Rock, Paper, Scissors is a children’s game in which the two players simultaneously display one of… 1 answer below »

Rock, Paper, Scissors is a children’s game in which the two players simultaneously display one of three hand symbols. Table 8.6 presents the normal form. The zero payoffs along the diagonal show that if players adopt the same strategy then no payments are made. In other cases, the payoffs indicate a $1 payment from loser to winner under the usual hierarchy (rock breaks scissors, scissors cut paper, paper covers rock).

As anyone who has played this game knows, and as the underlining procedure reveals, none of the nine boxes represents a Nash equilibrium. Any strategy pair is unstable because it offers at least one of the players an incentive to deviate. For example, (scissors, scissors) provides an incentive for either player 1 or 2 to choose rock; (paper, rock) provides an incentive for 2 to choose scissors. The game does have a Nash equilibrium—not any of the nine boxes in Table 8.6 but in mixed strategies, defined in the next section.