An airline transports 100 passengers every day and each traveler brings a carry-on bag. There are two types of travelers: (1) "contributors", who pay to store the carry-on bag in the cargo area, and (2) "free riders", who bring the carry-on bag to the plane until they are asked to store it for free. Let C denote the number of "contributors" and F the number of "free riders", such that C + F = 100 travelers. Each "contributor" receives a payoff equal to C and each "free rider" receives a payoff equal to 10 + 9C

Question: What is the maximum total benefit that the group can achieve (X) and the predicted total benefit using game theory (Y)?

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