A mother is torn among choosing her son Leonardo and her daughter Meryl to have the last bar of chocolate in her cupboard. As both her children's needs the chocolate and she needs to be fair, she decides to resolve the issue by having her children compete in the playground game of rock-Paper-scissors. According to the rules of the game, a rock (fist) breaks scissors (two fingers striking out), scissors cut paper (flat hand), and paper smothers rock. If both players end up taking the similar there is a tie and the game is repeated.

a) Determine the payoff matrix for this rock-paper-scissors game