Strategic Investment and Market Integration



It can be shown that twice the capacity needed to deter entry in a single market game does not
su
ffice to deter entry in the multi-market game. For this purpose, let к be exactly twice the capacity
needed to deter entry in a single market game. Capacity
k/2 in a market without entry results
in a price which is strictly higher than the price the incumbent would set as a monopolist, if the
capacity constraint was not binding. If unilateral entry in market 1 occurs, pro
ht maximization
under the binding capacity constraint requires

^ (p™Pl)   d^ U'Γ)

(12)


dpψ    ~ dp^

It is not satished, however, if the capacity is evenly distributed between the markets. In this
case, the RHS is strictly negative and the incumbent will increase its pro
ht by setting a lower
price in its monopoly market and move some productive capacity to this market.10 Accordingly,
the resulting price in market 1 is higher. But
hrms compete in strategic complements and a
price increase by the incumbent is followed by a price increase by the entrant, which increases the
pro
ht of the entrant in equilibrium and, therefore, entry is not deterred. Hence, as in the case of
strategic substitutes, the multi-market incumbent must install more capacity to deter entry in the
multi-market game.

8 Applications

(i) Franchising and Strategic Delegation

Franchising is a long-term vertical contract between a franchisor (the incumbent) and a franchisee.
Through the contract, the franchisor collects revenues from a franchise fee as well as from the
wholesale markup. The contract allows the incumbent to strategically design the terms of the
contract in order to overcome its own incentives in the future.11 Had
held (1991) shows that in
a model of horizontal product di
fferentiation, strategically designed franchise contracts can deter
entry.

Following Hadheld (1991), we can analyze market commitments through strategic delegation
in our model. Consider a franchise contract which is a standard-form, long-term-duration contract
10It can be shown that the equality is (1/2) a(1/2) (2 + g) bp!ln + (1/4) bgp1 = a 2bpm
11This idea of strategic delegation was hrst suggested by Schelling (1980) .

19



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