Strategic Investment and Market Integration

Proposition 5 If D and S are satisfied in the third version of the two-market game, Γ3_t, then the
incumbent installs capacity nx < feɜ ≤ x + (n — 1) χ^m to deter entry.

Proof. Appendix B ■

In the previous sections, the difficulties of entry deterrence in the first, second and third versions
of the multi-market game have been characterized. It takes more capacity than п times the
deterrence level x to deter entry of many potential competitors in a sequential or simultaneous
market structure. More specifically, the established firm installs exactly the same capacity to deter
entry in Γ^, Γ2_l and rɜ. Thus, the unique optimal deterring capacity is independent of the market
situation, as described in the first, second and third versions of the multi-market game.

Proposition 6 If conditions D and S are satisfied, the global capacity required to deter entry in
the п-market game is independent of the timing of the game, i.e. sequential or simultaneous entry
of potential competitors, and the size of the potential entrant.

Proof. Appendix C. ■

This proposition is interesting for two reasons. First, it might be difficult for the incumbent to
obtain information about potential entrants ex ante, but our results suggest that such information
might not be necessary. The result implies that an incumbent does not need information about
the timing and the number of potential entrants to determine its entry-deterring strategy. The
results of the model apply to several different situations, for example both to a situation with one
large competitor and to a situation with competition from a series of local competitors.

Not surprisingly, it also follows that the difference between the single-market game and the
multi-market game increases with the number of markets in the multi-market game.

If condition D holds with equality, the entry-deterring capacity per market in an п-market
game increases in the number of markets and converges to χ^m, as п goes to infinity.

The intuition for this result is that unilateral entry in a single market is harder to deter as
partial exit to the remaining п — 1 markets becomes increasingly attractive. As the number of
monopoly-markets increases, the alternative to fight entry in a single market looks less and less
attractive, in comparison to using the capacity in the remaining monopoly markets. It should,

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