On the Range of Equilibria Utilities of a Repeated Epidemic Dissemination Game with a Mediator

We consider eager-push epidemic dissemination in a complete graph. Time is divided into synchronous stages. In each stage, a source disseminates a stream of bits, partitioned into $\nu$ 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 acquiescent and that they do not collude. We model interactions as an infinitely repeated game with discounting. 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 a symmetric cipher primitive and pseudo-random number generator, 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 cooperation may be sustained for any fanout while minimising the relative overhead of monitoring.