#### Distributed Signaling Games

##### Moran Feldman, Moshe Tennenholtz, Omri Weinstein

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, making it a game between information providers, as opposed to a traditional mechanism design problem. In this paper we introduce {\em 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. On the other hand, we show that if the information structure of each mediator is assumed to be "local", then there is an efficient algorithm that finds a near-optimal ($5$-approximation) distributed signaling scheme. In the context of non-cooperative games, the outcome generated by the mediators' signals may have different value to each (due to the auctioneer's desire to align the incentives of the mediators with his own by relative compensations). 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.

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