# MESOB: Balancing Equilibria & Social Optimality

arXiv: https://arxiv.org/abs/2307.07911 · HTML: https://mlsanity.com/paper/2307.07911/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [Game-Theoretic Multiagent Reinforcement Learning](https://mlsanity.com/paper/2011.00583/) (2020)
- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis](https://mlsanity.com/paper/2002.04131/) (2020)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Markov-Nash Equilibria in Mean-Field Games with Discounted Cost](https://mlsanity.com/paper/1612.07878/) (2016)
- [Convergence of Learning Dynamics in Stackelberg Games](https://mlsanity.com/paper/1906.01217/) (2019)
- [Learning Graphon Mean Field Games and Approximate Nash Equilibria](https://mlsanity.com/paper/2112.01280/) (2021)
- [Multiplicative Pacing Equilibria in Auction Markets](https://mlsanity.com/paper/1706.07151/) (2017)
- [MF-OMO: An Optimization Formulation of Mean-Field Games](https://mlsanity.com/paper/2206.09608/) (2022)
- [A tale of a Principal and many many Agents](https://mlsanity.com/paper/1608.05226/) (2016)
- [MFGLib: A Library for Mean-Field Games](https://mlsanity.com/paper/2304.08630/) (2023)
- [Discrete time McKean-Vlasov control problem: a dynamic programming approach](https://mlsanity.com/paper/1511.09273/) (2015)
- [Optimization frameworks and sensitivity analysis of Stackelberg mean-field games](https://mlsanity.com/paper/2210.04110/) (2022)
- [Terminal Ranking Games](https://mlsanity.com/paper/1906.09628/) (2019)

## Built on by (most cited first, 1 of 1)

- [Steering No-Regret Agents in MFGs under Model Uncertainty](https://mlsanity.com/paper/2503.09309/) (2025)

## Abstract (arXiv)

Motivated by bid recommendation in online ad auctions, this paper considers a general class of multi-level and multi-agent games, with two major characteristics: one is a large number of anonymous agents, and the other is the intricate interplay between competition and cooperation. To model such complex systems, we propose a novel and tractable bi-objective optimization formulation with mean-field approximation, called MESOB (Mean-field Equilibria & Social Optimality Balancing), as well as an associated occupation measure optimization (OMO) method called MESOB-OMO to solve it. MESOB-OMO enables obtaining approximately Pareto efficient solutions in terms of the dual objectives of competition and cooperation in MESOB, and in particular allows for Nash equilibrium selection and social equalization in an asymptotic manner. We apply MESOB-OMO to bid recommendation in a simulated pay-per-click ad auction. Experiments demonstrate its efficacy in balancing the interests of different parties and in handling the competitive nature of bidders, as well as its advantages over baselines that only consider either the competitive or the cooperative aspects.