We analyze a model in which a firm with multiple locations chooses capacity and prices to maximize efficiency. We find that the firm provisions capacity in such a way that the expected fraction of demand that will be unfilled is lower in locations with greater expected demand. The firm also sets lower prices in larger locations. Finally, if a customer is indifferent between multiple locations, then it is more efficient to place this customer in a location with greater expected demand. These theoretical results are consistent with empirical evidence that we present from a major public cloud provider.

This paper analyzes a mechanism for selling items in auctions in which the auctioneer specifies a cap on the ratio between the maximum and minimum bids that bidders may use in the different auctions. Such a mechanism is widely used in online advertising through the caps that companies impose on the minimum and maximum bid multipliers that advertisers may use in targeting. When bidders» values are independent and identically distributed, using this mechanism results in higher revenue than allowing bidders to condition their bids on the targeting information in an arbitrary way and also almost always results in higher revenue than not allowing bidders to target. Choosing the optimal cap on the ratio between the maximum bid and the minimum bid can also be more important than introducing additional competition in the auction. However, if bidders» values are not identically distributed, pure-strategy equilibria may fail to exist.

We consider a model of repeated online auctions in which an ad with an uncertain click-through rate faces a random distribution of competing bids in each auction and there is discounting of payoffs. We formulate the optimal solution to this explore/exploit problem as a dynamic programming problem and show that efficiency is maximized by making a bid for each advertiser equal to the advertiser's expected value for the advertising opportunity plus a term proportional to the variance in this value divided by the number of impressions the advertiser has received thus far. We then use this result to illustrate that the value of incorporating active exploration in an auction environment is exceedingly small.

Contests are widely used as a means for effort elicitation in settings ranging from government R&D contests to online crowdsourcing contests on platforms such as Kaggle, Innocentive, or TopCoder. Such rank-order mechanisms---where agents' rewards depend only on the relative ranking of their submissions' qualities---are natural mechanisms for incentivizing effort when it is easier to obtain ordinal, rather than cardinal, information about agents' outputs, or where absolute measures of quality are unverifiable. An increasing number of online contests, however, rank entries according to some numerical evaluation of their absolute quality---for instance, the performance of an algorithm on a test dataset, or the performance of an intervention in a randomized trial. Can the contest designer incentivize higher effort by making the rewards in an ordinal rank-order mechanism contingent on such cardinal information? We model and analyze cardinal contests, where a principal running a rank-order tournament has access to an absolute measure of the qualities of agents' submissions in addition to their relative rankings, and ask how modifying the rank-order tournament to incorporate cardinal information can improve incentives for effort. Our main result is that a simple threshold mechanism---a mechanism that awards the prize for a rank if and only if the absolute quality of the agent at that rank exceeds a certain threshold---is optimal amongst all mixed cardinal-ordinal mechanisms where the fraction of the jth prize awarded to the jth-ranked agent is any arbitrary non-decreasing function of her submission's quality. Further, the optimal threshold mechanism uses exactly the same threshold for each rank. We study what contest parameters determine the extent of the benefit from incorporating such cardinal information into an ordinal rank-order contest, and investigate the extent of improvement in equilibrium effort via numerical simulations.

In second price auctions with symmetric bidders, we find that improved targeting via enhanced information disclosure decreases revenue when there are two bidders and increases revenue if there are at least four bidders. With asymmetries, improved targeting increases revenue if the most frequent winner wins less than 30.4% of the time, but can decrease revenue otherwise. We derive analogous results for position auctions. Finally, we show that revenue can vary non-monotonically with the number of bidders who are able to take advantage of improved targeting.

We consider a model of repeated online auctions in which an ad with an uncertain click-through rate faces a random distribution of competing bids in each auction and there is discounting of payoffs. We formulate the optimal solution to this explore/exploit problem as a dynamic programming problem and show that efficiency is maximized by making a bid for each advertiser equal to the advertiser's expected value for the advertising opportunity plus a term proportional to the variance in this value divided by the number of impressions the advertiser has received thus far. We then use this result to illustrate that the value of incorporating active exploration into a machine learning system in an auction environment is exceedingly small.

Motivated by the problem of learning the qualities of user-generated content on the Web, we study a multi-armed bandit problem where the number and success probabilities of the arms of the bandit are endogenously determined by strategic agents in response to the incentives provided by the learning algorithm. We model the contributors of user-generated content as attention-motivated agents who derive benefit when their contribution is displayed, and have a cost to quality, where a contribution's quality is the probability of its receiving a positive viewer vote. Agents strategically choose whether and what quality contribution to produce in response to the algorithm that decides how to display contributions. The algorithm, which would like to eventually only display the highest quality contributions, can only learn a contribution's quality from the viewer votes the contribution receives when displayed. The problem of inferring the relative qualities of contributions using viewer feedback, to optimize for overall viewer satisfaction over time, can then be modeled as the classic multi-armed bandit problem, except that the arms available to the bandit and therefore the achievable regret are endogenously determined by strategic agents --- a good algorithm for this setting must not only quickly identify the best contributions, but also incentivize high-quality contributions to choose amongst in the first place. We first analyze the well-known UCB algorithm Ma [Auer et al. 2002] as a mechanism in this setting, where the total number of potential contributors or arms, K, can grow with the total number of viewers or available periods, T, and the maximum possible success probability of an arm, γ, may be bounded away from 1 to model malicious or error-prone viewers in the audience. We first show that while Ma can incentivize high-quality arms and achieve strong sublinear equilibrium regret when K(T) does not grow too quickly with T, it incentivizes very low quality contributions when K(T) scales proportionally with T. We then show that modifying the UCB mechanism to explore a randomly chosen restricted subset of √{T} arms provides excellent incentive properties --- this modified mechanism achieves strong sublinear regret, which is the regret measured against the maximum achievable quality γ, in every equilibrium, for all ranges of K(T) ≤ T, for all possible values of the audience parameter $\gamma$.

In many social computing applications such as online Q&A forums, the best contribution for each task receives some high reward, while all remaining contributions receive an identical, lower reward irrespective of their actual qualities. Suppose a mechanism designer (site owner) wishes to optimize an objective that is some function of the number and qualities of received contributions. When potential contributors are {\em strategic} agents, who decide whether to contribute or not to selfishly maximize their own utilities, is such a "best contribution" mechanism, Mb, adequate to implement an outcome that is optimal for the mechanism designer? We first show that in settings where a contribution's value is determined primarily by an agent's expertise, and agents only strategically choose whether to contribute or not, contests can implement optimal outcomes: for any reasonable objective, the rewards for the best and remaining contributions in Mb can always be chosen so that the outcome in the unique symmetric equilibrium of Mb maximizes the mechanism designer's utility. We also show how the mechanism designer can learn these optimal rewards when she does not know the parameters of the agents' utilities, as might be the case in practice. We next consider settings where a contribution's value depends on both the contributor's expertise as well as her effort, and agents endogenously choose how much effort to exert in addition to deciding whether to contribute. Here, we show that optimal outcomes can never be implemented by contests if the system can rank the qualities of contributions perfectly. However, if there is noise in the contributions' rankings, then the mechanism designer can again induce agents to follow strategies that maximize his utility. Thus imperfect rankings can actually help achieve implementability of optimal outcomes when effort is endogenous and influences quality.

Many websites rank user-generated content (UGC) using viewer votes, displaying higher quality contributions more prominently and suppressing lower quality ones. Such an allocation of attention constitutes a mechanism, which can influence the quality of content elicited from attention-motivated contributors. In this paper, we analyze equilibrium behavior in the widely used rank-order mechanism, where contributions are allocated positions on the page in decreasing order of their ratings, and the proportional mechanism which distributes attention in proportion to the number of positive ratings, in a game-theoretic model where agents are motivated by attention and the cost of making a contribution is increasing in its quality.