Moshe Babaioff, Yuval Grofman, Brendan Lucier, Raghuvansh R. Saxena
原文摘要
We study mechanism design by an incumbent seller facing competition from an entrant seller of a substitute good. The incumbent commits to a potentially randomized mechanism before her competitor responds. A unit-demand buyer with fixed, publicly known values for the two goods observes both mechanisms and may interact with them in either order. How should a revenue-maximizing incumbent design her mechanism when her product is superior or inferior to her competitor's? We determine the incumbent's exact optimal revenue and characterize all mechanisms that obtain it. Commitment and randomization allow her to earn strictly positive revenue even against an arbitrarily superior product, despite earning nothing under posted-price (i.e., Bertrand) competition. Optimal mechanisms can require a continuum of lottery options, even though the buyer selects only one in equilibrium: unselected options shape the competitor's incentives rather than screen private buyer information. We also show that the buyer's ability to choose the interaction order can be strictly beneficial to the incumbent, even though the incumbent is always visited first at equilibrium. Finally, we show that without commitment, every pure Nash equilibrium yields Bertrand revenues even with randomized mechanisms.
We study the power of money burning in bilateral trade. In this problem, a seller owns an indivisible item, a buyer would like to acquire it, and each of these two traders has a private value for the item and the values are sampled from independent distributions. We ask whether the traders can benefit from a mechanism that burns money, that is, one that charges the buyer more than it pays the seller, so that neither trader enjoys the difference (money burnt is a loss for the traders). Is it possible that the traders will ever be better off if the trade mechanism can burn money? For Bayesian incentive-compatible mechanisms and for deterministic dominant-strategy incentive-compatible (DSIC) mechanisms, it is known that money burning is always a waste and can only hurt the traders. Maybe surprisingly, we show that once a DSIC mechanism can use randomization, money burning can significantly benefit the traders, and the gain of each of them can be arbitrarily large. In contrast, we show that the power of DSIC randomized mechanisms that burn money is still very limited in the sense that they cannot guarantee any constant fraction of the first-best gains-from-trade.