3 Sequential Competition from Local Entrants
A multi-market firm, type m, has advertised its product and now meets demand for its product
in n markets, numbered 1 to n. In each market, there is a potential entrant, type e, who might
raise enough funding from creditors to establish a firm in market t, selling the same product as
the multi-market enterprise.
Entry in a local market is associated with a fixed cost A, which can be considered an advertising
cost, that makes consumers in the local market aware of the entrant. Advertising makes all
consumers in the market aware of the firm and its products, but does not affect aggregate demand
for the homogenous goods. There is no personal arbitrage, since consumers are only aware of firms
advertising in their home market. Accordingly, prices need not be internationally equalized.
In the first version of the multi-market game, we focus on a situation where each potential
competitor considers advertising in a single market only and, consequently, intends to remain
local. At the beginning of the game none of the potential entrants has a sufficiently correct
specification for starting production. But as time passes, one after another, they finish the process
of specification and raise enough credit to enter the local market. This will first happen to entrant
1, then to entrant 2, etc. As soon as a player has specified the product correctly, he must decide to
enter or stay out of the market. If he decides to stay out, he is no longer a potential competitor.8
If a local firm enters a market, the incumbent and the entrant choose outputs simultaneously and
the market clears as a duopoly. If the potential entrant stays out, monopoly will prevail.
After this description of the market situation in the first version of the multi-market game, we
turn to a formal specification of the model. The game, Γ^, has n + 1 players, player m and player
1,..., n (n ≥ 1). There are n separate markets, labelled 1,.., n. The game is played over a sequence
of periods 0,..., n. In period 0, the incumbent, player m, must choose a pre-entry capacity k, which
is immediately announced to all players. At the beginning of period t = 1, ...,n, player t decides
to enter or stay out of market t. Player t’s decision is announced to all players. If player t decides
to enter, player m and player t will choose .rr∣rι and xf simultaneously, where subscripts refer to
8This assumption is made to simplify the analysis. It is not restrictive. Indeed, it can be shown that a potential
entrant will not benefit from delaying its entry decision.