##### 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

.