EFX doesn't imply MMS

Dependencies:

1. Fair division
2. EFX
3. Maximin share allocations

$\newcommand{\defeq}{:=}$ Let $t \in \{-1, 1\}$. Consider a fair division instance with 2 agents having equal entitlements and identical additive valuations. Let there be 5 items of values $3t$, $3t$, $2t$, $2t$, and $2t$. Let $A \defeq (\{3t, 2t\}, \{3t, 2t, 2t\})$. Then $A$ is EFX but not MMS.

Proof

The MMS is $6t$, since $P = (\{3t, 3t\}, \{2t, 2t, 2t\})$ is an MMS partition. But in $A$, some agent doesn't get her MMS.

Dependency for: None

Info:

• Depth: 6
• Number of transitive dependencies: 10

Transitive dependencies:

1. /sets-and-relations/countable-set
2. /analysis/sup-inf
3. σ-algebra
4. Set function
5. Fair division
6. Envy-freeness
7. Maximin share of a set function
8. Maximin share allocations
9. Submodular function
10. EFX