Dynamic Price Competition in Auto-Insurance Brokerage

Brazilian data on auto-insurance present an intriguing fact: the coexistence of policies being sold with zero and positive brokerage fees. We extend the Bertrand model of price competition to a dynamic environment in which agents face a .xed cost to switch to a new (unmatched) broker. This incumbent?s advantage drives unmatched brokers to set fees aggressively. We explicitly derive symmetric re-cursive Nash equilibrium in which zero and positive brokerage fees are played with positive probability. We then use the mixed-strategy equilibrium distribution to perform a maximum likelihood estimation of the model parameters. Using data on brokerage fees alone, this structural econometric procedure allows us to identify: (i) the number of brokers effectively bidding to a given consumer; (ii) the insuree?s cost of switching brokers; and (iii) the expected life-time discounted profits of matched and unmatched brokers.