Fair division

Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth observation satellites. It is an active research area in mathematics, economics (especially social choice theory), dispute resolution, etc. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods. The archetypal fair division algorithm is divide and choose. It demonstrates that two agents with different tastes can divide a cake such that each of them believes that he got the best piece. The research in fair division can be seen as an extension of this procedure to various more complex settings. There are many different kinds of fair division problems, depending on the nature of goods to divide, the criteria for fairness, the nature of the players and their preferences, and other criteria for evaluating the quality of the division. Formally, a fair division problem is defined by a set (often called "the cake") and a group of players. A division is a partition of into disjoint subsets: , one subset per player. The set can be of various types: may be a finite set of indivisible items, for example: , such that each item should be given entirely to a single person. may be an infinite set representing a divisible resource, for example: money, or a cake. Mathematically, a divisible resource is often modeled as a subset of a real space, for example, the section [0,1] may represent a long narrow cake, that has to be cut into parallel pieces. The unit disk may represent an apple pie. Additionally, the set to be divided may be: homogeneous – such as money, where only the amount matters, or heterogeneous – such as a cake that may have different ingredients, different icings, etc.