Truthful Learning Mechanisms for Multi-Slot Sponsored Search Auctions with Externalities

Sponsored search auctions constitute one of the most successful applications of microeconomic mechanisms. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and to assure both the advertisers and the auctioneer a non-negative utility. Nonetheless, in sponsored search auctions, the click-through-rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard truthful mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs at the same time as implementing a truthful mechanism with a revenue loss as small as possible compared to an optimal mechanism designed with the true CTRs. Previous work showed that, when dominant-strategy truthfulness is adopted, in single-slot auctions the problem can be solved using suitable exploration-exploitation mechanisms able to achieve a per-step regret (over the auctioneer's revenue) of order $O(T^{-1/3})$ (where T is the number of times the auction is repeated). It is also known that, when truthfulness in expectation is adopted, a per-step regret (over the social welfare) of order $O(T^{-1/2})$ can be obtained. In this paper we extend the results known in the literature to the case of multi-slot auctions. In this case, a model of the user is needed to characterize how the advertisers' valuations change over the slots. We adopt the cascade model that is the most famous model in the literature for sponsored search auctions. We prove a number of novel upper bounds and lower bounds both on the auctioneer's revenue loss and social welfare w.r.t. to the VCG auction and we report numerical simulations investigating the accuracy of the bounds in predicting the dependency of the regret on the auction parameters

Strategic Learning in Teams

This paper analyzes a two-player game of strategic experimentation with three-armed exponential bandits in continuous time. Players face replica bandits, with one arm that is safe in that it generates a known payoff, whereas the likelihood of the risky arms’ yielding a positive payoff is initially unknown. It is common knowledge that the types of the two risky arms are perfectly negatively correlated. I show that the efficient policy is incentive-compatible if, and only if, the stakes are high enough. Moreover, learning will be complete in any Markov perfect equilibrium with continuous value functions if, and only if, the stakes exceed a certain threshold

Learning and payoff externalities in an investment game

This paper examines the interplay of informational and payoff externalities in a two-player irreversible investment game. Each player learns about the quality of his project by observing a private signal and the action of his opponent. I characterize the unique symmetric equilibrium in a timing game that features a second-mover advantage, allowing for arbitrary correlation in project qualities. Despite private learning, the game reduces to a stochastic war of attrition. In contrast to the case of purely informational externalities, all investments happen at the same real time instant—irrespective of the sign of the correlation—and beliefs never get trapped in a no-learning region, provided that the second-mover advantage is sufficiently high.Accepted manuscrip

Experimenting with Strategic Experimentation: Risk Taking, Neighborhood Size and Network Structure

This paper investigates the effects of neighborhood size and network structure on strategic experimentation. We analyze a multi-arm bandit game with one safe and two risky alternatives. In this setting, risk taking produces a learning externality and an opportunity for free riding. We conduct a laboratory experiment to investigate whether group size and the network structure affect risk taking. We find that group size has an effect on risk taking that is qualitatively in line with equilibrium predictions. Introducing an asymmetry among agents in the same network with respect to neighborhood size leads to substantial deviations from equilibrium play. Findings suggests that subjects react to changes in their direct neighborhood but fail to play a best-response to their position within the network.strategic experimentation, experiment, bandit game, risk taking

On the Optimal Amount of Experimentation in Sequential Decision Problems

We provide a tight bound on the amount of experimentation under the optimal strategy in sequential decision problems. We show the applicability of the result by providing a bound on the cut-off in a one-arm bandit problem

Advancing Subgroup Fairness via Sleeping Experts

We study methods for improving fairness to subgroups in settings with overlapping populations and sequential predictions. Classical notions of fairness focus on the balance of some property across different populations. However, in many applications the goal of the different groups is not to be predicted equally but rather to be predicted well. We demonstrate that the task of satisfying this guarantee for multiple overlapping groups is not straightforward and show that for the simple objective of unweighted average of false negative and false positive rate, satisfying this for overlapping populations can be statistically impossible even when we are provided predictors that perform well separately on each subgroup. On the positive side, we show that when individuals are equally important to the different groups they belong to, this goal is achievable; to do so, we draw a connection to the sleeping experts literature in online learning. Motivated by the one-sided feedback in natural settings of interest, we extend our results to such a feedback model. We also provide a game-theoretic interpretation of our results, examining the incentives of participants to join the system and to provide the system full information about predictors they may possess. We end with several interesting open problems concerning the strength of guarantees that can be achieved in a computationally efficient manner

A Truthful Learning Mechanism for Contextual Multi--Slot Sponsored Search Auctions with Externalities

International audienceSponsored search auctions constitute one of the most successful applications of \emph{microeconomic mechanisms}. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and, at the same time, to assure both the advertisers and the auctioneer a non--negative utility. Nonetheless, in sponsored search auctions, the click--through--rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard incentive compatible mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs as the same time as implementing a truthful mechanism with a revenue loss as small as possible compared to an optimal mechanism designed with the true CTRs. Previous works showed that in single--slot auctions the problem can be solved using a suitable exploration--exploitation mechanism able to achieve a per--step regret of order $O(T^{-1/3})$ (where $T$ is the number of times the auction is repeated). In this paper we extend these results to the general case of contextual multi--slot auctions with position-- and ad--dependent externalities. In particular, we prove novel upper--bounds on the revenue loss w.r.t. to a VCG auction and we report numerical simulations investigating their accuracy in predicting the dependency of the regret on the number of rounds $T$, the number of slots $K$, and the number of advertisements $n$

Imperfect Market Monitoring and SOES Trading

We develop a model of price formation in a dealership market where monitoring of the information flow requires costly effort. The result is imperfect monitoring, which creates profit opportunities for speculators, who do not act as dealers but simply monitor the information flow and quote updates in order to pick off stale quotes. Externalities associated with monitoring can help to sustain non-competitive spreads. We show that protecting dealers against the execution of stale quotes can result in larger spreads and be detrimental to price discovery due to externalities in monitoring. A reduction in the minimum quoted depth will reduce the spread and speculators' trading frequency. Our analysis is relevant for the SOES debate given that the behavior of speculators in our model is very similar to the alleged behavior of the real world SOES bandits.monitoring; bid-ask spread; automatic execution; SOES trading