Titolo: Computing Agents' Reputation within a Network
We propose a model of information transmission within a social network that exploits portfolio theory and option structures. The network aims to estimate an unknown (possibly multidimensional) parameter $\theta$ through multiple communication rounds. In every communication round, a different piece of information is shared: at the first communication round agents spread the estimated value of $\theta$, at the second communication round agents' ability at estimating $\theta$, at the third agents' ability at evaluating the ability at estimating $\theta$ and so on. The estimates of the unknown parameter and those of each agent's abilities to evaluate the reliability of the information received in every round, are interpreted as assets whose values evolve over time according to a compound Poisson process. Thus, after every communication round, each agent constructs a portfolio of options whose underlying is the estimate of the parameter or that of a specific agent's ability. Subsequently, a portfolio's weights are exploited to aggregate the information received in the communication round. A sufficient condition for reaching consensus within the social network is also provided. Finally, we describe how the proposed approach is able to describe and examine the information transmission mechanism in some real life situation.