Consider the one-shot, simultaneous move game below, and answer the accompanying questions:
Player & Strategy Firm B
Left Right
Firm A Up 4,4 0,0
Down 0,0 2,2
(a)List the strategies for Firm A and Firm B
(b)State the set of strategy profiles.
(c)Suppose Firm A plays Up. What is Firm B¡¦s best response?
(d)Suppose Firm B plays Right. What is Firm A¡¦s best response?
(e)Does firm A have a dominant strategy?
(f)What is (or are) the Nash equilibrium (equilibria) to this game?
(g)If you are firm A and are given the first move (instead of moving simultaneously), which move would you choose and why?
(h)Would Firm B object to your getting the first move? Explain
There is no question.
(a) The strategies for Firm A are Up and Down.
The strategies for Firm B are Left and Right.
(b) The set of strategy profiles is {(Up, Left), (Up, Right), (Down, Left), (Down, Right)}.
(c) If Firm A plays Up, Firm B's best response is to play Left. This is because playing Left guarantees Firm B a payoff of 4, which is higher than the payoff of 0 when playing Right.
(d) If Firm B plays Right, Firm A's best response is to play Down. This is because playing Down guarantees Firm A a payoff of 2, which is higher than the payoff of 0 when playing Up.
(e) Firm A does not have a dominant strategy. A dominant strategy is a strategy that yields the highest payoff regardless of the other player's strategy. In this case, the best strategy for Firm A depends on the strategy chosen by Firm B.
(f) The Nash equilibrium is (Down, Right), where both firms choose their best response to each other. In this strategy profile, neither firm has an incentive to deviate.
(g) If Firm A is given the first move, it would choose to play Down. This is because playing Down guarantees Firm A a payoff of 2, which is higher than the payoff of 4 when playing Up. Since Firm A knows that Firm B's best response to Up is Left, playing Down would give Firm A the highest expected payoff.
(h) Firm B would object to Firm A getting the first move because it would change the outcome of the game. If Firm A chooses to play Down first, Firm B's best response would be to play Left, resulting in a payoff of 2 for Firm B. However, if Firm A had played Up first, Firm B's best response would have been to play Right, resulting in a higher payoff of 4 for Firm B. Therefore, Firm B would prefer Firm A to move first in order to maximize its own payoff.