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. Cake cutting: PROP implies EEF for additive valuations
2. EFX implies EF1
3. EF1
4. EFX
5. PROP cake division doesn't exist for supermodular valuations
6. EEF doesn't imply EF for additive 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