Strategic Investment and Market Integration

to enter market t, the players will choose x™ and xf simultaneously. If player e decides to stay
out, monopoly will prevail in that market. At the end of the second period, all markets clear and
payoffs are distributed to player m and player e.

The incumbent’s payoff is given by eq. (1). Entry in market t is associated with a market-
specific fixed cost A > 0 for player e. Let E be the set of all markets that player e will enter.
Player e’s partial revenue, in a market it enters, is υ (xf, x™). The per-unit capital cost is c > 0.
The objective of player e is to maximize its total payoff:

π^e (x1, ..,χ",χT, .∙,xjΓ) =        (x_t^e, xΓ) — '■ — A)                       (8)

t∈E

Inequality D is also a sufficient condition on entry deterrence in the third version of the multi-
market game. If the incumbent invests in a sufficiently large capacity, which makes the capacity
constraint non-binding in every subgame, the optimal output in every market can be independently
determined. The potential competitor chooses its optimal strategy in each market separately, and
the best reply functions in all markets are identical. The unique Wash-equilibrium output in every
market is {x^,x∣}. Thus, player e’s partial revenue does not cover the fixed and variable costs in
any market and the total payoff is negative.

In fact, the strategic interaction in the second and third versions of the multi-market game
is identical, except for the coordination problem in the second version of the game. Two factors
make the strategic decisions in the two games identical with respect to entry deterrence. First,
the strategic variables x^, ...,x‰ are independent to the entrant in the third version of the multi-
market game and it will choose its optimal strategy in each market separately. Thus, player e’s
best reply function in market t is identical to player t’s best reply function in the second version
of the multi-market game.

Second, since the fixed cost A is the same in all markets, the revenue in each market the
potential competitor enters must cover the variable and fixed costs. Player e would only enter a
market where the expected payoff is positive, which exactly resembles the condition on entry for
a local competitor in Γ2_l. The analysis of the second version of the game therefore also applies to
the third version. Player m must install к > nx to deter entry in the n-market game fɜ.

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