Strategic Investment and Market Integration

4 Simultaneous Competition from Local Entrants

Consider a market situation similar to the first version of the multi-market game. In this ver-
sion, the incumbent owns a global patent expiring at the same time in all markets and potential
competitors can enter the local markets simultaneously. If a potential competitor challenges the
established firm in a local market, the incumbent and the entrant choose outputs simultaneously
and the market will clear as duopoly. If the potential entrant stays out, monopoly will prevail.

The rules of the second version of the multi-market game are defined as follows. The game, Γ^,
has n +1 players, player m and player 1,..., n (n ≥ 1). The game is played over two periods. In the
first period, the incumbent must choose a pre-entry capacity, к. At the beginning of the second
period, player t = 1,...,n must simultaneously decide to enter or stay out of market t. Player
t’s decision is immediately announced to all other players. If player t decides to enter market t,
then the incumbent and the entrant choose x'"^λ and xf simultaneously. At the end of the second
period, all markets clear and payoffs are distributed to the incumbent and players 1, ...,n. Player
m’s payoff is given by eq. (1) and player t’s payoff by eq. (2).

The analysis in the second version of the multi-market game is similar to the analysis in the
first version. If players compete in strategic substitutes and the necessary deterrence condition
is satisfied, entry can also be deterred in the second version of the game. To deter entry, the
established firm must install к > nx in the n-market game.

Consider, for instance, the two-market case. There are four subgames in the last stage of the
two-market game. In two of the four subgames, one potential competitor enters, and the other
stays out. To see why twice the single market deterrence capacity does not suffice, consider the
profit maximizing conditions when к = 2χ:

Xπ               Xπ

_χx1 (xfi^, f (χψ)) = — (2^χ - x^ 0)                       (7)

Strategic substitutes imply that the output in the duopoly market is strictly lower than the deter-
rence level, i.e. .x"f' < χ. Thus, entry would not be deterred.

Proposition 4 If D and S are satisfied in the second version of the n-market game, Γ^_l, then the
incumbent installs capacity nx < k_χ. ≤ x + (n — 1) χ⁰ to deter entry.

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