Envy-freeness


Envy-freeness is a criterion of fair division.
In an envy-free division, every agent feels that their share is at least as good as the share of any other agent, and thus no agent feels envy.

Definitions

A resource is divided among several agents such that every agent receives a share. Every agent has a subjective preference relation over different possible shares. The division is called envy-free if for all and :
If the preference of the agents are represented by a value functions, then this definition is equivalent to:
Put another way: we say that agent envies agent if prefers the piece of over his own piece, i.e.:
A division is called envy-free if no agent envies another agent.

History

EF was introduced to the problem of fair cake-cutting by George Gamow and Marvin Stern in 1958. In the context of fair cake-cutting, EF means that each agent believes that their share is at least as large as any other share. In the context of chore division, EF means that each agent believes their share is at least as small as any other share. The crucial issue is that no agent would wish to swap their share with any other agent.
See:
Later, EF was introduced to the economics problem of resource allocation by Duncan Foley in 1967. It became the dominant fairness criterion in economics. See, for example:
See also: