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ANALYSIS OF FINANCIAL MARKETS EVOLUTION BY UTILIZING THE THEORY OF COOPERATIVE GAMES IV.
Jan Červenka, Ondřej Černík, Jiří Mihola, Radim Valenčík
The achieved result may seem too "gentle”, i.e. describing too insignificant details of financial markets operation. In our opinion, this objection is not justified. Let us recall one of the main prerequisites of the starting model. That is that the utilization of investment opportunities by one entity does not depend on the utilization of investment opportunities by the second entity. Chapter 2 points out the phenomenon of position investment, i.e. the investment in one economic entity, or players, until the restriction of the possibility of utilization of investment opportunities of the second player with the objective to achieve increase in the profitability of one´s own investment opportunities. This phenomenon may take various forms. One of the possibilities to express this phenomenon or to depict it is to dynamize our model.
We will assume that after the financial market has been used to a certain extent under a specific starting situation, as well as those investment opportunities which could not be used without the influence of the financial market, subsequently then resulting in a certain split of revenues (salaries of players), players will play another game with new starting conditions. The amount of investment means available to either of the players will change as well as the function of marginal revenue from investment opportunities that they are offered.
There is a number of situations that may arise. Either the role of position investment may grow (thus the trouble which occurs during the utilization of investment opportunities as described in Chapter 3), or on the other hand the role of expanding the area of contracts which allows a bigger utilization of investment opportunities offered to individual players. Besides, it needs to be taken into consideration that the utilization of investment opportunities by one player may expand the area of investment opportunities available to the other player. (A standard example is the creation of job opportunities, i.e. conditions for investments till the increase in the income of the future employee through acquiring housing facility in the respective area or promoted education.)
We know little of the future (some say that one-way time flow is conditioned that we do not remember future), but everyone creates a certain idea based on their past experience. This idea is then reflected in our willingness or reluctance connected with concluding contracts where one party offers investment means and demands investment opportunities, whereas the other party demands investment means and offer investment opportunities. These contracts may take various forms. They may occur in the area of investments in firms and investments in people (human capital), human relations (social capital) as well as in decreasing transaction cost of different kind or obtaining information.
The reflection of results presented in our paper and the related discussion will be led through an outline of challenges resulting from the abovementioned issues.
The issue of position investment needs to be analysed in more detail and a suitable model needs to be found which would correspond to the real process of projecting the idea of players of the future split of salaries in the decision-making of the players on the current split of salaries. The basis of this model may be the connection of the typology of different modifications of the basic (initial) cooperative game in a follow-up and context ultimate game. During the decision-making process as to whether the players will or will not accept a certain split (which is in a way an ultimate game), they anticipate the split in the follow-up cooperative game where the position investment may or may not prevail.
Subsequently, it will be necessary to specify the relationship between the position investment (resulting in one player restricting the possibility to utilize investment opportunities by the second player) and its opposite, i.e. a case where the utilization of investment opportunities by one player creates conditions for the creation and utilization of investment opportunities by the second player. This shall resolve whether and to what extent the phenomenon of trouble will manifest itself during the utilization of investment opportunities. Here, it will be necessary to investigate specific cases and to put together their full listing (if possible). E.g. to distinguish a case where the restriction or on the other hand the creation of investment opportunities of the second player through a spontaneous or intentional action of the first player.
We may formulate a hypothesis that in terms of a long-term social development there are often tendencies, where the utilization of investment opportunities by one group of players creates conditions for generating and utilizing investment opportunities by other players. At present, the fulfilment of this tendency may be related to creating conditions for the investment in human capital. As part of this long-term tendency there are also periods where for various reasons the evolution of financial markets "stutters" (among others it shows the total effect of trouble phenomena during the utilization of investment opportunities) and where the position investment starts to prevail, leading to the culmination of social conflicts.
From this perspective, the solution to the cooperative game modelling the financial market may be found in the idea that the investment opportunities available to both players are used by the level of their profitability, i.e. such a solution where the players do not anticipate the influence of position investment and prefer the utilization of all current investment opportunities to the maximization of their own income. The reason is that there are prevailing positive effects of creating conditions for mutual generating and utilizing investment opportunities among players.
There are also other solutions to the cooperative game which is used to model the financial market. They correspond to different stages of the financial market development, or to excesses that occur on this market. These solutions can also be described through a relevant system of axioms which corresponds to one of the "possible worlds”. The formulation of the real issues this way is most contributive as we can anticipate the continuity of the real world. In this context, the comparison of prerequisites on which different models are based is priceless for the understanding of real development tendencies in the area of financial markets.
So far we have discussed only two economic entities, or rather players. Most tasks can easily be generalized to more players, which we decided not to do in order to ensure simple interpretation. There are also some tasks that need to take into account the possibility of the formation of coalitions and their influence on the split of salaries. However, these tasks belong to a relatively separate area of research and applications.
Financial markets modelling through the apparatus of mathematical analysis can be transformed in the form of several types of cooperative games. This form helps to highlight certain significant aspects of their functioning. It involves cooperative games with transferable utility, some of which may have the form of Nash bargaining solution (S, d) and some are similar to the water distribution problem (water-problem). The choice of the adequate model is directly connected with the interpretation of what we want to express and what task is being solved. The trouble phenomenon plays a significant role during the utilization of investment opportunities.
The apparatus, which we have developed, allows to present the issue of the operation and evolution of the financial markets as part of a more general type of tasks that focus on the solution to the issue of social wealth split. The comparison of this apparatus with other approaches (including those and especially those that are applied as part of the theory of cooperative games) allows to identify some of the current key problems.
From the methodological perspective, this outlined approach delivers significant information concerning the solution to real problems by utilizing the methods of different levels of abstraction and transitions among them.
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:
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