24.7 Everyday Application: Real-World Mixed Strategies: In the text, we discussed the “Matching Pennies” game and illustrated that such a game only has a mixed strategy equilibrium.

A. Consider each of the following and explain (unless you are asked to do something different) how you might expect there to be no pure strategy equilibrium, and how a mixed strategy equilibrium might make sense.

a. A popular children’s game, often played on long road trips, is “Rock, Paper, Scissors.” The game is simple: Two players simultaneously signal through a hand gesture one of three possible actions: Rock, Paper, or Scissors. If the two players signal the same, the game is a tie.

Otherwise, Rock beats Scissors, Scissors beats Paper, and Paper beats Rock.

b. One of my students objects: “I understand that Scissors can beat Paper, and I get how Rock can beat Scissors, but there is no way Paper should beat Rock. What … Paper is supposed to magically wrap around Rock leaving it immobile? Why can’t Paper do this to Scissors? For that matter, why can’t Paper do this to people? I’ll tell you why: Because Paper can’t beat anybody!”20 If Rock really could beat Paper, is there still a mixed strategy Nash equilibrium?