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

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