Econ 398 Homework 6 Suggested Solutions
1) Use the characterization from class to check for mixedstrategy Nash Equilibria.
First note that there are four pure strategy equilibria, each where one person drives Straight, and
the other person either swerves Left or swerves Right.
Next notice that Stop is dominated for Daisy by, for instance, a strategy that puts probability
weight of .4, .2, .4 respectively on the strategies Left, Straight, and Right.
So Stop won’t be used
in any Nash Equilibrium.
Consider strategies where one player plays a pure strategy and the other randomizes over two or
more strategies.
Notice that if BillyJo drives Straight, Daisy is willing to randomize over Left
and Right.
Furthermore, if she randomizes over Left and Right, BillyJo will drive Straight.
There is therefore a whole component of equilibria where BillyJo plays Straight (with
probability 1), and Daisy plays Left with probability
q
and right with probability
1q, where
q
∈
[0,1].
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Emre
 Probability, Game Theory, Left

Click to edit the document details