Many-to-Many Matching

Both sides can match with multiple partners: workers can take multiple part-time jobs, and firms can hire multiple workers. Pairwise stability prevents any unmatched worker-firm pair from mutually benefiting.

Algorithm Mode

Many-to-Many DA (Worker-proposing):
while ∃ worker w with unused quota
  and remaining acceptable firms:
    f ← w's top remaining firm
    if f has unused quota:
      add match (w, f)
    else if f prefers w to its
      worst current match w':
      remove (w', f), add (w, f)
    else: f rejects w

Quotas (adjust and rerun)

Preferences

Workers (blue, max jobs in brackets)

Firms (green, max hires in brackets)

Event Log

Echenique, F. and Oviedo, J. (2006). "A Theory of Stability in Many-to-Many Matching Markets." Theoretical Economics, 1, 233-273.