Abstract
A recurring theme in recent computer science literature is that proper design of signaling schemes is a crucial aspect of effective mechanisms aiming to optimize social welfare or revenue. One of the research endeavors of this line of work is understanding the algorithmic and computational complexity of designing efficient signaling schemes. In reality, however, information is typically not held by a central authority but is distributed among multiple sources (third-party “mediators”), a fact that dramatically changes the strategic and combinatorial nature of the signaling problem. In this article, we introduce distributed signaling games , while using display advertising as a canonical example for introducing this foundational framework. A distributed signaling game may be a pure coordination game (i.e., a distributed optimization task) or a non-cooperative game. In the context of pure coordination games, we show a wide gap between the computational complexity of the centralized and distributed signaling problems, proving that distributed coordination on revenue-optimal signaling is a much harder problem than its “centralized” counterpart. In the context of non-cooperative games, the outcome generated by the mediators’ signals may have different value to each. The reason for that is typically the desire of the auctioneer to align the incentives of the mediators with his own by a compensation relative to the marginal benefit from their signals. We design a mechanism for this problem via a novel application of Shapley’s value and show that it possesses some interesting properties; in particular, it always admits a pure Nash equilibrium, and it never decreases the revenue of the auctioneer (relative to his a priori revenue when there are no mediators).
Highlights
The topic of signaling has recently received much attention in the computer science literature on mechanism design [2, 4, 6, 5, 7, 12]
A recurring theme of this literature is that proper design of a signaling scheme is crucial for obtaining efficient outcomes, such as social welfare maximization or revenue maximization
The goal of this paper is to initiate an algorithmic study of such games, which we term distributed signaling games, via what we view as a canonical example: Bayesian auctions; and display advertising in the presence of third party external mediators
Summary
The topic of signaling has recently received much attention in the computer science literature on mechanism design [2, 4, 6, 5, 7, 12]. The bidders are advertisers who know that distribution, but only the web site owner knows the impression type instantiation, consisting of identifiers such as age, origin, gender and salary of the web-site visitor. The web-site owner decides on the information (i.e., signal) about the instantiation to be provided to the bidders, which bid their expected valuations for the impression given the information provided. The selection of the proper signaling by the web-site is a central mechanism design problem. For example, an impression associated with two attributes: whether the user is male or female on one side, and whether he is located in the US or out of the US on the other side This gives 4 types of possible users. One can verify that an auctioneer who reveals no information receives an expected payoff of $25, an auctioneer who reveals all information gets no payoff, while partitioning the impression types into two pairs, revealing only the pair of the impression which was materialized (rather than the exact instantiation) will yield a payoff of $50, which is much higher revenue
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