  We consider eager-push epidemic dissemination in a complete graph. Time is
divided into synchronous stages. In each stage, a source disseminates $\nu$
events. Each event is sent by the source, and forwarded by each node upon its
first reception, to $f$ nodes selected uniformly at random, where $f$ is the
fanout. We use Game Theory to study the range of $f$ for which equilibria
strategies exist, assuming that players are either rational or obedient to the
protocol, and that they do not collude. We model interactions as an infinitely
repeated game. We devise a monitoring mechanism that extends the repeated game
with communication rounds used for exchanging monitoring information, and
define strategies for this extended game. We assume the existence of a trusted
mediator, that players are computationally bounded such that they cannot break
the cryptographic primitives used in our mechanism, and that symmetric
ciphering is cheap. Under these assumptions, we show that, if the size of the
stream is sufficiently large and players attribute enough value to future
utilities, then the defined strategies are Sequential Equilibria of the
extended game for any value of $f$. Moreover, the utility provided to each
player is arbitrarily close to that provided in the original game. This shows
that we can persuade rational nodes to follow a dissemination protocol that
uses any fanout, while arbitrarily minimising the relative overhead of
monitoring.
