Consider the familiar "Rock, Paper, Scissors" game. Two players indicate either "Rock", "Paper", or "Scissors" simultaneously. The winner is determined by

Rock crushes scissors

Paper covers rock

Scissors cut paper

The loser gets a payoffff of -1 and the winner gets +1. If both players choose the same, both of them gets 0.

1. Write down the (payoffff) matrix of the game. Does either player has a dominant strategy?

If the game has one or more pure-strategy Nash equilibrium, fifind all of them. If the game does not have a pure-strategy Nash equilibrium, explain why.

2. Now consider a difffferent set of rules to determine the winner:

Rock crushes scissors

Rock flflies right through paper (Rock beats paper)

Scissors cut paper

Write down the (payoffff) matrix of the new game. Does either player has a dominant strategy?

If the new game has one or more pure-strategy Nash equilibria, fifind all of them. If the new game does not have a pure-strategy Nash equilibrium, explain why.