This competency will allow you to demonstrate your ability and skill in constructing and analyzing game trees from payoff matrices.
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|
|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.
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