Q1. The Basics a. Explain why chess is not a static game of comple...

Q1. The Basics
a. Explain why chess is not a static game of complete information.
b. Consider the following game: I write down a number € {1,2,3} on a card and set it down. If you guess the right number, I give you $1. If you guess the wrong number, you give me $1. Don't solve it; just explain why this is a static game of complete information and draw the matrix representation of the game.
c. Explain what a dominated strategy is, and what a dominant strategy is.
d. Explain the three criteria we use to evaluate solution concepts, and use them to compare Dominant Strategy Equilibrium with Nash Equilibrium.
e. What is a Pareto dominated outcome? Compare with a Pareto optimal/efficient outcome.

Q2. IESDS Practice
Consider the following matrix form game:
Player 2    X       Y          Z
Player 1
A             1,4    4,5       8,2
B             5,4    1,6       7,5
C             0,11    3,9      10,2
a. Use Iterated Elimination of Dominated Strategies to find the unique solution.
b. Use Nash your Equilibrium to find the unique solution. Show your (considerably
Show work. smaller amount of) work.

Q3: Chicken
Chicken is a classic game regarding brinksmanship; one version is portrayed in the movie Rebel Without a Cause, where two teenagers drive directly at one another in metal cars, waiting for the other to chicken out and swerve. Consider a game where two young rebels/world leaders are hurtling towards each other. The two can be Chicken (C) or Macho (M). If both are chicken, we reach the status quo. If one is Macho and the other is Chicken, the Macho one "wins." If both go Macho, a catastrophe occurs. The game can be described in matrix form as follows:
Player 2          Chicken       Macho
Player 1
Chicken             0,0            -1,1
Macho               1,-1       -100000
                                        -100000,
a. Are there any dominated strategies? If so, which ones?
b. Find any pure strategy NE.
c. Find the MSNE. What is the expected payoff for Player 1?

Q4: Cournot with cost advantages
Consider the Cournot Duopoly we studied in Chapter 4, but firm 2 has a marginal cost of 10 while firm 1 has a marginal cost of 0. As a reminder, demand is p(q) = 100-9:9=91+92-
a. Generate the best response functions for firms 1 and 2.
b. Roughly graph the best response correspondences (if you need more info on this, check the book or come to office hours.)
c. Explain the first iteration you would take if you were using IESDS. (Just provide one correct answer.)
d. Solve the easier way by finding the Nash Equilibrium.