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When selling information products, the seller can provide some free partial information to change peoples valuations so that the overall revenue can possibly be increased. We study the general problem of advertising information products by revealing partial information. We consider buyers who are decision-makers. The outcomes of the decision problems depend on the state of the world that is unknown to the buyers. The buyers can make their own observations and thus can hold different personal beliefs about the state of the world. There is an information seller who has access to the state of the world. The seller can promote the information by revealing some partial information. We assume that the seller chooses a long-term advertising strategy and then commits to it. The sellers goal is to maximize the expected revenue. We study the problem in two settings. (1) The seller targets buyers of a certain type. In this case, we prove that finding the optimal advertising strategy is equivalent to finding the concave closure of a simple function. The function is a product of two quantities, the likelihood ratio and the cost of uncertainty. Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve for the optimal mechanism by a finite-size convex program. The convex program will have a polynomial size if the state of the world has a constant number of possible realizations or the buyers face a decision problem with a constant number of options. For the general problem, we prove that it is NP-hard to find the optimal mechanism. (2) When the seller faces buyers of different types and only knows the distribution of their types, we provide an approximation algorithm when it is not too hard to predict the possible type of buyers who will make the purchase. For the general problem, we prove that it is NP-hard to find a constant-factor approximation.
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We define the notion of Bayes correlated Wardrop equilibrium for general nonatomic games with anonymous players and incomplete information. Bayes correlated Wardrop equilibria describe the set of equilibrium outcomes when a mediator, such as a traffic information system, provides information to the players. We relate this notion to Bayes Wardrop equilibrium. Then, we provide conditions -- existence of a convex potential and complete information -- under which mediation does not improve equilibrium outcomes. We then study full implementation and, finally, information design in anonymous games with a finite set of players, when the number of players tends to infinity.
We identify the first static credible mechanism for multi-item additive auctions that achieves a constant factor of the optimal revenue. This is one instance of a more general framework for designing two-part tariff auctions, adapting the duality framework of Cai et al [CDW16]. Given a (not necessarily incentive compatible) auction format $A$ satisfying certain technical conditions, our framework augments the auction with a personalized entry fee for each bidder, which must be paid before the auction can be accessed. These entry fees depend only on the prior distribution of bidder types, and in particular are independent of realized bids. Our framework can be used with many common auction formats, such as simultaneous first-price, simultaneous second-price, and simultaneous all-pay auctions. If all-pay auctions are used, we prove that the resulting mechanism is credible in the sense that the auctioneer cannot benefit by deviating from the stated mechanism after observing agent bids. If second-price auctions are used, we obtain a truthful $O(1)$-approximate mechanism with fixed entry fees that are amenable to tuning via online learning techniques. Our results for first price and all-pay are the first revenue guarantees of non-truthful mechanisms in multi-dimensional environments; an open question in the literature [RST17].
We study competition among contests in a general model that allows for an arbitrary and heterogeneous space of contest design, where the goal of the contest designers is to maximize the contestants sum of efforts. Our main result shows that optimal contests in the monopolistic setting (i.e., those that maximize the sum of efforts in a model with a single contest) form an equilibrium in the model with competition among contests. Under a very natural assumption these contests are in fact dominant, and the equilibria that they form are unique. Moreover, equilibria with the optimal contests are Pareto-optimal even in cases where other equilibria emerge. In many natural cases, they also maximize the social welfare.
A decision-maker is deciding between an active action (e.g., purchase a house, invest certain stock) and a passive action. The payoff of the active action depends on the buyers private type and also an unknown state of nature. An information seller can design experiments to reveal information about the realized state to the decision-maker and would like to maximize profit from selling such information. We fully characterize, in closed-form, the revenue-optimal information selling mechanism for the seller. After eliciting the buyers type, the optimal mechanism charges the buyer an upfront payment and then simply reveals whether the realized state passed a certain threshold or not. The optimal mechanism features both price discrimination and information discrimination. The special buyer type who is a priori indifferent between the active and passive action benefits the most from participating in the mechanism.
Online advertising on platforms such as Google or Facebook has become an indispensable outreach tool, including for applications where it is desirable to engage different demographics in an equitable fashion, such as hiring, housing, civic processes, and public health outreach efforts. Somewhat surprisingly, the existing online advertising ecosystem provides very little support for advertising to (and recruiting) a demographically representative cohort. We study the problem of advertising for demographic representativeness from both an empirical and algorithmic perspective. In essence, we seek fairness in the outcome or
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