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On ad exchange platforms the place for advertisement is sold throughdifferent kinds of auctions. However, it is not uncommon the situation wherethe seller repeatedly encounters only one buyer, thus the posted price auctiondegenerates into a monopoly-monopsony game with asymmetric information andnearly an infinite number of rounds; on each round the seller proposes theprice and the buyer accepts or rejects it.  I learned this problem from a discussion with members of Yandex research teamand my main motivation was to find an incentive-compatible seller's strategy.In this short paper such a strategy is proposed and a corresponding distortionat the top type lower bound (Spence-Mirrlees property, actually) for thesurplus of the buyer is established; this shows that the proposed strategy isthe best possible.  The key ingredients are the following. The main leash that the buyer has isthe frequency of accepted deals. Once this frequency (as a function on thebuyer's type) is fixed, the strategy randomly chooses between the {\itrewarding} price which incentivises the buyer to reveal his type (the higherthe type, the more average surplus the buyer has), the {\it adaptation} pricewhich allows the buyer to communicate that his type is higher then the currentguess of the cook, and the {\it type confirmation} price which disincentivisesthe buyer to pretend that his type is higher than it is.

New mechanism for repeated posted price auction with a strategic buyer without discounting