“…Finally, we have restricted insurance firms to a particular class of contracts (i.e., those that reimburse a constant percentage of realized expenses). We first note that coinsurance is a very common arrangement in practice (e.g., 64 percent of insured employees face coinsurance on hospital admissions, according to Kaiser Family Foundation, ) and in theoretical studies (e.g., Frech and Ginsburg, ; Ma and McGuire, ; Vaithianathan, ; Nell, Richter, and Schiller, ). Even so, a natural extension of the model would be to allow a broader class of contracts, including: copays or deductibles (where the household pays for the first dollars of a claim), payment caps (where the household is responsible for 100 percent of expenses above some amount), fixed payments (where the insurer pays a fixed amount on any claim, as well as coinsurance on actual expenses), or maximum out‐of‐pocket clauses (where coinsurance drops to 0 percent on any expenses beyond some threshold) .…”