Ph.D. Research Proposal Exam: Jair Certorio

Monday, June 17, 2024
2:00 p.m.
AVW 2168
Maria Hoo
301 405 3681

ANNOUNCEMENT:  Ph.D. Research Proposal Exam


Name:  Jair Certorio


Professor Nuno C. Martins (Chair/Advisor)

Professor Richard J. La (Co-advisor)

Professor P. S. Krishnaprasad


Date/Time:  Monday, June 17, 2024 at 2 PM

Location:  AVW 2168


Title: Tractable Design of Dynamical Policies for Population Games



For large populations of agents designing incentives that can guide the agents into making better choices and improve their outcome is challenging. Especially when the choices of the agents affect the evolution of an exogenous process that we wish to control. The interaction between the two dynamical systems makes it difficult to design incentives that can change their behavior while satisfying requirements, such as constraints on the trajectory of the exogenous process. Evolutionary game theory is a natural framework for studying the strategic choices of agents and their learning that determines their strategy revisions. And, for large populations of learning agents noncooperatively selecting strategies from a common set, the framework of population games allows for amenable design and analysis.
    Our work focuses on problems of incentive design for a large number of agents whose choices influence the evolution of an exogenous process. Our approach modifies the payoffs of available strategies by providing incentives with the goal of incentivizing agents to follow a desired strategy distribution or obtain guarantees on the behavior of the exogenous process. We apply a population game approach to find such incentives. We investigate the following four problems: 1) designing incentives for agents during an epidemic outbreak scenario, 2) designing bounded incentives for populations that affect the evolution of an exogenous process aiming to guarantee convergence of the state to a desired equilibrium, generalizing the design concept from the first problem, 3) studying incentive design methods that do not rely on the population's dynamics being $\delta$-passivity. Unlike the first two problems, that design incentives for evolutionary dynamics that are $\delta$-passive. 4) investigating properties of hybrid protocols, which is when agents can alternate between different learning rules at each revision time.

    So far we obtained results for the first two problems. For the first one, we solved for an optimal social state that minimizes the transmission rate given a long-term budget constraint on the incentive. Then we determined a dynamic payoff mechanism that leads the population's strategy distribution to converge to the optimal social state. Our convergence proof uses a Lyapunov function which can be used to bound the peak number of infected agents during the outbreak. The Lyapunov function can be leveraged during design to select a payoff mechanism that meets a requirement on the peak number of infected agents. Initially we considered a disease with negligible lethality. We later extended the results to cases in which the disease has nonnegligible lethality and also to cases with two populations.

    On the second problem, we determined a more general incentive design method for populations coupled to an exogenous system, with explicit constraints for the type of exogenous process that can be controlled with the proposed method. We showed that the result can be applied to previous work on epidemic population games, and also to other exogenous processes such as the Leslie-Gower model for the interaction between populations of hosts and parasites. Like in the first problem, we proved convergence using a Lyapunov function, that can be used to bound the transient behavior of the system. But, in this problem we also obtained a bound on the instantaneous cost of implementing this incentive.

Audience: Faculty 

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