Optimal Algorithm for Bayesian Incentive-Compatible Exploration

We consider a social planner faced with a stream of myopic selfish agents. The goal of the social planner is to maximize the social welfare, however, it is limited to using only information asymmetry (regarding previous outcomes) and cannot use any monetary incentives. The planner recommends actions to agents, but her recommendations need to be Bayesian Incentive Compatible to be followed by the agents. Our main result is an optimal algorithm for the planner, in the case that the actions realizations are deterministic and have limited support, making significant important progress on this open problem. Our optimal protocol has two interesting features. First, it always completes the exploration of a priori more beneficial actions before exploring a priori less beneficial actions. Second, the randomization in the protocol is correlated across agents and actions (and not independent at each decision time).Comment: EC 201

Learning Valuation Distributions from Partial Observation

Auction theory traditionally assumes that bidders' valuation distributions are known to the auctioneer, such as in the celebrated, revenue-optimal Myerson auction. However, this theory does not describe how the auctioneer comes to possess this information. Recently, Cole and Roughgarden [2014] showed that an approximation based on a finite sample of independent draws from each bidder's distribution is sufficient to produce a near-optimal auction. In this work, we consider the problem of learning bidders' valuation distributions from much weaker forms of observations. Specifically, we consider a setting where there is a repeated, sealed-bid auction with $n$ bidders, but all we observe for each round is who won, but not how much they bid or paid. We can also participate (i.e., submit a bid) ourselves, and observe when we win. From this information, our goal is to (approximately) recover the inherently recoverable part of the underlying bid distributions. We also consider extensions where different subsets of bidders participate in each round, and where bidders' valuations have a common-value component added to their independent private values