Exercise S12 in Chapter 4 introduced the game “Evens or Odds,” which has no Nash equilibrium in pure strategies. It does have an equilibrium in mixed strategies. (a) If Anne plays 1 (that is, she puts...

Exercise S12 in Chapter 4 introduced the game “Evens or Odds,” which has no Nash equilibrium in pure strategies. It does have an equilibrium in mixed strategies.

(a) If Anne plays 1 (that is, she puts in one finger) with probability p, what is the expected payoff to Bruce from playing 1, in terms of p? What is his expected payoff from playing 2?

(b) What level of p will make Bruce indifferent between playing 1 and playing 2?

(c) If Bruce plays 1 with probability q, what level of q will make Anne indifferent between playing 1 and playing 2?

(d) Write the mixed-strategy equilibrium of this game. What is the expected payoff of the game to each player?