Is Being Unable to Change a Bad Thing?

In my laboratory, we conduct research that provides insights into various corporate strategic problems through game theory. The phrase "through game theory" is key, as we generally do not work with real-world data. Our objective is to use mathematical models and logic alone, unconstrained by past cases or data, to derive messages like, "in this situation, this is the better course of action."

I would like to discuss some specific research we have recently conducted, but first, as a preliminary step, let's consider the following problem.

Consider two companies, each planning to offer one new product. Consumers will purchase only one product, the one they prefer, based on its quality and price. The importance placed on quality versus price varies greatly among individuals. Furthermore, improving quality incurs a corresponding cost. Under these conditions, how should each company set the quality and price of its product to maximize its own profit?

Now, solving this problem with a game theory model yields the result that it is mutually rational for the companies to differentiate, with one offering a high-quality, high-price product and the other a low-quality, low-price product, and that the profit is higher for the company offering the "high-quality, high-price product" (*). This result provides a very clear understanding of the advantages of high-end products, but of course, it is contingent on the initial assumptions. If the assumptions about the distribution of consumer preferences for quality versus price or the cost structure change significantly, the results will naturally change as well. However, demonstrating something "almost obvious," such as "if there are very many price-conscious consumers, the company offering the low-quality product will have an advantage," can hardly be called an insight. Furthermore, since this is not a case study, refining the model to fit a specific reality is not the essence of the research. We must avoid needlessly complicating the model, as doing so would turn the observation of its logic into a black box.

Nevertheless, related research continues to be published. However, I noted that most studies assume that "the quality of a new product can be freely determined by bearing a cost proportional to its quality." Together with a graduate student, I developed a model that introduces a constraint here. In reality, many companies already have their own core products and develop new ones based on them. However, significantly altering the quality from that of an existing product is not easy, even if it means lowering the quality. This is due to concerns about damaging the brand image or because it can lead to a struggle with the company's own culture if various organizational changes are required. In short, "it is difficult to change." We termed this a "repositioning cost," defining it as a cost that increases with the deviation (whether higher or lower) from the quality of the existing product, and incorporated it into our new model.

Solving the model under this condition, we found that when the hurdle for repositioning is high, a company with a very high-quality existing product ends up with low profits. Despite offering a high-end product, much of the demand is captured by a low-end competitor. This is because the difficulty of repositioning prevents the company from adjusting its quality to meet market needs, resulting in an overpriced product, while simultaneously allowing a competitor to offer a reasonably priced one. The "inability to change" clearly becomes a disadvantage (see left figure).

On the other hand, when the quality of the existing product is at a more moderate level, the high hurdle for repositioning can actually work to the company's advantage. This is because it sends a message to the competitor that "I will not change," which in turn leads the competitor to lower its quality for the sake of differentiation (see right figure). The crucial thing here is to convince the competitor that you "absolutely will not change." If this message is not conveyed, it will result in head-to-head competition, and you will not be able to earn as much profit.

Of course, this series of results merely offers one insight, and how useful individuals find it for solving real-world problems will vary. However, what is truly appealing is that this approach, unbound by reality, can expand one's repertoire of diverse perspectives. By delving into underlying intentions, it can sometimes clarify the ambiguous aspects of reality that are difficult to grasp from data alone. It is also a great privilege that students can conduct research by fully utilizing the mathematical skills they have cultivated, all while contemplating the business world they will one day enter. Working closely together, we have published many papers. Looking ahead, everyone in my lab will continue to strive to contribute to the acquisition of sophisticated insights.

(*) The reason for this is that if both companies offer products of similar quality, intense price competition ensues. Therefore, in the presence of strongly price-conscious consumers, it is more profitable to target a different consumer segment than the competitor, even with smaller profit margins. Ultimately, however, the company targeting quality-conscious consumers—those who think, "I want quality even if it's expensive"—can set a higher price and earn greater profits.