Lecture 7 - Nash Equilibrium: Shopping, Standing and Voting on a Line

We first consider the alternative “Bertrand” model of imperfect
competition between two firms in which the firms set prices rather
than setting quantities. Then we consider a richer model in which
firms still set prices but in which the goods they produce are not
identical. We model the firms as stores that are on either end of a
long road or line. Customers live along this line. Then we return
to models of strategic politics in which it is voters that are
spread along a line. This time, however, we do not allow candidates
to choose positions: they can only choose whether or not to enter
the election. We play this “candidate-voter game” in the class, and
we start to analyze both as a lesson about the notion of
equilibrium and a lesson about politics.