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Distributed Signaling Games
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
(-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