Player 1 first observes the quality (q) of the indivisible good he owns
before proposing a price (p) at which he will sell the good to Player 2,
who responds to the offer by either accepting or rejecting. Trade takes
place at a price of p if Player 2 accepts; otherwise no trade takes place.
Player 1's payoff equals the revenue (p or 0) he receives, irrespective of
quality; Player 2's payoff equals q − p if trade takes place, and otherwise
equals 0. Quality can take two values, L and H, where H > L > 0, and is
equally likely to take each value. Describe all separating and all pooling
equilibria of this game.
Separating and pooling equilibria in Akerlof model