Price of Anarchy of Algorithmic Monoculture

TL;DR

This paper analyzes the social welfare impact of monoculture in decision-making systems, showing that decentralized optimization has a bounded inefficiency with a tight constant bound of 2 on the price of anarchy.

Contribution

It generalizes previous models of monoculture in matching markets and provides a tight bound on the price of anarchy for the associated game.

Findings

Monoculture can lead to significant social welfare loss.

Decentralized optimization is nearly optimal with a bounded price of anarchy.

The paper establishes a tight constant bound of 2 on the price of anarchy.

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.