Implicit Client Sorting and Bonus Malus Contracts

In an earlier paper, we showed that, in a multi-period setting (but with no multi-period commitment) with two client types (adverse selection) and a competitive insurer environment, a comparasin between periodic repetitions of the classic Rothschild-Stiglitz separating equilibrium contract menu and a second contract based on Bayesian learning (which we identify as a bonus-malus contract) yields situations in which either one or the other will be used, depending on the parameter which is used to discount future wealth. The fact that the two contract formats are mutually exclusive (i.e. cannot co.exist) depends critically on all clients having the same discount factor. In the current paper, we relax the assumption of common discount factors, and we find that situations exist in which both contract formats may co-exist.