Competition and market dynamics in duopoly: the effect of switching costs

Abstract

A dynamic game framework is developed to study market dynamics between two manufacturers/service providers competing on pricing and switching costs. In this game, a portion of consumers may choose to upgrade their products by repurchasing from one of the providers in each period. The switching cost is the one-time costs when consumers “switch” from one provider to another. Switching costs provide consumers an incentive to continue buying from the same firm even if its competitors offer functionally identical but incompatible products. In practice, the switching costs can be increased or decreased by firms through designing products. A mixed logit demand model, which can arbitrarily closely approximate any discrete choice behavior of consumers, is adopted to characterize the dynamic market evolution under stochastically varying consumer preferences. We find that switching costs are usually beneficial to the firm with a dominant market share. Moreover, large switching costs can be detrimental to the firm with a disadvantaged market share, so it wants to decrease switching costs. On the contrary, small switching costs have a negative effect on the demand of the firm with a weak market share but benefit its profit by leading a high price. We implement a simulation study to validate our theoretical results on market dynamics.

Appendices

Appendix A. Transition probability matrix of the relative preference

We assume that the relative preference of consumers for the follower $r_{t}^{}$ can change over periods following Markov chains. The transition of $t+1$ (the next period) depends on the current $r_{t}^{}$ with three probabilities: increasing one unit, decreasing one unit, or remaining the same. In our numerical experiment, we set $r_{t}^{}$ as a discrete variable with an upper bound 3 and a lower bound $-3$. The transition probability matrix is as follows (Table 2).

Table 2 Transition probability of $r_{t}^{}$

Appendix B. Follower dominates the market share

The situations where the follower dominates the market share are shown in Figs. 7, 8, and 9. In the exogenous switching cost scenario (Fig. 7), the results are basically consistent with the situation where the leader dominates the market share. With the improvement of consumers’ relative preference, switching costs still maintain the leader’s market share to a certain extent. Except in early periods, both firms set a higher prices with exogenous switching costs.

In the endogenous switching cost scenario (Figs. 8 and 9), both firms use a low price strategy in early periods. Without initial switching costs, the follower is more active in increasing switching costs in early periods. With initial switching costs, the willingness of the two firms to invest in switching cost drops significantly.

Fig. 7

Market share, equilibrium price, and profit trends in each period in the exogenous switching cost scenario (follower dominates the market share)

Fig. 8

Market share, equilibrium price, and profit trends in each period in the endogenous switching cost scenario (follower dominates the market share)

Fig. 9

Ratio of switching cost investments and switching cost trajectory in each period (follower dominates the market share)