Jen suspects that Brad is having an affair with Angie, and wants to divorce him. Her prenuptial agreement specifies that if she files for divorce, she receives $60,000, but that her award will double if she can provide solid evidence of an affair. Jen's lawyer can prove the affair only if he hires a private detective out of his own pocket. A detective good enough to uncover the affair will cost the lawyer $10,000.
The lawyer, a paragon of virtue, will tell Jen that he employed the detective even if he does not. The lawyer has offered Jen two payment alternatives. Plan A requires Jen to pay the lawyer a flat fee of $25,000 regardless of the outcome; Plan B calls for her to pay to the lawyer 1/3 of the settlement amount.
a. Determine the relevant payouts for all of the possible outcomes, and draw the extensive form of the game Jen and the lawyer are playing.
b. Find the equilibrium outcome to this game. Will Jen choose the flat fee? Does the lawyer hire a detective?
c. Discuss the implications of the type of payment scheme on the incentives and payoffs each player faces. Then extend your implications to the business world by discussing paying workers an annual salary vs. paying them a certain amount for each finished product they produce (called "piece-rate compensation").