Guide for solving the 2000 exam for 14.122
Courtesy of James Vickery.
Used with permission.
See the lecture notes or FT for the formal definition. We care about continuity at infinity because
if this property is satisfied, then checking a pr
14.122 Problem Set #1
1. Find a game which is not solvable by pure strategy iterated strict dominance but
which does have an unique pure strategy Nash equilibrium.
2. Consider the model of Cournot competition discussed in class where the inverse
14.122 Problem Set #2
1. Find all of the Nash equilibria of the following games.
2. Consider a game in which two students simultaneously choose eort levels e1 , e2
[0, 1] in studying for an exam. The exam is graded on a curve and eort directly determ
14.122 Problem Set #3
1. Prove the following theorem (known as the Debreu-Fan-Glicksburg Theorem), which
establishes sucient conditions for the existence of a pure strategy Nash equilibrium in
certain games with continuous action spaces.
Theorem 1 Let G b
14.122 Problem Set #4
1. For each of the extensive forms below say whether the set of successors of the
indicated nodes are or are not subgames.
2. Find all of the subgame perfect equilibria of the following extensive form game and
give the payoffs obtain
14.122 Problem Set #5
1. Suppose two rms are engaged in repeated Cournot competition with demand being
P (q1 , q2 ) = 1 (q1 + q2 ). Show that using punishments which involve a permanent reversion
to the static Cournot equilibrium (q1 = q2 = 1 ) the rms ca