Question 16
(Bayesian Game ) Consider a variant of the situation modelled by Battle of sexes (BOS) (as discussed in lectures) in which player 1 is unsure whether player 2 prefers to go out with her or prefers to avoid her, whereas player 2, as before, knows player 1’s preferences. Specifically, suppose player 1 thinks that with probability 1/2 player 2 wants to go out with her, and with probability 1/2 player 2 wants to avoid her. The situation is depicted in the following matrix of a static game with incomplete information:
With the help of this game matrix, we may come up with the following table depicting expected payoff of player 1 corresponding to different actions of both types of player 2.
Based on the above data, answer the given subquestions.
What is the Bayesian Nash equilibrium Strategy of both types of player 2 in this game?
(B,S)
(B,B)
(S,B)
(S,S)