At a party, you have the following:
a very small flag tied to a cocktail stick.
You must devise a way of dividing the cake equally among your guests (you're not having any cake). The trouble is, they don't trust you to divide the cake up equally, so if you exercise any discretion in enforcing the rules you set for the guests or try to cut the cake yourself, they'll accuse you of favoritism. The guests can be expected to try to maximise their share of the cake subject to your rules, and to do so in a rational manner. Initally, the cake is on the table, you and the n guests are currently standing in a circle around the cake, and the flag and knife are lying on the table next to the cake.
To make things clearer, we'll impose some restrictions on the players' behaviour. Players make a series of moves, one after another, until everyone has a piece of cake, and you set the rules as to which moves they are allowed to make under what circumstances. The moves are:
- making a radial cut in the cake
- sticking the flag in the cake or taking it out
- picking up the knife/handing it to another player (you can have rules which specify which player)
- taking a single piece of cake (which has already been cut away from the rest of the cake) and leaving the game.
Anyone have any ideas? I think I can come up with a system under these conditions.