Shouldn’t the hostel-goer forego a 1/n share of their Minimum Satisfactory Compensation (since the other n-1 participants also pay a share)? The best outcome is for the most-willing participant to take the hostel, and the total cost incurred by the group is equal to this person’s MSC. If we want to divide this total cost equally among all group members, the n-1 each pay a 1/n share and the 1 forgoes a 1/n share from their actual compensation.
Alternatively, one could argue that the cost should be distributed proportionally-more to participants who would be more harmed by having to stay in the hostel (since they receive more benefit from the ideal arrangement vs. an alternative of, say, picking someone at random).
How do the incentives work out if everyone pays 1/n of their own bid?
Shouldn’t the hostel-goer forego a 1/n share of their Minimum Satisfactory Compensation (since the other n-1 participants also pay a share)? The best outcome is for the most-willing participant to take the hostel, and the total cost incurred by the group is equal to this person’s MSC. If we want to divide this total cost equally among all group members, the n-1 each pay a 1/n share and the 1 forgoes a 1/n share from their actual compensation.
Alternatively, one could argue that the cost should be distributed proportionally-more to participants who would be more harmed by having to stay in the hostel (since they receive more benefit from the ideal arrangement vs. an alternative of, say, picking someone at random).
How do the incentives work out if everyone pays 1/n of their own bid?