1. Beyond Dominant Resource Fairness David Parkes (Harvard) Ariel Procaccia (CMU) Nisarg Shah (CMU)

2. Motivation Allocation of multiple resources (e.g., CPU, RAM, bandwidth) Users have heterogeneous demands Today: fixed bundles (slots) Allocate slots using single resource abstraction 2

3. The DRF mechanism Assume proportional demands (a.k.a. Leontief preferences) Example: o User wishes to execute multiple instances of a job that requires 2 CPU and 1 RAM o Indifferent between 5 CPU and 2 RAM, and 4 CPU and 2 GB o Happier with 4.2+2.1 Dominant resource fairness [Ghodsi et al. 2011]: equalize largest shares 3

4. DRF animated 4 User 1 alloc. User 2 alloc. Total alloc.

5. Properties of DRF Pareto optimality Envy freeness: users do not want to swap allocations Sharing incentives (a.k.a. fair share, proportionality, IR): users receive at least as much value as an equal split Strategyproofness: reporting true demands is a dominant strategy Exciting application of fair division theory! 5

6. Indivisible tasks Demands specified as fraction of resource r that user i needs to run one instance of its task User’s utility strictly increases with number of complete instances of task 6

7. PO+SI+SP are incompatible 7 User 1 demand User 2 demand Allocation User 1 demand User 2 demand Allocation

8. Envy freeness PO and EF are trivially incompatible Need to relax the notion of envy freeness [Budish 2011, Lipton et al. 2004, Moulin and Stong 2002] Envy freeness up to one bundle (EF1) = i does not prefer j’s after removing one copy of i’s task Theorem: PO+EF1+SP impossible 8

9. Sequential Minmax SI+EF1+SP trivial SI+PO+SP, EF1+PO+SP impossible Can we achieve PO+SI+EF1? The S EQUENTIAL M INMAX mechanism: allocate at each step to minimize maximum allocated share after allocation Theorem: Mechanism is PO+SI+EF1 9

10. Sequential Minmax illustrated 10 User 1 demand User 2 demand User 1 alloc. User 2 alloc. Total alloc.

11. Discussion Additional results in paper o An extension of DRF to settings with possibly zero demands and endowments, which satisfies group strategyproofness o Lower bounds on social welfare maximization Current work: dynamic fairness 11