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.

翻译：受在线广告拍卖中竞价推荐的启发，本文考虑了一类多层级、多智能体的博弈问题，其主要特征包括：一是存在大量匿名智能体，二是竞争与合作之间复杂的相互作用。为建模这类复杂系统，我们提出了一种新颖且易于处理的、结合均场近似的双目标优化框架，称之为MESOB（均场均衡与社会最优性平衡），并配套提出了一种职业度量优化方法MESOB-OMO用于求解该框架。MESOB-OMO能够在MESOB目标中实现竞争与合作的近似帕累托有效解，并特别允许以渐进方式实现纳什均衡选择与社会均衡化。我们将MESOB-OMO应用于模拟的按点击付费广告拍卖中的竞价推荐场景。实验表明，该方法在平衡多方利益、处理竞标者的竞争性方面具有有效性，并且相对于仅考虑竞争或合作方面的基线方法具有优势。