Construct Game Trees

An athlete has hired G & B Consulting for some advice, and you have been assigned to the project. The reason why this athlete is in need of a consulting firm is that he knows that he is going to test positive for performance-enhancing drugs on a recent random screening. Inevitably, the league is going to issue a press release as it is standard policy. The athlete is wondering if there is any overall advantage to him to make a press release of his own before the league does in the hopes that it may help his image and future prospects as well as give him a little bit more influence over the incident will play out in the media.

A coworker of yours who is also working on the project creates this payoff matrix:

League

No Press Release

Press Release

Athlete

No press release

(1, 2)

(1, 2)

Press Release

(2, 1)

(0, 0)

Part 1: You recognize that this is not a simultaneous game, and the payoff matrix is not the best form of analysis. Construct a game tree to model this scenario. Compose an email to your coworker to explain why a game tree should be used instead of this payoff matrix, and make a note of any cells that should be excluded.

Part 2: Perform backward induction on the game tree to find the optimum strategy. Show all steps and describe your process for inclusion in the final report to the client.

Part 3: Create a report to present to the candidate with your results. Clearly state your recommended strategy in simple terms, then also include all relevant technical information.

REQUIREMENTS:
Report attempted and includes thorough information. Little-to-no errors in communication or results.
- Backwards induction is complete. Optimum strategy is demonstrated. All of work shown with little-to-no errors.

- Game tree construction is complete. All of the components of the question are addressed. All work shown with little-to-no errors.