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Unformatted text preview: 2 B2(s1) 1
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4 1/2 s1 1 B2(s1) 1
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4 1/2 1 s1 1
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One round of elimination yields S1 = [0, 1/2], S2 = [0, 1/2]
2
2
Second round of elimination yields S1 = [1/4, 1/2], S2 = [1/4, 1/2]
It can be shown that the endpoints of the intervals converge to the
intersection
Most games not solvable by iterated strict dominance, need a stronger equilibrium notion 24 Game Theory: Lecture 2 Nash Equilibrium Pure Strategy Nash Equilibrium
Deﬁnition
(Nash equilibrium) A (pure strategy) Nash Equilibrium of a strategic
game �I , (Si )i ∈I , (ui )i ∈I � is a strategy proﬁle s ∗ ∈ S such that for all
i∈I
∗
∗
ui (si∗ , s−i ) ≥ ui (si , s−i )
for all si ∈ Si .
Why is this a “reasonable” notion?
No player can proﬁtably deviate given the strategies of the other
players. Thus in Nash equilibrium, “best response correspondences
intersect”.
Put diﬀerently, the conjectures of the players are consistent: each
∗
player i chooses si∗ expecting all other players to choose s−i , and each
player’s conjecture is veriﬁed in a Nash equilibrium.
25 Game Theory: Lecture 2 Nash Equilibrium Reasoning about Nash Equilibrium
This has a “steady state” type ﬂavor. In fact, two...
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 Spring '10
 AsuOzdaglar

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