Research map / Multi-agent systems and games / Games and equilibria
On Fair Division under Heterogeneous Matroid Constraints
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Capped Round Robin (CRR) for allocation | Agents with uniform-matroid constraints and heterogeneous additive valuations · Complete feasible allocation | F-EF1 existence | Helped |
| Run CRR in opposite agent orders across the two categories | Agents with partition-matroid constraints sharing at most two categories but possibly different capacities · Complete feasible allocation | F-EF1 existence | Helped |
| Use per-category CRR ordered by the acyclic feasible-envy graph | Agents with identical additive valuations and partition matroids with identical categories but possibly different capacities · Complete feasible allocation | F-EF1 existence | Helped |
| Use Iterated Priority Matching | Agents with heterogeneous binary valuations and partition matroids with heterogeneous capacities · Complete feasible allocation | F-EF1 existence | Helped |
| Use Round Robin Squared (RR²) | Two agents with heterogeneous additive valuations and partition-matroid constraints · Complete feasible allocation | F-EF1 existence | Helped |
| Use the proposed algorithms for identical base-orderable matroid constraints | Two agents with heterogeneous additive valuations · Complete feasible allocation | F-EF1 existence | Helped |
| Use the proposed algorithm for identical base-orderable matroid constraints | At most three agents with heterogeneous binary valuations · Complete feasible allocation | F-EF1 existence | Helped |
| Allow agents to have different partitions of items into categories | Two agents with partition-matroid constraints, even with identical binary valuations · Complete feasible allocation | F-EF1 existence | Hurt |
| Replace matroid constraints with matroid-intersection, matching, conflict-graph, or budget constraints | Two agents with identical binary valuations and identical non-matroid constraints · Complete feasible allocation | F-EF1 existence | Hurt |
| Require EFX instead of F-EF1 | Two agents with identical valuations and identical uniform-matroid constraints · Complete feasible allocation | EFX existence | Hurt |
| Choose a maximum Nash welfare allocation rather than an EF1-guaranteeing allocation rule | Agents with identical partition-matroid constraints and binary valuations · Complete feasible allocation | F-EF1 guarantee | Hurt |
| Require Pareto efficiency in addition to the Iterated Priority Matching outcome | Heterogeneous partition capacities and binary valuations when capacities may exceed one · Complete feasible allocation | Pareto efficiency | Mixed |
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