Curtailing Ex-Post Fraud in Risk Sharing Arrangements

This paper considers a situation in which the outcome of a random variable, x~, must be split between two individuals, but only one of them (the agent) actually observes the true value that the variable takes. The agent reports a value of the variable to the principal, who then either accepts this report and each participant receives a predetermined share of the reported value of x~, or he rejects the report and carries out an investigation into the true value of x~. If the investigation reveals that the agent reported falsely (fraud), then each participant receives a predetermined payoff that depends on both the true value of x~ and the value of x that the agent reported. The paper finds a payoff function for the case of discovered fraud that provides the proper incentives for the agent to always report truthfully independently of his utility function. The model has direct applications for both tax evasion and insurance fraud.