Poznámka česky na konci článku.
ANALYSIS OF FINANCIAL MARKETS EVOLUTION BY UTILIZING THE THEORY OF COOPERATIVE GAMES II.
Jan Červenka, Ondřej Černík, Jiří Mihola, Radim Valenčík
We introduce a model of the financial market with two entities, either of which disposes of investment opportunities (where to invest) and investment means (what to invest). Combining a certain amount of investment means and a certain investment opportunity results in a certain yield. The current income the economic entities dispose of will be considered investment means. The future income obtained as a result of combining investment opportunities and investment means will be regarded their yield.
We shall assume that both economic entities will maximize their future yield, which means exactly the same if we say that they are going to use investment opportunities in an order depending on their profitability, i.e. the function of marginal revenue from investment opportunities (whose variable is the sum of investment means), which are available to both economic entities, is a function non-increasing in its whole domain. The functions of marginal revenue from investment opportunities of both entities are connected, whereas the minimum of one of the functions is smaller than the maximum of the second function and the maximum of the first function is bigger than the minimum of the second function, see Graph No. 1:
Graph No. 1: Supply and demand of investment means and investment opportunities
Source: Own creation
* x1, x2 - x1refer to the sum of investment means which are available to both economic entities
* y is the future yield in marginal quantities
* f(x), g(x), or g(x2 - x) non-decreasing connected functions of the marginal revenue from investment opportunities, g(x) is modified for a more suitable graphic formulation of a related situation
* Arrows on functions f(x) and g(x2 - x) express the direction how the investment opportunities available to the respective entities are gradually used, the domain of both functions is a closed interval ⟨0, x2⟩
* E1(xE, yE) is a point where f(x) = g(x) = f(x2 - x) = g(x2 - x); this point uses all investment opportunities of both entities by the level of their profitability
* The light-blue area shows the size of the maximum Pareto improvement as a result of financial market impact, where one of the entities gives up its less profitable investment opportunities and offers them to the other entity
The total yield of the first (similarly the second) of the economic entity is:
0ʃx1f(x).d(x) = x1ʃx2f(x 2 - x).d(x)
0ʃx1g(x).d(x) = x1ʃx2g(x 2 - x).d(x)
In case the price of investment means is defined by the equality of marginal revenues, i.e. f(x) = g(x), the investment opportunities of both entities will be used by the level of their profitability. The size of the compensation of the entity that offered its investment means to the second entity for the implementation of investment opportunities will be yE(xE - x1).
In terms of mathematical analysis, the problem seems to be solved. It is a task which is a specific case of water distribution problem, however, with some specifying conditions. See e.g. (Beal et al 2013), (Brink et al 2011), (Houba et al 2013).
The problem lies in the conditions that this solution is based on. Those explicitly stated will be tackled in the next chapter. Transformation of the model in the form of a cooperative game will show other prerequisites.
With a touch of an overstatement and to get a better idea of the system, we can say that the prerequisite of non-decreasing nature of functions f(x) and g(x) contains other two not quite obvious prerequisites, either of which brings us in a world of a different economic system than the one we live in.
Let us recall that we have spoken about "economic entities", intentionally to be able to interpret all our assumptions both on the example of the producer and the consumer (or even the state, in the sense of neo-classic distinction, or rather discursus which is applied during the interpretation of the mainstream micro-economy). According to the current mainstream microeconomic theory, however, the consumer does not maximize his future income, but his utility. We may regard every act of consumption as a combination of the act of consumption (completed with joyful experience) as well as act of investing in the future income (resulting in increased future income). However, this implies that the order in which the consumer acquires property is not defined solely by the marginal revenue of the future income defined by the obtained property. The related two hidden (or not quite obvious) assumptions can then be formulated (as regards the actual meaning) as follows:
1. The consumer´s decision-making is not generally defined by his preferences, but entirely by the size of the marginal revenue of the property which is acquired.
