Objective:

The Iranian insurance industry, particularly in motor vehicle insurance, has an oligopolistic structure in which a few large companies hold the dominant market share, while a number of smaller firms seek to increase their share through pricing and non-pricing strategies. Despite the critical importance of pricing for the financial sustainability and profitability of insurance companies, in practice, many pricing decisions are based on managerial experience, short-term competitive pressures, and regulatory constraints, and the systematic use of analytical models for determining optimal rates is rarely observed. Furthermore, previous studies have often focused on actuarial aspects or examined competition in general terms, without modeling the pricing behavior of firms within a multipolar game framework. The main objective of this research is to simulate a premium pricing model in an oligopolistic market and to investigate the effects of variables such as price elasticity, potential market demand, and support costs on equilibrium price, market share, and profit of insurance companies, in order to contribute to the scientific analysis of pricing behavior and support managerial decision-making.

Method:

The present study is a combination of game theory (simultaneous Nash game model), mathematical modeling, numerical simulation, and sensitivity analysis. The Bertrand competition model was selected, in which the demand for each insurance company is defined as a function of its own selling price and the prices of competitors. The profit function of each company was modeled as the difference between revenue from price and costs (including support costs), and using first-order conditions, the equilibrium prices were derived by solving a system of simultaneous equations in MATLAB software. The baseline scenario included three insurance companies with different elasticity coefficients, costs, and market power. A comprehensive sensitivity analysis was performed on four key parameters: the own-price elasticity coefficient, the cross-price elasticity coefficient (competitors' prices), potential market demand, and support costs. All analyses were conducted within a static game framework with complete information, no supply capacity constraints, and the assumption of simultaneous independent decision-making by the players. It was also shown that adding new firms to the model increases the complexity of the optimal solution linearly, and the model is generalizable to any number of players.

Findings:

Simulation results showed that changes in each of the key parameters have significant and sometimes nonlinear effects on equilibrium price, market share, and company profits. An increase in the own-price elasticity coefficient (i.e., a more competitive market) led to a sharp decline in equilibrium price (over 75% for the powerful company) and a dramatic drop in profit (over 99% for the weaker company), indicating that overly competitive markets are not profitable for any player. In contrast, an increase in the cross-price elasticity coefficient (competitors' prices) – indicating a "hysterical" or volatile market – allowed the powerful company to raise its price by about 6% and increase its profit by more than 15%, although this condition reflects market instability and unstable customer behavior. The most influential parameter was potential market demand; with a fourfold increase in this parameter, the offering price of the first company increased more than four times, its attracted demand increased more than four times, and its profit increased more than 27 times. Conversely, an increase in support costs, despite a slight price increase, could not compensate for the profit decline, and more than 58% of the first company's profit was eliminated. It was also found that a simultaneous increase in demand sensitivity to own price can reduce equilibrium prices and profits for some firms, and that companies must simultaneously evaluate the effects of price changes on profit, market share, and competitors' reactions.

Conclusion:

The proposed model based on game theory is an effective tool for analyzing the pricing behavior of insurance companies in oligopolistic markets and for supporting managerial decision-making. The most important managerial implications are prioritizing large and growing markets, focusing on quality competition and value-added services rather than pure price competition, reducing price elasticity by increasing customer loyalty, preventing market volatility, and rigorously controlling cost structures. It was also found that increasing prices alone cannot compensate for rising costs, and the only practical solution is cost management and productivity improvement. Given the study's limitations, including the static nature of the model, the stochastic nature of the data, and the absence of uncertainty, it is recommended that future research develop dynamic pricing models based on differential games with real and controlled data in order to enhance the accuracy and efficiency of pricing analyses. This research was financially supported by the Insurance Research Institute.