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Price of Anarchy of Algorithmic Monoculture

Robert Kleinberg, Erald Sinanaj, Éva Tardos

Abstract

Several recent works investigate the effects of monoculture, the ever increasing phenomenon of (possibly) self-interested actors in a society relying on one common source of advice for decision making, with an archetypal driving example being the growing adoption and predictive power of machine learning models in matching markets, e.g. in hiring. Kleinberg and Raghavan (PNAS, 2021) introduced a model that captures the effects of monoculture in a one-sided matching market with advice, demonstrating that a higher accuracy common signal (such as an algorithmic vendor) might incentivize society as a whole to rationally adopt it, but as a collective it would be better off if each instead adopted less accurate, but private advice. We generalize their model and address the open question of their work in quantifying the social welfare loss. We find that monoculture and more generally decentralized optimization is close to optimal: we show a tight constant bound of 2 on the price of anarchy (and more general notions) for the induced game.

Price of Anarchy of Algorithmic Monoculture

Abstract

Several recent works investigate the effects of monoculture, the ever increasing phenomenon of (possibly) self-interested actors in a society relying on one common source of advice for decision making, with an archetypal driving example being the growing adoption and predictive power of machine learning models in matching markets, e.g. in hiring. Kleinberg and Raghavan (PNAS, 2021) introduced a model that captures the effects of monoculture in a one-sided matching market with advice, demonstrating that a higher accuracy common signal (such as an algorithmic vendor) might incentivize society as a whole to rationally adopt it, but as a collective it would be better off if each instead adopted less accurate, but private advice. We generalize their model and address the open question of their work in quantifying the social welfare loss. We find that monoculture and more generally decentralized optimization is close to optimal: we show a tight constant bound of 2 on the price of anarchy (and more general notions) for the induced game.

Paper Structure

This paper contains 19 sections, 20 theorems, 42 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Work
  3. Setup
  4. The price of anarchy
  5. Case 1:
  6. Case 2:
  7. Generality of our assumptions
  8. Mallow's model
  9. Schur-concave rankings
  10. Trusting a ranking blindly
  11. Lower bounds and violation of assumptions
  12. A tight lower bound construction
  13. Arbitrary advice spaces lead to arbitrarily bad results
  14. On stochastic inconsistency
  15. Conclusion
  16. ...and 4 more sections

Key Result

theorem 1

The Price of Anarchy of the Obedience-Constrained Random Serial Dictatorship mechanism, in which firms obtain their rankings from a stochastically consistent advice space, is bounded above by 2. $\blacktriangleleft$$\blacktriangleleft$

Figures (1)

  • Figure 1: Candidates E and S are snatched, while A, B, D are available to the corresponding firms.

Theorems & Definitions (41)

  • definition 1: Stochastically Consistent
  • theorem 1
  • lemma 1
  • proof : \ref{['thm:PoA']}
  • proposition 1
  • proof
  • theorem 2
  • proof
  • proposition 2
  • definition 2: Majorization
  • ...and 31 more