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.