Market Entry and Market Partition

Abstract

This chapter, which is based on (Forrest et al. 2017), investigates market entry of small firms and market characteristics that motivate such firms to penetrate markets. By emphasizing firm scales, this chapter provides a dynamic picture of entrant-incumbent relations and conditions on how, when, and where small entrants will penetrate markets. Conceptually, this chapter generalizes and unifies both resource partitioning and mutual forbearance theories into one with much increased utility for applications. It is shown that (1) penetration into markets is possible only when smaller entrants solidify large incumbents’ positions while target niches large incumbent firms cannot occupy, (2) market evolution can be measured by either integration or modularity of the large incumbents, etc.

Appendix: Proofs of Theorems

The Proof of Theorem 4.1

(⇒, the neccessity) Suppose that by randomizing its price over the interval [0,1] between its marginal costs and the reservation value for a loyal consumer to make his/her purchase from his/her firm, a micro firm enters into the oligopoly market occupied by m incumbent firms. Without loss of generality, let us treat these firms collectively as one aggregate firm, because these m firms are in a state of mutual forbearance. So, the magnitude of the consumer surplus must satisfy β = 1 − α > 0. And if β = 1 − α ≤ α/m, then Theorems 3.4 and 3.5 jointly imply that the entrant will be a firm that is as large scale as any of the incumbent firms. So, we conclude that 0 < β = 1 − α ≤ α/m.

(⇐, the sufficiency) Assume that the consumer surplus satisfies 0 < β = 1 − α ≤ α/m. Firstly, let α₀ be a real number so that β = 1 − α > α₀ > 0, and α = ℓα₀, where ℓ is a large natural number, indicating that the market has been largely taken by the incumbent firms.

Secondly, let us imagine that the aggregate firm is divided into ℓ many identical “firms,” namely, i, i = 1, 2, …, ℓ. Each of them provides consumers with identical products and enjoys the market share α₀ = α/ℓ of loyal consumers. These imaginary firms compete over the switchers with adjustable prices. Because these imaginary firms are really equal partitions of the same aggregate firm, they have the same constant marginal cost, which is set to 0 without loss of generality; the managements of these firms are fully aware of the pricing strategies used by all the firms (because the firms are managed by the same administrative unit), and they establish their best, identical responses by playing the Nash equilibrium through their unified self-analyses.

Thirdly, these ℓ imaginary firms do not have any symmetric pure strategy Nash equilibrium. (For the setup here, there is no need to consider asymmetric pure strategy Nash equilibrium, because all these imaginary firms take identical actions.) In fact, for any symmetric pure strategy portfolio (x₁, x₂, …, x_ℓ), where x_i = x_j, for i, j = 1, 2, …, ℓ, a randomly chosen Firm j (∈{1, 2, …, ℓ}) can slightly lower its price from x_j to ${x}_j^{\prime}$ to produce additional profits for all the firms as long as ${x}_j^{\prime}\beta >\left({x}_j-{x}_j^{\prime}\right)\alpha$, which is possible to do by adjusting ${x}_j^{\prime}$ sufficiently close to x_j. So, (x₁, x₂, …, x_ℓ) is not a Nash equilibrium. Even so, (Forrest et al. 2017b) show that these ℓ firms do have a symmetric mixed strategy Nash equilibrium.

For the rest of this proof, it is similar to the sufficiency proof of Theorem 3.4. So, all the details are omitted. QED