Costly miscalibration

We consider a platform which provides probabilistic forecasts to a customer using some algorithm. We introduce a concept of miscalibration, which measures the discrepancy between the forecast and the truth. We characterize the platform's optimal equilibrium when it incurs some cost for miscalibration, and show how this equilibrium depends on the miscalibration cost: when the miscalibration cost is low, the platform uses more distant forecasts and the customer is less responsive to the platform's forecast; when the miscalibration cost is high, the platform can achieve its commitment payoff in an equilibrium, and the only extensive-form rationalizable strategy of the platform is its strategy in the commitment solution. Our results show that miscalibration cost is a proxy for the degree of the platform's commitment power, and thus provide a microfoundation for the commitment solution.