# Coordinating the Crowd: Inducing Desirable Equilibria in Non-Cooperative Systems

arXiv: https://arxiv.org/abs/1901.10923 · HTML: https://mlsanity.com/paper/1901.10923/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2019.

## Built on by (most cited first, 12 of 12)

- [Learning to Mitigate AI Collusion on Economic Platforms](https://mlsanity.com/paper/2202.07106/) (2022)
- [Learning to Shape Rewards using a Game of Two Partners](https://mlsanity.com/paper/2103.09159/) (2021)
- [Inducing Equilibria via Incentives: Simultaneous Design-and-Play Ensures Global Convergence](https://mlsanity.com/paper/2110.01212/) (2021)
- [Learning to Share in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2112.08702/) (2021)
- [Learning to Control Unknown Strongly Monotone Games](https://mlsanity.com/paper/2407.00575/) (2024)
- [Equilibrium Inverse Reinforcement Learning for Ride-hailing Vehicle Network](https://mlsanity.com/paper/2102.06854/) (2021)
- [Differentiable Arbitrating in Zero-sum Markov Games](https://mlsanity.com/paper/2302.10058/) (2023)
- [Equilibrium Bandits: Learning Optimal Equilibria of Unknown Dynamics](https://mlsanity.com/paper/2302.13653/) (2023)
- [Bayesian Optimization Framework for Efficient Fleet Design in Autonomous Multi-Robot Exploration](https://mlsanity.com/paper/2408.11751/) (2024)
- [An Automated Reinforcement Learning Reward Design Framework with Large Language Model for Cooperative Platoon Coordination](https://mlsanity.com/paper/2504.19480/) (2025)
- [A Soft Inducement Framework for Incentive-Aided Steering of No-Regret Players](https://mlsanity.com/paper/2508.21672/) (2025)
- [Barriers to Welfare Maximization with No-Regret Learning](https://mlsanity.com/paper/2411.01720/) (2024)

## Abstract (arXiv)

Many real-world systems such as taxi systems, traffic networks and smart grids involve self-interested actors that perform individual tasks in a shared environment. However, in such systems, the self-interested behaviour of agents produces welfare inefficient and globally suboptimal outcomes that are detrimental to all - some common examples are congestion in traffic networks, demand spikes for resources in electricity grids and over-extraction of environmental resources such as fisheries. We propose an incentive-design method which modifies agents' rewards in non-cooperative multi-agent systems that results in independent, self-interested agents choosing actions that produce optimal system outcomes in strategic settings. Our framework combines multi-agent reinforcement learning to simulate (real-world) agent behaviour and black-box optimisation to determine the optimal modifications to the agents' rewards or incentives given some fixed budget that results in optimal system performance. By modifying the reward functions and generating agents' equilibrium responses within a sequence of offline Markov games, our method enables optimal incentive structures to be determined offline through iterative updates of the reward functions of a simulated game. Our theoretical results show that our method converges to reward modifications that induce system optimality. We demonstrate the applications of our framework by tackling a challenging problem within economics that involves thousands of selfish agents and tackle a traffic congestion problem.