New mechanism for repeated posted price auction with a strategic buyer without discounting
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The repeated posted price auction is a game with two players: the seller and the buyer. This game consists of rounds, indexed by natural numbers i=1,2,..., and in each round the seller proposes to the buyer a unit of good (think of fish or a place for advertisement) with the price Q_i. Let the buyer's valuation of this good be q∈ R_>0, we call q the type of the buyer. In each round the buyer has two options: accept the deal (and then we set a_i=1) or reject it (we set a_i=0). In this round, the buyer's surplus is a_i(q-Q_i) and the seller's revenue is a_iQ_i. I propose a strategy S for the seller and argue why the resulting revenue is the best that the seller can achieve among a reasonable class of strategies.
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