User:AndrewLeung920/Bertrand competition

Bertrand Competition with Asymmetric marginal costs
In Bertrand Competition, we have made several assumptions, for instance, each firm produces identical goods and cost. However, this is not the case in the real world because there are a lot of factors that lead the cost of different firms to become slightly different like the cost of renting and the larger scale of the firm can enjoy economies of scale. Thus, different researchers tried to investigate the result of Bertrand Competiton with asymmetric marginal cost. According to the experiment from “Bertrand competition with asymmetric costs: Experimental evidence”, the author found that there is a negative relationship between the level of asymmetry in the cost and the price set by the firms (J Boone, et al, 2012). It means that firms have different incentives to set their prices.

Thomas Demuynck et al. (2019) conducted research to find out a solution in pure strategies in Bertrand competition with asymmetric costs. Ha has defined the Myopic Stable Set (MSS)for Normal-form games. Suppose there are two firms, we use C for the marginal cost, C1 stands for the marginal cost of firm 1 and C2 stands for the marginal cost of firm 2. From the result, there are two cases:

C1 = C2 = C

This is the case of the basic Bertrand Competiton which both firms have the same marginal cost. From the figure, MSS has illustrated that there is only one unique point that both firms are going to set their price. It is the pure strategy of Nash equilibrium.

C1 < C2

It means that the marginal cost of Firm 2 is higher than the marginal cost of Firm 1. Under this situation, firm 2 can only set their price equal to their marginal cost. On the other hand, Firm 1 can choose its price between its marginal cost and Firm 2’s marginal cost. Thus, there are a lot of points for Firm 1 to set its price.

As you can see, Firms may not set their price equal to their marginal cost under asymmetric costs, unlike the standard Bertrand Competition Model. From the situation, firms with the lower marginal cost can choose whatever they want within the range between their marginal cost and other firms’ marginal costs. There is no absolute answer to which price they should set, it is just based on different factors, for example, the current market situation.

At the same time, Subhasish Dugar et al. (2009) conducted research about the relationship between the size of cost asymmetry and Bertrand Competition. They found that there is no huge difference when the cost asymmetry is small as there is relatively little impact on competition. However, the lower-cost firm will undercut the price and capture a large market share when the size of cost asymmetry is large.

Bertrand Competiton with Network effects
Also, the standard Bertran Comepetion also assumes that all consumers will choose the product from the firm with a lower price and the firm can only set their price based on their marginal costs. However, it is not perfectly correct as the theory did not mention the network effects. Consumers will buy a product based on the number of other consumers using it. It is very rational, like when you purchase sports shoes, most of us will prefer Nike and Adidas. As they are relatively huge brands and both of them have a strong customer network, we will have a certain confidence guarantee with many people are using their products.

However, Christian and Irina (2008)found a different result if the market has a network effects. Firms will prefer to set their price aggressively in order to attract more customers and increase the company network. Masaki (2018) also mentioned firms can gain a larger customer base by setting their prices aggressively and they will attract more and more customers through network effects. It creates a positive feedback loop. As you can see, firms are not only setting their price blindly but also willing to gain a larger customer network.