Target-Oriented Regret Minimization for Satisficing Monopolists

We study a robust monopoly pricing problem where a seller aspires to sell an item to a buyer. We assume that the seller, unaware of the buyer’s willingness to pay, ambitiously optimizes over a space of all individually rational and incentive compatible mechanisms with a regret-type objective criterion. We particularly adopt a robust satisficing approach, which has been touted as a promising alternative of robust optimization, and aim at minimizing the excess regret above the predetermined target level. We interpret our pricing problem both probabilistically and distributionally robustly, and we analytically show that the optimal mechanism involves the seller offering a menu of lotteries that charges a buyer-dependent participation fee and allocates the item with a buyer-dependent probability. Then, we consider two additional variants of the problem where the seller restricts her attention to a class of only deterministic posted price mechanisms and where the seller is relieved from specifying the target regret in advance. Finally, we determine a randomized posted price mechanism that is readily implementable and equivalent to the optimal mechanism, compute its statistics, and quantify the strength of the entailed randomization. Besides, we compare the proposed mechanism with a robust benchmark and numerically find that the former is predominantly superior to the latter in terms of the expected regret and the expected revenue especially when the coefficient of variation of the buyer’s value is under a hundred percent.