The effect of a noise trader on the equilibrium in repeated prediction markets

This work aims to study the equilibrium properties of a repeated prediction market when a noise trader comes into play. Bottazzi and Giachini have completely probed the system where two fractional Kelly traders invest in such a market, finding sufficient conditions for dominance, vanishing or coexistence of the agents.I have extended these conditions in the case in which there is a noise trader, other then the two Kelly ones.Then, numerical simulations have been run in order to confirm the analytical results.It has been found that for some set of parameters the noise trader vanishes, for example when the believes of one or two agents are close to the truth; but there are also set of parameters for which the noise trader dominates or survives, coexisting with one Kelly trader. It is then not trivial to neglect the presence of agents that act irrationally in such a market, supposing that the markets kicks them out after a transient: it is possible that they survive or even dominate the market.