Bertrand competition

[3] Considering the simple framework, the underlying assumptions of the Bertrand model are as follows: Furthermore, it is intuitively deducible, when considering the law of demand of firms' competition in the market: In the Bertrand model, the competitive price serves as a Nash equilibrium for strategic pricing decisions.

Setting identical prices above unit cost leads to a destabilizing incentive for each firm to undercut the other, aiming to capture the entire market and significantly boost profits.

This lack of equilibrium arises from the firms competing in a market with substitute goods, where consumers favor the cheaper product due to identical preferences.

The Bertrand model of price competition in a duopoly market producing homogenous goods has the following characteristics: Firm

) in the Bertrand model is the mutual best response; an equilibrium where neither firm has an incentive to deviate from it.

As illustrated in the Diagram 2, the Bertrand-Nash equilibrium occurs when the best response function for both firm's intersects at the point, where

[7] This is known as the Bertrand paradox; as two competitors in a market are sufficient to generate competitive pricing; however, this result is not consistent in many real world industries.

There are various reasons why this may not hold in many markets: non-price competition and product differentiation, transport and search costs.

The Bertrand model can be extended to include product or location differentiation but then the main result – that price is driven down to marginal cost – no longer holds.

If a single firm does not have the capacity to supply the whole market then the "price equals marginal cost" result may not hold.

With capacity constraints, there may not exist any pure strategy Nash equilibrium, the so-called Edgeworth paradox.

[12] Moreover, some economists have criticized the model as leading to impractical outcomes in situations, where firms have fixed cost

[7] There is a big incentive to cooperate in the Bertrand model; colluding to charge the monopoly price,

[13] However, not colluding and charging marginal cost is the non-cooperative outcome and the only Nash equilibrium of this model.

[14] The Bertrand and Cournot model focus on different aspects of the competitive process, which has led to the model identifying different set of mechanisms that vary the characteristics of the market demand that are exhibited by the firms.

Whereas the Bertrand model assumes that the firm with the lowest price acquires all the sales in the market.

[15] Moreover, both models are criticised based on the assumptions that are made in comparison to the real-world scenario.

If capacity and output can be easily changed, Bertrand is generally a better model of duopoly competition.

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 Competition with asymmetric marginal cost.

Thomas Demuynck et al. (2019) conducted research to find out a solution in pure strategies in Bertrand competition with asymmetric costs.

[18] Ha has defined the Myopic Stable Set (MSS)for Normal-form games.

Under this situation, firm 2 can only set their price equal to their marginal cost.

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.

[19] They found that there is no huge difference when the cost asymmetry is small as there is relatively little impact on competition.

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.

[20] Firms will prefer to set their price aggressively in order to attract more customers and increase the company network.