A simple model of competitive testing

Multiple agents are competing for a prize. Each agent is privately informed about his type. The principal who allocates the prize wants to give it to the agent with the highest type. Each agent can take a test that reveals his type at a cost. I show that an increase in competition makes the principal more informed when the cost is high, and less informed when the cost is low. Nevertheless, the principal always benefits from greater competition. Making the test mandatory for receiving the prize is Pareto-dominated by voluntary verification unless competition is low.