Consider the following bilateral trade game. There is a buyer (b) and a seller (s). The seller owns an object that is worth 1 to the buyer and zero to the seller. They both simultaneously announce prices 0 ≤ pb ≤ 1 and 0 ≤ ps ≤ 1, respectively. If pb ≥ ps, then the buyer gets the object and pays the seller’s price. Otherwise, they do not trade. When they do not trade payoffs are zero for both, and when they trade the payoff to the buyer is 1 − ps and the seller gets ps.
Find the set of rationalizable strategies.