It can be shown that twice the capacity needed to deter entry in a single market game does not
suffice 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, proht maximization
under the binding capacity constraint requires
dπ^ (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 proht 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
proht 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 Hadheld (1991) shows that in
a model of horizontal product differentiation, 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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