Use a matrix to model a$$ two$-$player game of$$ rock$-$paper$-$scissors with a payoff of $1$ if you$$ win,

dash$1$

if you$$ lose, and $0$ if you tie.

Part $2$

Construct the payoff matrix for this game.

Player$1/$Player $2$

Rock

Paper

Scissors

Rock

$$

$$

$1/1$

$0/0$

$1/0$

$0/1$

$-1/1$

$1/-1$

$$

$$

$1/1$

$1/-1$

$0/1$

$1/0$

$-1/1$

$0/0$

$$

$$

$1/0$

$0/1$

$1/1$

$-1/1$

$0/0$

$1/-1$

Paper

$$

$$

$1/1$

$1/0$

$0/0$

$1/-1$

$0/1$

$-1/1$

$$

$$

$1/1$

$1/-1$

$0/1$

$-1/1$

$0/0$

$1/0$

$$

$$

$0/1$

$1/1$

$-1/1$

$1/0$

$1/-1$

$0/0$

Scissors

$$

$$

$0/0$

$-1/1$

$0/1$

$1/1$

$1/0$

$1/-1$

$$

$$

$0/0$

$0/1$

$1/0$

$1/-1$

$-1/1$

$1/1$

$$

$$

$0/0$

$1/-1$

$-1/1$

$0/1$

$1/1$

$1/0$

Part $3$

The Nash equilibrium$$ is:

A$.$

$$Rock$/$Rock$.$

B$.$

$$Paper$/$Rock$.$

C$.$

$$Paper$/$Scissors$.$

D$.$

$$Scissors$/$Paper$.$

E$.$

There is no Nash equilibrium.

Part $4$

Why should you use a mixed strategy to play this$$ game?

A$.$

Predictable behavior by one player can be taken advantage of by the other player.

B$.$

Random behavior generally leads to a Nash equilibrium.

C$.$

Mixed strategy has the advantage of requiring less effort to generate an optimal outcome.

D$.$

Pure strategy is a more efficient way to reach higher payoff outcomes.

Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.Use a matrix to model a two$-$player game of rock$-$paper$-$scissors with a payoff of $1$ if you win, $1$ if you lose, and $0$ if you tie.The Nash equilibrium is:Why should you use a mixed strategy to play this game?