Construct game trees | Mathematics homework help


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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:


No Press Release

Press Release


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.

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.

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