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Game theory
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Game theory final exam:
Full Marks (100%):
You will receive full marks if you answer all questions correctly and at least 70% of the class chooses the "Full Marks" strategy.
If you answer all questions correctly but fewer than 70% of the class chooses the "Full Marks" strategy, your grade will be 90%
Half Marks (50%):
You will receive half marks if you answer all questions correctly but at least 30% of the class chooses the "Half Marks" strategy.
If you choose this strategy and the class distribution aligns as specified, your grade will be 50% irrespective of the correctness of your answers.
Fail (0%) with Incentive:
You will receive a failing grade if you choose the "Fail" strategy or if your answers are incorrect and less than 30% of the class chooses the "Fail" strategy.
If you choose the "Fail" strategy and at least 30% of the class also chooses the "Fail" strategy, you will receive a special incentive: Automatic 'A' grade in the next course module, regardless of your performance in this exam.
Additionally, if more than 70% of the class chooses "Fail" or "Half Marks" strategies combined, everyone will fail regardless of individual choices.
I think you need an inverse incentive:
If you are the only one to use "Fail" strategy, you finish with 100% and everybody's result will be mutliplied by 0.8