A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...

Fair Division, unlike most research on fairness in the social sciences and mathematics, is devoted solely to the analysis of constructive procedures for actually dividing things up and resolving disputes, including...

Distributed applications are realized by cooperation of objects. A state of the object depends on in what order the object exchanges request and response messages and computes requests. In this paper, we newly define a significantly precedent order of messages based on a conflicting relation among requests. The objects can be mutually consistent if the objects take messages in the significantly...