Strategic Investment and Market Integration

Proof. Appendix B ■

The first and the second version of the multi-market game differ in one important respect. If
the incumbent installed enough capacity to deter simultaneous entry by all potential competitors
but not enough to deter unilateral entry by one potential competitor, then the potential entrants
would face a coordination problem in the second version of the game. This coordination problem
does not occur in the first version where player 1 enters and player 2 stays out. In the second
version, both potential competitors wish to enter if they are the only entrant, but not otherwise. ⁹

The coordination problem in the second version of the game remains unsolved, since both Nash
equilibria are strict. This problem will not be further dealt with, since we are mainly interested in
the conditions on entry deterrence. In a real market situation, however, the coordination problem
may affect the entrants’ decisions and, possibly, facilitate entry-deterrence.

5 Competition from a Multi-Market Entrant

Once more, a multi-market firm has advertised and meets demand for its product in n markets. In
the third version of the multi-market game, a single potential competitor, another multi-market
company, considers entry in all markets selling the same product as the established firm. The
incumbent’s global patent expires at the same time in all markets and the potential competitor
may enter all local markets simultaneously. Entry in each market is associated with a fixed sunk
cost, which can be considered an advertising cost. The multi-market entrant remains unknown in
all markets where it does not advertise. If the second multi-market firm enters the local market,
the incumbent and the entrant choose their output simultaneously and the market will clear as a
duopoly.

The rules of the third version of the game are defined as follows. The game, rɜ, has two
players, called player m and player e. The game is played over a sequence of two periods. In the
first period, the established firm must choose a pre-entry capacity, k. At the beginning of the
second period, the potential competitor must decide to enter or stay out in n separate markets
called t = 1, ...,n. Player e’s decision is immediately announced to player m. If player e decides
⁹This is a version of the "chicken” game.

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