Trusting: Alone and together

We study the problem of an agent continuously faced with the decision of placing or not placing trust in an institution. The agent makes use of Bayesian learning in order to estimate the institution's true trustworthiness and makes the decision to place trust based on myopic rationality. Using elements from random walk theory, we explicitly derive the probability that such an agent ceases placing trust at some point in the relationship, as well as the expected time spent placing trust conditioned on their discontinuation thereof. We then continue by modelling two truster agents, each in their own relationship to the institution. We consider two natural models of communication between them. In the first (``observable rewards'') agents disclose their experiences with the institution with one another, while in the second (``observable actions'') agents merely witness the actions of their neighbour, i.e., placing or not placing trust. Under the same assumptions as in the single agent case, we describe the evolution of the beliefs of agents under these two different communication models. Both the probability of ceasing to place trust and the expected time in the system elude explicit expressions, despite there being only two agents. We therefore conduct a simulation study in order to compare the effect of the different kinds of communication on the trust dynamics. We find that a pair of agents in both communication models has a greater chance of learning the true trustworthiness of an institution than a single agent. Communication between agents promotes the formation of long term trust with a trustworthy institution as well as the timely exit from a trust relationship with an untrustworthy institution. Contrary to what one might expect, we find that having less information (observing each other's actions instead of experiences) can sometimes be beneficial to the agents.