The paper studies Akerlof's market for lemons in a new way. We firstly construct mixed Perfect Bayesian Nash equilibria in which all qualities are sold on the market even if the seller's strategy set is reduced to prices. Then we turn to the best-reply matching (BRM) approach developed by Droste, Kosfeld & Voorneveld (2003) for games in normal form. In a BRM equilibrium, the probability assigned by a player to a pure strategy is linked to the number of times this strategy is a best reply to the other players’ played strategies. We extend this logic to signaling games in extensive form and apply the new obtained concept to Akerlof’s model. This new concept leads to a very simple rule of behaviour, which is consistent, different from the Bayesian equilibrium behaviour, different from Akerlof’s result, and can be socially efficient.