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.
Please use this information to answer the following questions.In the game of two romantics, when p = 0.9,
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