2. The utilization of investment opportunities by one economic entity, i.e. e.g. by the consumer, is not related to the utilization of investment opportunities and the yield resulting from the utilization of these investment opportunities by another economic entity. (It is impossible to restrict the possibility to utilize investment opportunities of the second economic entity e.g. by investing in a certain type of property.)
Let us have a look at both prerequisites in more detail:
a) Issue of preferences
In order to come up with a theoretical formulation of the problem of maximization of the consumer´s utility in line with his preferences, the most difficult aspect is considered the way of adequately formulating the utility in a form of a representation, i.e. issues related to the relation between the ordinal and cardinal formulation of the utility. However, the problem lies in the interpretation of the very nature and essence of the "maximization of utility". If we fix something as the source of utility, we can verify through our self-reflection that everything that helps us achieve the desired utility also brings a certain appreciable utility (in the sense of individual feeling), which can even be more intense than the obtained final utility. Whatever helps us achieve the utility may have a form of a situation we are experiencing, activities we perform and the tools we are using. Our mind operates in such a way that it transfers the joyful experience from the final achievement of the utility to the intermediation implicating the achievement of the original experience. A typical example is when a certain activity focused on obtaining the utility (e.g. fishing) becomes something we are immersed in and we start to consider our preferences. The phenomenon which can be described as the transfer of utilities to intermediating activities, means and situations implicating the achievement of the utility is not rare but omnipresent.
From this point of view, the target aspect of human behaviour may be viewed not as the "maximization of the utility in compliance with preferences", but as the maximization of the future income where the mechanism of experience is the mechanism of decision-making on the most suitable alternatives of the maximization of the current value of the future income. A mechanism which may fail sometimes, a mechanism which (even if it does not fail) is not quite precise but it is the most suitable mechanism which allows a relatively effective on-line decision-making. If we say that one maximizes his future income or the current value of the future income through mechanisms operating in his mind (connected among others with his experience), we oversimplify here. However, we do not simplify that much if we say that one maximizes his utility (viewed as a complex of experience) in compliance with his preferences. Rational decision-making then means that it can respond to changing conditions and choose such alternatives that bring about the highest value of the current income. In this context, M. Friedman (1957) regards the target orientation of consumers´ behaviour as the formation and operation of assets comprising human as well as non-human capital by the level of their profitability in order to maximize the current value of the future income. Subsequently, we can identify various types of our rationality restriction in the abovementioned sense, such as time delays, incomplete information, failure of preferences etc.
b) Issue of mutual independence during the utilization of investment opportunities by various entities. Economic theory tackled the abovementioned issue in connection with the phenomenon of the so-called position goods, see e.g. (Mlčoch 2007), (Štika 2009). Our approach views the acquisition of these goods as one of the forms of position investment, or the investment in economic position. The goal of the investment in economic position by one economic entity is to restrict the possibility to utilize investment opportunities for the other economic entity and this way to increase the yield from the implementation of one´s own investment opportunities of the first economic entity. Position investment deepens social inequality of opportunities and in some cases it results in various forms of economic segregation. Not the operation of the market (mechanisms based on free exchange), but the position investment is the cause of phenomenon called "the rich growing richer and the poor growing poorer".
Besides the position investment, there is also an opposite phenomenon – utilization of investment opportunities by one economic entity creates conditions for the creation or utilization of investment opportunities of the second economic entity. A standard example is the investment in a firm that provides job opportunities as well as opportunities to enhance the qualification of employees etc., or the investment in innovations that will launch an innovation wave and offer a room for other innovators to assert themselves.
From the methodological perspective, it is reasonable to ask whether it is meaningful to work with our "pure model” which neglects the existence of position investment, or rather it excludes it. The answer is yes. The main reason is to demonstrate the real evolutionary dynamics of financial markets.
Poznámka v češtině:
Příspěvek byl přednesen na 7. mezinárodní konferenci VŠFS na téma "FINANČNÍ TRHY V PROCESU GLOBALIZACE SVĚTOVÉ EKONOMIKY". V češtině i s poznámkami byl zveřejněn 19.-27.4.2015 na blogu:
První pokračování viz:
(Pokračování příspěvku v angličtině)