Fair division is an optimisation problem in game theory of dividing a set of resources among several parties who have an entitlement to them so that each party receives their due share. The central tenet of fair division is that such a division should be performed by the players themselves, without the need for external arbitration, as only the players themselves really know how they value the goods.

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. The archetypal fair division algorithm is divide and choose. The research in fair division can be seen as an extension of this procedure to various more complex settings.

The 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), and dispute resolution.

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 ${\displaystyle C}$ (often called "the cake") and a group of ${\displaystyle n}$ players. A division is a partition of ${\displaystyle C}$ into ${\displaystyle n}$ disjoint subsets: ${\displaystyle C=X_{1}\sqcup X_{2}\sqcup \cdots \sqcup X_{n}}$, one subset per player.

The set ${\displaystyle C}$ can be of various types:

Additionally, the set to be divided may be:

Finally, it is common to make some assumptions about whether the items to be divided are:

Based on these distinctions, several general types of fair division problems have been studied: