When agents choose bundles autonomously: guarantees beyond discrepancy

Researchers have broken a fundamental barrier in fair division problems where autonomous agents choose resource bundles. They achieved an exponential improvement over the previous Θ(√n) discrepancy limit, guaranteeing each agent receives at least PROP - O(log n) value when selecting sequentially. The polynomial-time algorithm works for additive valuations and shows even stronger guarantees for three restricted valuation classes, including ordered settings and bounded influence hypergraphs. This represents a major theoretical advance in multi-agent resource allocation.