Contracting for research is often infeasible because research inputs are unobservable and research outcomes cannot be verified by a court. Sponsoring a research tournament can resolve these problems. A model is presented in which contestants compete to find the innovation of highest value to the tournament sponsor. The winner receives a prespecified prize. The tournament game has a unique subgame-perfect equilibrium. Free entry is not optimal because equilibrium effort by each researcher decreases in the number of contestants. An optimally designed research tournament balances the probability of overshooting the first-best quality level against the probability of falling short.

A market in which the owner of a durable good, X, contracts with an expert for diagnostic and treatment services is studied. Good X may be in one of three states: "health," "disease," or "failure." Only experts can determine whether X is healthy or diseased and perform treatment. The owner cannot tell whether recommended treatment is really needed. This creates an information-based demand for health insurance by risk-neutral consumers. Imperfections in the market for spot insurance may give rise to free diagnostic checks, strategic procrastination, and long-term health maintenance agreements.

A market in which the owner of a durable good, X, contracts with an expert for diagnostic and treatment services is studied. Good X may be in one of three states: "health," "disease," or "failure." Only experts can determine whether X is healthy or diseased and perform treatment. The owner cannot tell whether recommended treatment is really needed. This creates an information-based demand for health insurance by risk-neutral consumers. Imperfections in the market for spot insurance may give rise to free diagnostic checks, strategic procrastination, and long-term health maintenance agreements.