ABSTRACT
So far we have attempted, with some success and some failure, to "fairly" divide a cake among n players using different interpretations of "fair." If the problem is to give each player what he or she considers a portion of size at least 1/n (i.e., simple fair division), we know a number of ways to do that. If we are to give each an envy-free portion, that is tougher. We might try giving players strictly more than 1/n of the cake or finding pieces on which there is some agreement of value. Still other interpretations of fair have been formalized and studied. We will now explicitly list some of these (see box on p. 62).
