Hierarchical Population Control: from Mean-Field Games to Social Welfare Optimization

Invited Talks (RAWLS 1086) Hierarchical Population Control: from Mean-Field Games to Social Welfare Optimization Wei Zhang, Ohio State University Many complex Cyber-Physical Systems (CPS) involve interactions among a large number of agents with decoupled dynamics but loosely coupled decisions due to their shared environment and resources. Such systems are often operated using a hierarchical control architecture, where a coordinator determines some macroscopic control signal to steer the population to achieve some desired group objective while respecting local preferences and constraints for individual agents. The design of hierarchical population control depends crucially on the information available to the coordinator, the rationality assumption of the agents, the individual agent dynamics and constraints, and the complex population dynamic behaviors induced by the hierarchical control strategy. This talk will introduce and discuss two emerging classes of hierarchical population control (HPC) problems, one for non-strategic agents and one for strategic agents. For non-strategic agents, the HPC problem becomes a PDE constrained optimization problem, for which some preliminary results will be briefly discussed. For strategic agents, the HPC problems are formulated as reverse Stackelberg problems, for which meanfield game becomes an important tool to characterize population behaviors. Along this direction, I will present our very recent result that establishes equivalence between an important class of mean-field control problems and the classical social welfare optimization problems in functional space. Mean-field Games: Incentive and Reputation Mechanisms Vijay Subramanian, University of Michigan Motivated by systems with a large number of strategic players, such as in Internet marketplaces, we explore the use of incentive and reputation mechanisms in mean-field games. First, we consider real-time streaming of video to co-located wireless devices where cooperation among the devices would lead to greater system efficiency. Based on ideas drawn from truth-telling auctions, we design a mechanism that achieves this cooperation via appropriate transfers (monetary payments or rebates) in a setting with a large number of devices, and with peer arrivals and departures. Furthermore, the complexity of calculating the best responses under this regime is low. We implement the proposed system on an Android testbed, and illustrate its efficient performance using real world experiments. Next, with crowd-sourcing as the underlying motivation, we explore the impact of perceived and real reputations of agent behaviors in Internet marketplaces. We model such an Internet marketplace using a set of servers that choose prices for performing jobs. Each server has a queue of unfinished jobs, and is penalized for delay by the market-maker via a holding cost. A server completes jobs with a low or high quality, the likelihood of which is private information of the server, and jobs truthfully report the “quality” with which they were completed. The best estimate of quality based on these reports is the perceived reputation of the server. A server bases its pricing decision on the distribution of its competitors offered prices and reputations. An entering job is given a random sample of servers, and chooses the best one based on a linear combination of price and reputation. We seek to understand how prices would be determined in such a marketplace when there are a large number of users. This is joint work with Jian Li, Rajarshi Bhattacharyya, Suman Paul, Vamseedhar Reddyvari Raja, Srinivas Shakkottai at Texas A&M University and Vinod Ramaswamy at the University of Colorado, Boulder.