This
protocol for
fair cake division works in a wide variety of situations. Since there are only
2 players, no
coalitions are possible, which of course makes things simpler.
Here's the protocol: Alice cuts the cake into 2 pieces (which can be any size!); then Bob picks his piece. Note that Bob's piece will never be smaller than Alice's (otherwise he'd have picked the other piece). Thus Bob is convinced the division was "fair". On the other hand, Alice can always divide the cake equally, thus getting as much as Bob; anything else leads her to get less cake. Thus the cake is split equally, and neither party can complain about cheating!