Modeling interactions between institutions of housing markets based on nonlinear functions of costs

Objective: to study the optimal pricing strategies of firms in the “realtor - bank - insurer” system under nonlinear cost functions.Methods: game theory, supply chain coordination, multi-criteria optimization. Results: the housing market is one of the most dynamically developing segments of the economy. Pricing patterns in this market are not always subject to market laws, since they are influenced by other factors, such as the availability of loans, the presence of agents, the rates in the insurance market, etc. To analyze the pricing processes, the authors consider a vertically integrated system of interaction of agents “realtor - bank - insurer”. A system of optimality conditions for housing market agents (realtor, bank, and insurer) under nonlinear cost functions is derived, corresponding to different types of scale effects. The results of numerical experiments are presented, showing the nature of price interdependencies in these markets in cases of convexity or concavity of the agents’ cost functions.Scientific novelty: in contrast to the “realtor - bank - insurer” system with linear cost functions, our study demonstrates the following insights: first, if all agents have concave cost functions, then the housing price, mortgage interest rate, and insurance rate are lower compared to the situation in which agents have convex cost functions; second, an increase in the intra-system commission rate leads to an increase in the price of the agent who pays the commission, and a decrease in the price of the agent who receives it; third, an increase in the commission rate causes a sharper reduction in the agent’s price if the agent has a convex cost function and the counterparty has a concave one, than in the opposite case.Practical significance: the results can be applied in the elaboration of state programs for the development of the housing market, mortgage subsidies and regulation of the insurance market; in addition, on the basis of our recommendations, firms in the “realtor - bank - insurer” system can make mutually beneficial decentralized decisions.

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