Consider a modified $$rock$,$ paper, scissors" game as shown in table $2\mathrm{.}1.$ Suppose you are the

row player and you will play with the column player for a large number of rounds to decide

the winner and loser.

$1$

L R

U $4,02,2$

M $5,24,2$

D $3,25,0$

Table $1\mathrm{.}2$: Game $2$

Rock Paper Scissors

Rock $0,0-2,23,-3$

Paper $2,-20,0-1,1$

Scissors $-3,31,-10,0$

Table $2\mathrm{.}1$: Game of chicken

$($a$)(10$ its$)$ In the beginning you play with strategy $(1$

$3$

$,$

$1$

$3$

$,$

$1$

$3$

$)$ and the other player plays with

strategy $(1$

$2$

$,$

$1$

$4$

$,$

$1$

$4$

$).$ Who will be more likely to win the game in a long run. Please justify your

answer.

$($b$)(10$ its$)$ Suppose after some time you realized your opponent$$s strategy and started to adjust your strategy in order to win the game. Which strategy will you use instead? What is the

pattern of a winning strategy to your opponent?