the easiest way to solve problems with a continuous strategy space, is to solve for players’ best response (BR) function. The BR function tells you, for any t−i that the other player chooses, what choice of ti would maximize player i’s payoffs? I.e. BRi(t−i) = t

(a) Often, the easiest way to solve problems with a continuous strategy space, is to solve
for players’ best response (BR) function. The BR function tells you, for any t−i that
the other player chooses, what choice of ti would maximize player i’s payoffs? I.e.
BRi(t−i) = t
∗
i
, where u (t
∗
i
, t−i) ≥ u(ti
, t−i), ∀ti
. Let’s solve for player 1’s BR function.
i. Suppose t2 < v c . Verify that BR1(t2) = {t1|t1 > t2}.
ii. Next, suppose t2 =
v
c
. What is BR1

v
c


?
iii. Finally, if t2 >
v
c
, what is BR1(t2)?
(b) What is player 2’s BR function?
(c) Now, recall that in a Nash equilibrium, neither player can benefit by deviating. That is,
both players must be playing according to their best response, which can only happen
if t1 ∈ BR1(t2) and t2 ∈ BR2(t1). Find all Nash equilibria in this game. That is, find
all pairs (t
∗
1
, t∗
2
) such that t
∗
1
is a best response to t
∗
2
, and t
∗
2
is a best response to t
∗
1
.