Question

While there is a degree of differentiation among general merchandise retailers like Target and Kmart, weekly newspaper circulars announcing sales provide evidence that these firms engage in price competition. This suggests that Target and Kmart simultaneously choose to announce one of two prices for a given product: a regular price or a sale price. Suppose that when one firm announces the sale price and the other announces the regular price for a particular product, the firm announcing the sale price attracts$\mathbf{50}$million extra customers to earn a profit of \($\mathbf{7}$billion, compared to the \)$\mathbf{4}$billion earned by the firm announcing the regular price. When both firms announce the sale price, the two firms split the market equally (each getting an extrarole="math" localid="1657018179629" $\mathbf{25}$million customers) to earn profits of \($\mathbf{2}$billion each. When both firms announce the regular price, each company attracts only its 50 million loyal customers and the firms each earn \)$\mathbf{4}$billion in profits. If you were in charge of pricing at one of these firms, would you have a clear-cut pricing strategy? If so, explain why. If not, explain why not and propose a mechanism that might solve your dilemma. (Hint: Unlike Walmart, neither of these two firms guarantees “Everyday low prices.”)

Short answer

The two companies decide to adopt a policy like Walmart's in which both offer low prices every day (or sale price). Both firms will share the market share equally and will obtain profits of $2$$ billion each with the equilibrium (sale, sale) ($2,2$).

Step-by-step solution

Observing the data matrix

Kmart and Target retailers compete in a simultaneous one-shot game in which their weekly newspapers show two price modalities for their products, sale price and regular price. Kmart and Target simultaneously announce one of these two prices for their products to attract more customers.

The combinations of income obtained by each price modality (in billions of dollars) can be observed in the following data matrix.

Explaining why not and propose a mechanism that solve your dilemma 

The matrix explains the profits in billions of dollars that each retailer will obtain by implementing their unique simultaneous pricing strategy. If Kmart decides to apply a regular price, Target's best option is to apply a Sale price generating the first Nash equilibrium (Sale, Regular) ($7,4$). Likewise, if Kmart decides to apply a Sale price, Target will decide to apply a Regular price generating the second Nash equilibrium (Regular, Sale) ($4.7$).

Therefore, assuming that we are in charge of making Target's pricing decision, there will be no clear-cut pricing strategy. Thus, no Nash equilibrium exists where the companies obtain the maximum payoff possible.

A solution to this dilemma is that both companies decide to adopt a policy like Walmart's in which both offer low prices every day (and Sale prices). In this policy, both firms will share the market share equally and will obtain profits of $ billion each with the equilibrium (Sale, Sale) ($2,2$).