O.R. Applications
A note on price and quality competition between asymmetric firms

https://doi.org/10.1016/j.ejor.2007.03.021Get rights and content

Abstract

This paper analyzes the impact of asymmetry between firms on the outcome of price and quality competition from a microeconomic viewpoint. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. The asymmetry arises from the difference in consumers’ loyalty to each firm; that asymmetry then determines a character of differentiation between firms. Our purpose is to show how asymmetry influences competition under varying consumers’ price- and quality-sensitivity. In doing so, we extend earlier work in the area of price and quality competition. We show that in both the moderately quality-sensitive and price-sensitive markets, higher consumers’ sensitivity as well as lower consumers’ loyalty to any firm leads to intense competition, resulting in a decrease of both firms’ equilibrium profits. On the other hand, in highly quality-sensitive market, asymmetry compels the smaller firm to change its competitive strategy. In general, this is more beneficial to the larger firm, as the smaller firm’s profit tends to decline. In the worst case, the smaller firm is driven out of business under equilibrium.

Introduction

In this paper, we consider a price and quality-based competition between two firms. Consumers buy a product in consideration of not only its price but also its quality level, which is a measurable value exhibiting a “more is better” property. Under this demand structure, firms compete with each other in determining their prices and quality levels to maximize profits. Using a game theoretic approach, we investigate this competition theoretically by looking at the asymmetry between two firms that arises from differences in their consumers’ loyalty. The purpose of this paper is to analyze the competition in terms of the welfare of both firms and consumers from a microeconomic viewpoint.

From MPHPT (2003) and Matsubayashi (2007), we can see an example of price and quality competition in the real world, where Internet service providers (ISPs) compete in the emerging broadband Internet market in Japan. We recognize that in offering broadband Internet services, competing firms may employ different mechanisms from “natural” price competition. That is, consumers may very well require not only an acceptable price (user’s fee), but also a level of quality necessary for comfortable downloading of broadband contents (e.g. movies, voice, etc). This is confirmed by the results of a consumer questionnaire conducted by MPHPT (2004) in which they state that consumers consider some factors of quality level (e.g. the maximum circuit speed rate, connection rate, etc.) in making their choice of ISP. Such firms should thus consider, i.e. optimize at least two factors – price and quality level in generating profits. This action well create a “price and quality competition.”

We develop our analysis in a microeconomic framework. Specifically, our model depends on and extends that of Shaffer and Zhang (2002). They consider an asymmetry arising from a consumers’ loyalty which is defined as the minimum price differential to induce his/her from the less preferred firm. However, their work focuses on promotion strategy under price competition, and so does not consider quality – the key factor in our study.

There are a number of the microeconomic literatures in existence, which focus on price and quality competition. Specifically, the spatial competition model originated by Hotelling (1929) is one that is widely used as a model for a price–quality decision, where a customer’s “location” can be interpreted by an “ideal-point” of the consumer’s taste preference. However, the quality decision in much of the marketing literature based on the Hotelling model (e.g. Tyagi, 2000, Syam et al., 2005) is assumed to have no direct cost implications. In contrast, Banker et al., 1998, Matsubayashi, 2007 investigate a price and quality competition under a duopolistic setting, where the consumers’ demand is modeled as a linear function of price and quality levels, and the cost as a quadratic function of the quality level. Banker et al. (1998) also explore the impact of asymmetry in demand/cost structure between firms on their competition. However, since their model focuses on competition only in the highly quality-sensitive market (in terms of our paper), it is not clear how the price- and quality-sensitivity influences firms’ decisions and the resulting competition. On the other hand, Matsubayashi (2007) characterizes price and quality competition by focusing on the degree of horizontal differentiation between symmetric firms. The topics of interest here are thus asymmetry between firms due to the difference in degrees of loyalty to each firm, and the impact of it on competition under varying degrees of consumers’ sensitivity.

As previously noted, we herein extend the model of Shaffer and Zhang (2002) to a price and quality competition. That is, we consider consumers’ loyalty, which is defined as the minimum perceived price (weighted combination of the price and quality levels) able to induce them to purchase from their less preferred firm. If the degrees of consumers’ loyalty are similar between both firms, then they are symmetric and horizontally differentiated. In contrast, if they are different, then the firms are asymmetric and vertically differentiated.

With this demand structure, and the quadratical cost impact of quality-improving, we formulate a non-cooperative game, where two firms compete with each other in determining their prices and quality levels simultaneously.2 Although the timing and sequence of decisions depend on circumstances, we here concentrate our focus on a one-shot decision as a short-term strategy of both price and quality. Under varying levels of price- and quality-sensitivity of the market, the outcome of the game is characterized and the impacts of the asymmetry between the two firms on the outcome are analyzed in terms of the welfare of each firm and the consumers, i.e., the profits and the perceived price.

