Question 1 (1 point) In the following game, what is the Nash equilibrium? For each cell, the first number is the payoff for firm A, and the second number is the payoff for firm B. Firm A High Low Firm B High Low 2,2 6,0 0,6 4, 4 Firm A chooses low; Firm B chooses high Firm A chooses high; Firm B chooses high Firm A chooses low; Firm B chooses low Firm A chooses high; Firm B chooses low

Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium.                                         Firm 2                                 Launch       Don’tFirm 1      Launch     60, -10      100, 0                  Don’t       80, 30      120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.

Consider the following game:                                 Player 2                                  In     Out  Player 1      In     -2,-2    2, 0                      Out    0, 2     0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?

Consider the following price game:                   Firm 1     Firm 2                   High         Low         High  20, 20       12, 24          Low  24, 12       14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?