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Finding the mixed-equilibrium strategies for zero-sum games can yield results that seem perplexing at first.

Finding the mixed-equilibrium strategies for zero-sum games can yield results that seem perplexing at first. In the children’s game Rock-Paper-Scissors the optimal mixed strategy is for each player to randomly choose each option one-third of the time. But suppose that when rock beats scissors, the winning player scores 2 points, not 1. How would you expect optimal play to change? Interestingly, the players play rock less, not more. Paper is played one-half of the time, and rock and scissors both drop to one-fourth. Why? Create a payoff matrix and use it to verify that the strategies specified result in a mixed-strategy equilibrium for the modified Rock-Scissors-Paper game. Explain the reasons why rock is played less, not more, using game theory concepts.

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