Question

Check my work 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 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 Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff of $400. If both players a. Write the above game in normal form. Player 2 Strategy $ A A Player 1 $ B b. Find each player's dominant strategy, if it exists. Player 1's dominant strategy: (Click to select Player 2's dominant strategy: (Click to select c. Find the Nash equilibrium of this game. (Click to select d. Which strategy pair has the highest aggregate payoff? d. Which strategy pair has the highest aggregate payoff? (Click to select e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? (Click to select

Answer 1

(a)

Player 2 Strategy A Player 1 A $ 400 400 $ 100 J 600 $ B 600 $ $ 100 200 $ 200 tA

(b)

A dominant strategy is the strategy chosen by a player irrespective of strategy chosen by the other player.

For Player 1, best strategy is B whether Player 2 chooses A or B, since payoff is higher in each case (600 > 400 & 200 > 100).

Player 1's dominant strategy - Strategy B

For Player 2, best strategy is B whether Player 1 chooses A or B, since payoff is higher in each case (600 > 400 & 200 > 100).

Player 2's dominant strategy - Strategy B

(c)

Nash equilibrium exists when each player chooses its strategy on basis of strategy chosen by the other player.

When Player 2 chooses A, Player 1's best strategy is B since payoff is higher (600 > 400).

When Player 2 chooses B, Player 1's best strategy is B since payoff is higher (200 > 200).

When Player 1 chooses A, Player 2's best strategy is B since payoff is higher (600 > 400).

When Player 1 chooses B, Player 2's best strategy is B since payoff is higher (200 > 200).

Therefore, Nash equilibrium is: (Player 1 chooses B, Player 2 chooses B) [see below]

Player 2 Strategy A Player 1 A $ 400 400 $ 100 600 600 100 200 200

(d)

Aggregate payoff is highest when (Player 1 chooses A, Player 2 chooses A) [Aggregate payoff = 400 + 400 = 800].

NOTE: As per Answering Policy, 1st 4 parts are answered.