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1
1
More Than Two Players
UGBA 143:
Game Theory and Business Decisions
2
Overview
So far, we have looked at:
– Normal form games
– Continuous games
Typically, between two players
Today:
– More complex strategic situations
– Many players
3
Cournot competition:
More than two firms
Unit cost is $1 per unit
Market demand curve is:
price = 8 – (total quantity produced) / 5,000
3 firms, producing quantities
Q
1
, Q
2
, Q
3
.
We can use the same technique as before (i.e. 2 firms)
to solve for the Nash equilibrium quantities (
Q
1
*,Q
2
*,Q
3
*)
and price
P*
What happens when there are 4 firms? 5 firms? More?
4
Cournot competition:
More than two firms
3 firms:
Given
Q
2
,Q
3
, Firm 1’s profit is
Q
1
(7 – (
Q
1
+
Q
2
+
Q
3
) / 5,000),
so Firm 1’s best response is (35,000 – (
Q
2
+
Q
3
)) / 2
Remember to apply symmetry when you can!
The Nash equilibrium is:
Q
1
* =
Q
2
* =
Q
3
* = 35,000 / 4
With
n
firms, the Nash equilibrium is
Q
i
* = 35,000 / (
n
+1)
5
Friends at the Bar
Alice, Barb, Cindy are deciding between going to
a bar and staying at home
Staying at home yields payoff 1
Going to the bar yields:
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 Spring '08
 XuanmingSu

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