Probabilistic Theory of Stock Exchanges - страница 32

) seeking to bargain for the best terms for themselves in concluding a deal and achieving market goals. Let us note that in reality the actions of market agents include the procedures of concluding final deals along with quotations, but these procedures are automatically accounted by means of changing quotations by market agents after the conclusion of deals. Therefore, there is no need to Explicitly include the procedure of concluding transactions in the structure of agents' actions, it is enough to take into account only the quotation process in the course of trading.

Fig. 1.3. Diagram of buyer and seller trajectories. The dynamics of the classical two-agent market economy in the economic space of price (a) and quantity (b) is depicted. Together, both parts of the figure represent the evolution of the economy over time in two-dimensional PQ-space.

This whole trading process, or simply bargaining, can be interpreted as a dynamic business exchange game between buyer and seller with the purpose of making a profit or achieving some other goal.

Let’s suppose that the negotiations went well and ended with the conclusion of a sale and purchase deal at time t_>1^>E. This means that at that moment in time the values of prices (p^>D(t) and (p^>S(t)) and quantities (q^>D(t) and (q^>S(t)) in the quotations become equal, since obviously only specific mutually agreed price р_>1^>Е and quantity q_>1^>Е of goods can be specified in the contract. Let us assume that in this bargaining model it makes some sense to call these price and quantity values the market price and quantity of the commodity and to assume that the market itself comes to or reaches its equilibrium state at these price and quantity values. Formally, this is described using the following equations for the market price and quantity:

So, for the two-agent model we obtained this trivial but significant result: the very fact of reaching equilibrium makes it possible to conduct a transaction and maximize the volume of trades in monetary terms. In this simple case the conclusion is quite obvious: no agreement, no equilibrium, no transaction, trading volume is zero. But we will further show that this conclusion has a rather universal nature, which agrees with the postulated trade volume maximization principle. By the way, it is easy to show that in the framework of the neoclassical theory the maximum trade volume in natural terms, i.e. the maximum quantity of traded goods is reached at the equilibrium point.