markets and superscripts to firm-type. If player t decides to stay out of market t monopoly will
prevail in that market. The output decision is immediately announced to all players. At the end
of period t, the market clears and payoffs are distributed to player m and player t. Next, for
t = 1,..., n — 1 period t + 1 begins and is played according to the same rules. The game ends after
period n.
Player m’s payoff is the sum of n partial payoffs for t = 1,..., n. Player m’s revenue in market
t is υ (ʃ^,ʃf). The cost of capital is additive and the marginal cost is c > 0. The objective of
player m is to maximize its total payoff:
"™ (k,xψ,..,x^,xeι,..,xen) = ∑ V (xΓ,xte) — ck (1)
t=1,..,n
and it is required that x™ + .. + x™ ≤ k. Setting up a firm, i.e. entering market t, is associated
with a fixed cost A > 0 for player t. Player t’s revenue is v (x^, x™). Marginal capital cost is c > 0
and additive. The objective of player t = 1, ...,n is to maximize its payoff:
{v (xf, xtn) — cxf — A if it enters
t t t (2)
0 if it stays out
Next, we introduce some notation before proceeding with the analysis. I will define strate-
gic substitutes, introduce a necessary and sufficient condition on entry-deterrence and define the
deterrence level.
We shall call x∖ a strategic substitute for x^', if the partial cross-derivative of the profit function
with respect to the strategic variables is strictly negative. Strategic substitutes imply that when
a firm has a more aggressive strategy, the optimal response of the other firm is to play less
aggressively. The condition that x't is a strategic substitute for x^' is referred to as S:
(S)
∂2 π (xt ,x*)
∂x∖∂ x^
Second, a best-reply function with a non-binding capacity restriction on player m in the one-
period game Γ, denoted βm (xf ), is introduced. Correspondingly, the entrant’s best reply function