Two pipeline ?rms are contemplating entry into a market of deliver- ing crude oi

Question

Two pipeline ?rms are contemplating entry into a market of deliver-
ing crude oil from a port to a re?nery. Pipeline 1, the larger of the two ?rms,
is contemplating its capacity strategy, which we might broadly characterize as
"aggressive" and "passive". The "aggressive" strategy involves a large increase
in capacity aimed at increasing the ?rm’s market share, while the passive strat-
egy involves no change in ?rm’s capacity. Pipeline 2, the smaller competitor, is
also pondering its capacity expansion strategy: it will also be choosing between
"aggressive" and "passive" strategy. The following are the payo?s associated
with the actions (where the ?rst number in eac box reperesents P.a payo?s):
P.2
A P
P.1 A 75,25 100,30
P 90,45 110,40
a) If both ?rms decide their strategies simultaneously, what is the Nash
equilibrium?
b) If Pipeline 1 could move ?rst, what is its optimal strategy? What will
Pipeline 2 do? (In other words: ?nd the backward induction solution).

Explanation / Answer

Your notation is rather confusing however, I think I understand. Player 1 would rather 90 than 75 and 110 than 100. Player 2 would rather 30 than 25 and 45 than 40. The NE in this case is 90,45.

b) A P

A 75,25 100,30

P 90,45 110,40

If 1 moved first he would choose A and 2 would choose P. In this instance, 1 improves his payoff from 90 to 100.

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