To understand our model, we imagine an example of a service launch by two incumbent ISPs. Both ISPs have already succeeded in creating their loyal customers by their existing services and thus they know their brand loyalties almost exactly. In such a circumstance, the demand for the new service is likely to be affected only by the ISPs’ endogenous decisions. Our demand model roughly captures such a situation. In addition, when an ISP launches a new network service, its launch price and connection rate (as capacity provisioning) as well as other information on the service are usually determined and announced simultaneously. Our one-shot game reflects a simultaneous decision by two competitive ISPs in such a situation.

We first find that, in our game, unlike the simple Bertrand price competition, a Nash equilibrium does not exist if the market is highly quality-sensitive. Under the condition where existence of the equilibrium is ensured, firms in a price-sensitive market are better off setting their quality at the lowest level resulting in a simple price competition. As seen in the usual Bertrand price competition, an increase in consumers’ loyalty to one firm relaxes the intensity of this competition and allows both firms to benefit. However, also under Bertrand competition, higher consumers’ price-sensitivity leads to intense competition, resulting in a decrease of both firms’ equilibrium profits. Indeed, the mechanism underlying these results is common to that found in our quality competition in a moderately quality-sensitive market.

In contrast, as consumers’ quality-sensitivity becomes more severe, the outcome of competition between two firms drastically changes: to cover the disadvantage of the smaller firm in improving quality, it changes its strategy to lowering both price and quality levels. However, it is obvious that this strategy cannot benefit the smaller firm. The higher quality-sensitivity becomes, the more this difference in strategies between both firms appears essential. As a result, in contrast to the case of a moderately quality-sensitive market, the larger firm benefits while the smaller firm’s profit declines. In the worst case, the smaller firm is driven out (earns zero-profit) at equilibrium. The consumers’ surpluses of both firms are also asymmetric at equilibrium; that is, the equilibrium consumers’ surplus of the larger firm increases as the market becomes quality-sensitive while that of its rival decreases.

The rest of the paper is organized as follows. Section 2 introduces our proposed model and formulates a price and quality competition between two firms as a non-cooperative game. Section 3 gives the Nash equilibrium of the game and analyzes it under varying levels of consumers’ sensitivity. Section 4 summarizes our findings. All proofs of our results are given in Appendix .

Section snippets

The model

Let p(0  p) be the price and x (0  x) the quality level of commodity A, respectively. Here, x implies a summary level of all more-is-better quality attributes of A. Consumers buy commodity A based on the perceived price w  αp  βx, where α and β are positive parameters given by a market. We assume a duopoly market consisting of two firms, 1 and 2, offering A.

We next define a consumer’s loyalty as the minimum perceived-price differential to induce him to purchase a product from the less preferred

The Nash equilibrium and its analysis

In this section, we investigate the Nash equilibrium strategies of game G. As we state the following theorem, the equilibrium is clearly characterized by the sign of T  β  αϵ, i.e., the consumers’ valuation of quality level relative to price (normalized by the variable cost of the quality level).

Theorem 3.1

The Nash equilibrium in pure strategy (pi,xi) (i=1,2) is specifically given as follows:

  • 1.

    When T < 0, the unique equilibrium is as follows:p1=3αv+2l1+l23α,p2=3αv+l1+2l23α,x1=x2=0,

  • 2.

    When T  0, the equilibrium

Conclusion

In this study, we explored price and quality competition between two asymmetric firms by utilizing a game theoretic approach. The asymmetry is assumed to arise from the difference in consumers’ loyalty to each firm, which determines a character of differentiation between them. We investigated how this influences the competition under varying levels of consumers’ sensitivity in the market. We showed that the competition can be characterized by three types of market based on levels of consumers’

Acknowledgements

We thank Barnett Parker and three anonymous referees for helpful comments. The first author is supported by the Grant-in-Aid for Young Scientists (B) 18710138 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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    Lastly, our paper also relates to research on product or market classification. Several studies (Chung & Lee, 2017; Matsubayashi & Yamada, 2008; Wang et al., 2017) classify markets into quality-sensitive markets and price-sensitive markets based on the sensitivity difference of consumers to product price and quality. In light of the effect of variable cost on product category (Berry & Waldfogel, 2010), this paper differs by classifying products into cost-type and demand-type based on how cost and demand are sensitive to product quality level.

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