Microeconomic Theory
Econ 101A
Fall 2008
GSI: Eva Vivalt
Section Notes 9: Sequential Equlibrium, Imperfect Information, and Signalling
Games
1
Sequential Equilibrium
In solving for Nash equlibria, we assume that firms move simultaneously. Things change considerably if
one firm moves before the other in a sequence.
Assume now that firm 1 moves before firm 2 and that
each is able to anticipate the other’s reaction. These types of scenarios are often known as
Stackelberg
Games
.
1.1
Backwards Induction
The optimization technique used to solve for how the firms will behave is known as backwards induction.
This means that (assuming there are only 2 rounds in this example, with firm 1 “moving first”) we will
first solve for how firm 2 will act in the second round in response to how firm 1 acts in the first round,
and then we will move back in time to solve for how firm 1 will act in the first round, using our solution
for the second round to model firm 1’s anticipation of how firm 2 will react. The technique of backwards
induction is a fundamental technique in determining how to solve for optimal strategies in a number of
game theoretic situations.
1.2
Solving by BI in a TwoRound Game: First, Round Two
Firm 2’s problem is identical to that found in the Nash equilibrium. It takes
a
1
as given and maximizes
its profit over
a
2
, producing a best response function
r
2
(
a
1
).
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 Fall '08
 Staff
 Game Theory, Firm, worker, Imperfect Information, best response function, quantity Q1

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