Strategic decision making in complex systems: Game theory, Mechanism design and Optimization

This talk explores In this talk, I will first present a variety of problems that involve interactions among multiple decision-making agents. To predict the outcome of the interactions, game theory is used to quantify the effect of all interacting agents and derive equilibrium behaviour. This equilibrium guides any agent to derive its own optimal policy, or a system designer to design a system that achieves socially desirable outcome.Consider the advertising over social networks where various content providers compete to acquire customers by controlling their advertising strategies on a common platform. Any content provider would be interested in deriving the optimal advertising policy, that will also depend upon the policies of other agents due to common platform. Another application is a leader deriving optimal vaccination policies to eradicate an ongoing pandemic. It is known that vaccination alone does not lead to eradication, hence the leader can incentivize some influencers to motivate the common public. Here, the vaccination decision depends on various factors including the fraction of vaccinated people. Hence, a framework that can model the outcome for various vaccination strategies and disease characteristics can guide the leader to devise a strategy that can eradicate the disease.Further, there are systems for which centralized control is not possible and a system designer can utilize distributed control with some agents. The system designer provides agents with utilities functions; when agents make decisions based on utility, the system objective is determined. The system designer can choose utility functions that lead to a desirable system objective. I will present the bounds on system objective, specifically, price of anarchy, that can be achieved with this framework for various types of problems. I will also discuss the instability of non-desirable outcomes and an algorithm that escapes the worst outcomes and converges to desirable outcomes.Secondly, I will discuss the problem that I am working on in the industry. Here, the task is to optimally schedule shifts for the employees working at various warehouses and stores based on demand, preference, seniority, restrictions etc. This problem is modelled using mixed integer linear programming; however, the large scale of problem makes the direct solution using available solvers impossible. I will discuss the heuristics and methodologies that make the solution for these problems possible.