The owner of a professional basketball team is hiring a new coach. The chance that the team will get into the playoffs depends on how hard the coach works. If the coach is relaxed, the team has a 35% chance of getting into the playoffs. If the coach works hard, the team has a 60% chance of getting into the playoffs. Unfortunately, the owner cannot tell whether the coach is working hard.

The owner plans to offer the coach a salary of $70,000, plus a bonus if the team makes it into the playoffs. The owner wants to offer the minimum bonus needed to ensure the coach accepts the job offer and works hard.

The owner knows that the coach could earn $100,000 per year working elsewhere at a relaxed pace. If the coach works hard, he will face extra stress and unpaid overtime equivalent to a cost for him of $10,000 per year.

Treat this situation as a game where the owner moves first by specifying the size of the bonus, and then the coach moves second by deciding whether to accept the job and whether to work hard. Create a model, then analyze it and interpret the results to answer the following questions.

1. How large of a bonus should the owner offer to the coach?
2. If the offer is accepted, how much money on average should the owner expect to pay the coach per year in total salary and bonus?