Question 17
(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 1/3 player 2 wants to go out with her, and with probability 2/3 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.
Find out the value of a = ___________