Unformatted text preview: proﬁle s ∗ is a Nash equilibrium iﬀ
∗
si∗ ∈ Bi (s−i ) for all i ∈ I . Therefore, in Cournot as formulated above, unique Nash equilibrium.
s2
1 B1(s2)
1/2 B2(s1)
1/2 s1 1 Remark: When iterated strict dominance yields a unique strategy proﬁle, is this
necessarily a Nash equilibrium? unique Nash equilibrium?
28 Game Theory: Lecture 2 Examples Example: The Partnership Game
Let us return to the partnership game we started with.
Player 1 \ Player 2 work hard shirk
work hard
(−1, 1)
(2, 2)
shirk
(1, −1)
(0, 0)
There are no dominant or dominated strategies.
Work hard is a best response to work hard and shirk is a best
response shirk for each player.
Therefore, there are two pure strategy Nash equilibria (work hard,
work hard) and (shirk, shirk).
Depending on your conjectures (“expectations”) about your partner,
you can end up in a good or bad outcome. 29 Game Theory: Lecture 2 Examples Focal Points
What do we do when there are multiple Nash equilibria?
Our models would not be making a unique prediction. Two diﬀerent lines of attack:
Think of set valued predictions—i.e., certain outcomes are po...
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 Spring '10
 AsuOzdaglar
 Game Theory

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