Question

In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100.
Required:
a. Write the above game in normal form.
b. Find each player’s dominant strategy, if it exists.
c. Find the Nash equilibrium (or equilibria) of this game.
d. Rank strategy pairs by aggregate payoff (highest to lowest).
e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not?

Answer 1

Answer:

a) attached below

b)  Player 1 dominant strategy =  when he chooses strategy B

     Player 2 dominant strategy = when he chooses strategy B

c) Strategy A is the Nash equilibrium

d) AA  = $800

   AB , BA = $700

   BB = $400

e) Yes

Explanation:

A) The Game written in Normal form

     attached below

B) Determine each player dominant strategy

Player 1 dominant strategy =  when he chooses strategy B

Player 2 dominant strategy = when he chooses strategy B

C) The Nash Equilibrium of the game is when Both players choose strategy A because when they both choose Strategy they both earn $400 each

D) Ranking strategy pairs from Highest to lowest

   AA  = $800

   AB , BA = $700

   BB = $400

E) The outcome can be sustained

because The Nash equilibrium is the same as the highest ranking strategy pair ( i.e. AA  = $800 )