Here is a simplified version of the game “Win an additional mark if U can!”. •There are two players. •Each player names

[answerhappygod]

Here is a simplified version of the game “Win an additional mark
if U can!”.
•There are two players.
•Each player names an integer between 1 and 4.
•The player who names the integer closest to two thirds of the
average integer gets a reward of 10, the
other players get nothing.
•If there is a tie (i.e., choosing the same number), each player
gets reward of 5.
(a) Represent this game in Normal Form. (4 marks)
(b) Answer the following questions (3 marks)
•When player 2 chooses 4, what are the best responses for player
1?
•When player 1 chooses 3, what are the best responses for player
2?
•When player 2 chooses 2, what are the best responses for player
1?
•When player 1 chooses 1, what are the best responses for player
2?
•For player 1, is the strategy of choosing 4 strictly or very
weakly dominated by another strategy? If
so, which ones?
•For player 2, is the strategy of choosing 1 strictly or very
weakly dominated by another strategy? If
so, which ones?
(c) What is the Nash equilibrium of this game? (3 marks)
Find this out by applying the concept of dominated strategies to
rule out a succession of inferior strategies
until only one choice remains.