EF1

Dependencies:

1. Fair division
2. Envy-freeness

$\newcommand{\defeq}{:=}$ Let $([n], M, V, w)$ be a fair division instance for indivisible items (where each agent $i$ has entitlement $w_i$). An allocation $A$ is said to be EF1-fair to agent $i$ iff for every agent $j \in [n] \setminus \{i\}$, either $i$ doesn't envy $j$, or for some item $t \in A_i \cup A_j$, we have \[ \frac{v_i(A_i \setminus \{t\})}{w_i} ≥ \frac{v_i(A_j \setminus \{t\})}{w_j}. \] If the above condition is not satisfied for some $j \in [n] \setminus \{i\}$, we say that $i$ EF1-envies $j$.

Dependency for:

1. EFX implies EF1
2. Minimum EF1 share (M1S)

Info:

• Depth: 5
• Number of transitive dependencies: 5

Transitive dependencies:

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