  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.
