Game-theoretic threshold model of the stock market

The game-theoretic model of the binary threshold collective behavior of agents who participate in the sale and purchase of a single exchange asset is considered. The agents were divided into two groups — buyers and sellers. It was assumed that for each of the agents, a threshold of acceptable price exists; for the buyer — it is the upper price at which he still agrees to make the transaction, and for the seller — it is the lower «comfortable» price. It was taken into account that the agent decides whether to participate in the transaction by comparing his threshold price with the market price. It was assumed that the market price is affected by the volumes of supply and demand in accordance with the classic supply and demand curves. Empirical distribution functions of price thresholds are constructed, which are used to characterize Nash equilibrium, and also allow to study the limit transition to an infinite number of agents in the future. A theorem on the characterization of Nash equilibrium is proved, the first part of which shows the volumes of potential supply and demand. The second part of this characterization presents the state of agents based on the volumes of supply and demand. We studied examples of the existence and uniqueness conditions for Nash equilibrium. Focal points are found among all Nash equilibria.