MESOB: Balancing Equilibria & Social Optimality

TL;DR

This paper introduces MESOB, a novel bi-objective optimization framework using mean-field approximation to balance competition and cooperation in large multi-agent systems, demonstrated through ad auction simulations.

Contribution

The paper proposes MESOB and MESOB-OMO, new methods for modeling and solving complex multi-agent games with large populations, balancing social optimality and equilibrium in an efficient manner.

Findings

MESOB effectively balances competition and cooperation.

MESOB-OMO finds approximately Pareto efficient solutions.

Experimental results outperform baselines focusing on only one aspect.

Abstract

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.