Two Romantics

Ann and Bob had their first date. Each either felt romantic chemistry (C) or no chemistry (NC) with the other person. Each person knows his/her own feeling but does not know the feeling of the other person. Assume a common prior belief that the other person felt chemistry with probability Pr(C) = p and no chemistry with probability Pr(NC) = 1-p.

Ann and Bob are old-fashioned romantics and they made the following rule after the first date: No texts/calls/DMs. Instead, they can choose whether to appear (A) or not appear (NA) under the USyd Quadrangle clock tower at sunset on the next day. Their payoffs are given as follows:

(From a first-person perspective)

If I felt chemistry (C) and I appear (A) under the clock tower, my payoff is 100 if the other person also appears (A) and -100 if the other person doesn't (NA).

If I felt chemistry (C) and I choose not to appear (NA) under the clock tower, my payoff is -30 regardless of the other person's action (because I won't know anyway).

If I felt no chemistry (NC) and I appear (A) under the clock tower, my payoff is 20 if the other person appears (A) and -20 if the other person doesn't (NA).

If I felt no chemistry (NC) and I choose not to appear (NA) under the clock tower, my payoff is 10 regardless of the other person's action.

, when p = 0.4,

let A = Ann's highest expected payoff in any pure-strategy Bayesian Nash equilibrium;

let B = Ann's lowest expected payoff in any pure-strategy Bayesian Nash equilibrium.

A and B are expected payoffs under the common prior belief. They should be the entries in a game matrix that you created using methods we learned in L8.

What is A - B? Enter your answer in the box below. Round your answer to 1 decimal place if needed.