Restricted agents, pairwise fairness, and groupwise fairness

Dependencies:

1. Fair division

Let $(N, M, V, w)$ be a fair division instance. Let $A$ be a (partial) allocation and $F$ be a notion of fairness.

For $S \subseteq N$, we say that $A$ is '$F$-fair restricted to $S$' if the allocation $(A_i)_{i \in S}$ is $F$-fair for the instance $(S, \bigcup_{i \in S} A_i, (v_i)_{i \in S}, (w_i)_{i \in S})$.

Allocation $A$ is said to be pairwise-$F$-fair iff for all $S \subseteq N$ such that $|S| = 2$, it is $F$-fair restricted to $S$.

Allocation $A$ is said to be groupwise-$F$-fair iff for all $S \subseteq N$, it is $F$-fair restricted to $S$.

Dependency for:

1. MMS implies MXS
2. Leximin implies GMMS for idval
3. Additive chores and binary marginals
4. Additive goods and binary marginals
5. PROPx doesn't exist even if APS does
6. PROPm doesn't exist for mixed manna
7. PROP1+M1S allocation doesn't exist
8. GMMS doesn't imply APS

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