Envy-freeness

Dependencies:

1. Fair division

Let $A = (A_1, \ldots, A_n)$ be a (partial) allocation in a fair division instance. Let $w = (w_1, \ldots, w_n)$ be the vector of entitlements. Then

• Agent $i$ envies agent $j$ in $A$ iff $v_i(A_i)/w_i < v_i(A_j)/w_j$.
• Agent $i$ is envy-free (EF) in $A$ iff $i$ doesn't envy anyone.
• $A$ is envy-free (EF) iff all agents are envy-free in $A$.

Dependency for:

1. MEFS implies PROP for subadditive valuations
2. Cake cutting: PROP implies EEF for additive valuations
3. PROP implies EF for n=2
4. EFX implies EF1
5. EF1
6. EFX
7. PROP cake division doesn't exist for supermodular valuations
8. PROP but not MEFS
9. MEFS but not EEF
10. MEFS but not EEF for chores
11. MEFS+PROP doesn't imply EEF1 for chores
12. EEF doesn't imply EF1
13. EF doesn't imply PROP for supermodular valuations

Info:

• Depth: 4
• Number of transitive dependencies: 4

Transitive dependencies:

1. /sets-and-relations/countable-set
2. σ-algebra
3. Set function
4. Fair division