Patrick Hummel

A game-theoretic analysis of rank-order mechanisms for user-generated content

We investigate the widely-used rank-order mechanism for displaying user-generated content, where contributions are displayed on a webpage in decreasing order of their ratings, in a game-theoretic model where strategic contributors benefit from attention and have a cost to quality. We show that the lowest quality elicited by this rank-order mechanism in any mixed-strategy equilibrium becomes optimal as the available attention diverges. Additionally, these equilibrium qualities are higher, with probability tending to 1 in the limit of diverging attention, than those elicited by a more equitable proportional mechanism which distributes attention in proportion to the positive ratings a contribution receives, but the proportional mechanism elicits a greater number of contributions than the rank-order mechanism.

Learning and incentives in user-generated content: multi-armed bandits with endogenous arms

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 contributions 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 contributions 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

Preemptive Policy Experimentation

\gamma

Value of Targeting

.

Sequential or Simultaneous Elections? A Welfare Analysis

We develop a model of experimentation and learning in policymaking when control of power is temporary. We demonstrate how an early office holder who would otherwise not experiment is nonetheless induced to experiment when his hold on power is temporary. This preemptive policy experiment is profitable for the early office holder as it reveals information about the policy mapping to his successor, information that shapes future policy choices. Thus policy choices today can cast a long shadow over future choices purely through information transmission and absent any formal institutional constraints or real state variables. The model we develop utilizes a recent innovation that represents the policy mapping as the realized path of a Brownian motion. We provide a precise characterization of when preemptive experimentation emerges in equilibrium and the form it takes. We apply the model to several well known episodes of policymaking, reinterpreting the policy choices as preemptive experiments.

Candidate strategies in primaries and general elections with candidates of heterogeneous quality

We undertake a formal study of the value of targeting data to an advertiser. As expected, this value is increasing in the utility difference between realizations of the targeting data and the accuracy of the data, and depends on the distribution of competing bids. However, this value may vary non-monotonically with an advertiser’s budget. Similarly, modeling the values as either private or correlated, or allowing other advertisers to also make use of the data, leads to unpredictable changes in the value of data. We address questions related to multiple data sources, show that utility of additional data may be non-monotonic, and provide tradeoffs between the quality and the price of data sources. In a game-theoretic setting, we show that advertisers may be worse off than if the data had not been available at all. We also ask whether a publisher can infer the value an advertiser would place on targeting data from the advertiser’s bidding behavior and illustrate that this is impossible.

Position Auctions with Externalities

Should all voters vote on the same day or should elections be staggered? Using a model of voting and social learning, we illustrate that sequential elections place too much weight on early states but also provide late voters with valuable information. Simultaneous elections equally weigh states but place too much weight on voter priors, providing an inappropriate advantage to front‐runners. Simultaneous elections are thus preferred if the front‐runner advantage is small, but sequential elections are preferred if the advantage is large. Our quantitative welfare analysis of presidential primaries suggests that simultaneous systems slightly outperform sequential systems.

Pre-election polling and third party candidates

I consider a model in which candidates of differing quality must win a primary election to compete in the general election. I show that there is an equilibrium in which Democrats choose liberal policies and Republicans choose conservative policies, but higher quality candidates choose more moderate policies than lower quality candidates. In this equilibrium, higher quality candidates choose more moderate policies if they have a larger quality advantage or there is less uncertainty about the median voterʼs ideal point in the general election, and the candidates in a given primary choose closer policies to one another when there is a smaller quality difference between the candidates in a primary. I further show that if the candidates have policy motivations, then a low quality candidate may strategically choose to enter a primary even if running for office is costly and the candidate will lose the primary election with certainty in equilibrium.

When Does Improved Targeting Increase Revenue

This paper presents models for predicted click-through rates in position auctions that take into account the externalities ads shown in other positions may impose on the probability that an ad in a particular position receives a click. We present a general axiomatic methodology for how click probabilities are affected by the qualities of the ads in the other positions, and illustrate that using these axioms will increase revenue as long as higher quality ads tend to be ranked ahead of lower quality ads. We also present appropriate algorithms for selecting the optimal allocation of ads when predicted click-through rates are governed by a natural special case of this axiomatic model of externalities.

Bid-Limited Targeting

I analyze voters’ incentives in responding to pre-election polls with a third party candidate. Third party supporters normally have an incentive to vote strategically in the election by voting for one of the major candidates. But these voters would vote third party if the third party candidate is doing surprisingly well in the polls. Because voters are more likely to vote third party if the third party candidate is doing well in polls, voters who like the third party candidate best have an incentive to claim they will vote third party in the polls so that more voters will ultimately vote third party in the election. The differing incentives faced during polls and elections accounts for why third party candidates do better in polls than in elections.