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. PROP cake division doesn't exist for supermodular valuations
3. 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