Mrs. Jones is seeking a divorce from Mr. Jones. Under the terms of her prenuptial agreement, her settlement will be $100,000 if she can prove that Mr. Jones has had an affair, but $50,000 otherwise. Her lawyer, acting as her agent, can prove the affair only if he hires a private detective for $10,000, which will come out of the lawyer's fee. Mrs. Jones has the option of paying her lawyer a flat fee of $20,000 regardless of the outcome of the case or 1/3 of the settlement. The lawyer will hire the private detective only if it is profitable for him to do so.

1. Whose is the first move?

2. Draw a tree diagram for this "game in extensive form".

3. Express the strategies in normal form.

4. Which payment method will enable Mrs. Jones to win the case? (Use backward induction.)

5. Can you think of any other way (besides the flat fee and the 1/3 share) that Mrs. Jones might compensate the lawyer so as to get the best outcome for herself?