Strategic Investment and Market Integration

simplicity, we assume that the total unit-cost is independent of the strategy, i.e. ci + c2 = c. The
incumbent’s payoff is given by:

{n

ɪɪ V (^χt∖ ^xt) — ck                 global

''n¹                                                                                                    (S)

ɪɪ [v (x∕Γ>Xt) — cιq_t] + C2к — nG local
t=1

where q_t = max {x⁷f^l, k_t}. The potential competitor must incur a market-specific fixed cost A > 0
to enter market t. Let E be the set of all markets that player e will enter. Player e’s revenue
is υ (xf, xβ). The marginal capital cost is c > 0 and additive. The objective of player e is to
maximize its payoff given by eq. (8).

We shall call k_t a market commitment, if this part of the total capacity in a multi-market firm
is assigned to market t and cannot profitably be used for production of goods sold in other local
markets. A sufficient condition for market commitments is that the marginal cost to increase local
capacity is larger than the marginal incentive to increase the output in a monopoly market at the
deterring level x. We refer to this condition as (C). More precisely,

(C    C₁ > .f (^x,0)

Condition C simply guarantees that it is not profitable for player m to redistribute capacity to
a monopoly market, if entry occurs in other markets. If condition C is satisfied and condition D is
satisfied with equality, it is sufficient for player m to install a local capacity equal to the deterrence
level k_t = X and a multi-market capacity к = nx, to deter entry.

Proposition 7 If conditions C, D and S are satisfied in the fourth version of the п-market game,
Γ∏, local capacities k_t = X and global capacity k4_n = nx is sufficient to deter entry.

Proof. Entry deterrence is possible in Γ∏, due to (D). Player m will choose a local strategy and
installs capacity k_n = nx and k_t = x for t = 1,..,n. If player e enters all markets, symmetric
incentives imply that .x"f^l = x and D implies that the profit of player e is not positive. If player e
enters one market (w.l.o.g. market 1) and stays out of all other markets, the following inequality
must hold for the incumbent to deter entry

∂v             ∂     ∂V      ∖

(x, ■' (x)) + ci — — (X, 0) ≥ 0                         (10)

xι-∣                  у      xt-f        J

16

<<   14   15   16   17   18   19   20   >>

More intriguing information