantiation will be repeatedly discussed in more detail and step-by-step in this book. Concluding, let us stress that new probabilistic economic theory has been built on the basis of these principles in this book.

4. The Classical Economies

4.1. The Two-Agent Market Economies

As mentioned previously, below we will sequentially introduce into the theory the new concepts of physical modeling. They will be the building blocks in the construction of the body or framework of our models, which will also be filled step-by-step with new, concrete contents. We will start with the construction of the simplest physical economic models. In this paragraph we will create this with the use of analogies and formal methods of classical mechanics. These physical economic models will be referred to as the classical economies. Naturally in construction, we will use only first four principles, since only they have analogues in classical mechanics.

As we know, market agents are the buyers and sellers of goods and commodities, and as such are the major players in the market economy. They strongly interact with each other and with the institutions and the market’s external environment including other market economies. They continuously make decisions concerning the prices and quantities of good, and buy or sell those in the market. All the market agents’ actions govern the outcome of the market, which is the essence of the agent principle. We believe the agents to behave to a certain extent in a deterministic way, striving to achieve their definite market goals. This means that the behavior of market agents is, in turn, governed by the strict the economic laws in the market. The fact that these laws have until now been of a descriptive nature in classical economic theory, and they have not yet been expressed in a precise mathematic language, is not of key importance in this case. What is really important is that we believe all the market agents to act according to the economic laws of social cooperation that can be approximately described with the help of the market-based trade maximization principle.

Every market agent acts in the market in accordance with the rule of obtaining maximum profit, benefit, or some other criterion of optimality. In this respect, we believe the many-agent market economic systems to resemble the physical many-particle systems where all the particles interact and move in physical space. This is also in accordance with the same system-based maximization principle, such as the least action principle in classical mechanics which is applied to the whole physical system under study. The analogous situation exists in quantum mechanics (see below in the Part F).