Lemon Market This exercise illustrates that in situations in which a seller has more information than a buyer, transactions might not be possible.
Consider a used car market in which a fraction q of the cars (0 ≤ q ≤ 1) are in good condition and 1 - q are in bad condition (lemons). The seller (Player 2) knows the quality of the car he is offering to sell while the buyer (Player 1) does not know the quality of the car that he is being offered to buy.
Each used car is offered for sale at the price of $p (in units of thousands of dollars). The payoffs to the seller and the buyer, depending on whether or not the transaction is completed, are described in the following tables:
Depict this situation as a Harsanyi game with incomplete information, and for each pair of parameters p and q, find all the Bayesian equilibria.