| Abstract: |
This paper considers the problem of allocating bundles of heterogeneous and
indivisible objects to agents, when monetary transfers are not allowed and
agents reveal only ordinal preferences over objects, e.g., allocating players'
contract rights to teams in professional sporting leagues. Preferences over
objects are extended to incomplete preferences over bundles using pairwise
dominance. We provide a simple characterization of the class of draft rules:
they are the only allocation rules satisfying $\textit{efficiency}$,
$\textit{respectfulness of the priority}$, $\textit{envy-freeness up to one
object}$ and $\textit{resource-monotonicity}$. We also prove two impossibility
theorems: (i) $\textit{non-wastefulness}$, $\textit{respectfulness of the
priority}$ and $\textit{envy-freeness up to one object}$ are incompatible with
$\textit{weak strategy-proofness}$; (ii) $\textit{efficiency}$ and
$\textit{envy-freeness up to one object}$ are incompatible with $\textit{weak
strategy-proofness}$. If agents may declare some objects unacceptable, then
draft rules are characterized by $\textit{efficiency}$,
$\textit{respectfulness of the priority}$, $\textit{envy-freeness up to one
object}$, $\textit{resource-monotonicity}$ together with a mild invariance
property called $\textit{truncation-invariance}$. |