A trade war model

In this article, we propose a model that describes a trade war between two economic agents. The model is based on a system of two nonlinear differential equations of the first order. In this case, the economic state of each agent is described by a parameter that determines its overall economic potential and its ability to develop and wage a trade war with a competitor. The equations deployed within the model are descriptive and determine how changes in the parameters describing the agents' state depend on the current values of these parameters and the specifics of agents' "interaction" within the trade war framework. In particular, we account in the model the possibility for economic growth as well as a reduction in economic opportunities due to the actions of the competitor. Economic growth for each agent is given by a logistic-type law. The mutual influence of agents within the framework of the trade war is taken into account through a term that is proportional to the product of the values of the parameters that determine the economic state of the agents. To obtain the crucial properties of the proposed model, we determine its stationary solutions and investigate their stability. We show that, depending on the model's controlling parameters, one of two scenarios is possible. In the first scenario, one of the agents achieves its goal. Namely, the agent reaches the optimal economic state and makes the economic development of its opponent impossible, thereby terminating its opponent's activities. In the second scenario, both agents, as a result of the trade war, find themselves in a suboptimal economic state, and neither of them achieves the set goal. We use analytical mathematical estimates and numerical calculations to confirm the theoretical conclusions derived from the model.