I am nor sure that me willing to accept to be paid X to stay in the hostel, is similar to me willing to pay X/n for someone else to say there.
Say it is only me and another person, hotel cost 100$, hostel cost 50$, i am willing to stay in the hostel for 100$.
If i am staying in the hostel, i will get 100$ and pay 50$, meaning i will have +50$ - which i am happy with since i ask for the 100$
If i am staying in the hotel, i might pay the other person up to 100$, meaning i will spent up to 200$ - which i may be very annoy by, since now the hotel may not be worth the cost.
There a very realistic scenario here, in which there no balance between people cost of accepting to stay in the hostel, and the cost they willing to spend on the vacation/hotel.
I think the assumption in the problem is that the costs of renting the rooms (hotel and hostel) are either already covered or will be divided equally among the group. There is a cost imposed on the group (of just you and one other person in this case) of one fewer hotel room than expected. The problem is how to distribute this cost. You will get some and the other person will get some. Neither of you will necessarily be happy compared to the expected alternative of each getting a hotel room.
I am nor sure that me willing to accept to be paid X to stay in the hostel, is similar to me willing to pay X/n for someone else to say there.
Say it is only me and another person, hotel cost 100$, hostel cost 50$, i am willing to stay in the hostel for 100$.
If i am staying in the hostel, i will get 100$ and pay 50$, meaning i will have +50$ - which i am happy with since i ask for the 100$
If i am staying in the hotel, i might pay the other person up to 100$, meaning i will spent up to 200$ - which i may be very annoy by, since now the hotel may not be worth the cost.
There a very realistic scenario here, in which there no balance between people cost of accepting to stay in the hostel, and the cost they willing to spend on the vacation/hotel.
I think the assumption in the problem is that the costs of renting the rooms (hotel and hostel) are either already covered or will be divided equally among the group. There is a cost imposed on the group (of just you and one other person in this case) of one fewer hotel room than expected. The problem is how to distribute this cost. You will get some and the other person will get some. Neither of you will necessarily be happy compared to the expected alternative of each getting a hotel room.