Event
Ph.D. Dissertation Defense: Jair Certório
Wednesday, April 16, 2025
1:00 p.m.
AVW 1146
Maria Hoo
301 405 3681
mch@umd.edu
ANNOUNCEMENT: Ph.D. Dissertation Defense
Name: Jair Certório
Committee:
Professor Nuno C. Martins (Chair/Advisor)
Professor Richard J. La (Co-Advisor)
Professor P. S. Krishnaprasad
Professor Kaiqing Zhang
Professor Nikhil Chopra
Date/Time: Wednesday, April 16th, 2025, from 1:00 PM to 3:00 PM
Location: AVW 1146
Title: Tractable Design of Dynamical Policies for Population Games
Abstract:
Committee:
Professor Nuno C. Martins (Chair/Advisor)
Professor Richard J. La (Co-Advisor)
Professor P. S. Krishnaprasad
Professor Kaiqing Zhang
Professor Nikhil Chopra
Date/Time: Wednesday, April 16th, 2025, from 1:00 PM to 3:00 PM
Location: AVW 1146
Title: Tractable Design of Dynamical Policies for Population Games
Abstract:
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 system that we wish to control.
The interaction between the two dynamical systems makes it difficult to design incentives that can change their choices of strategy while satisfying requirements, such as constraints on the trajectory of the exogenous system.
Evolutionary game theory is a natural framework for studying the strategic choices of agents and their learning that determines their strategy revisions.
When a large number of agents noncooperatively select strategies from a common set, the framework of population games allows for amenable design and analysis.
We investigate the following three problems related to incentive design for a large number of agents whose choices influence the evolution of an exogenous system:
Problem 1: We consider populations of agents whose learning rule combines characteristics of several learning rules that were previously studied individually. We refer to such previously studied rules as canonical rules and as hybrid rules the ones that combine characteristics of the canonical rules. We show that the conic combination of all sensible δ-passive canonical rules will result in a δ-passive hybrid rule.
Problem 2: We consider agents during an epidemic outbreak scenario and design incentives to guide them into using strategies that mitigate the transmission of the disease. 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 an 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.
Problem 3: (a) We generalize the design concept from the second problem to obtain a more general incentive design method for populations coupled to an exogenous system, with explicit constraints for the type of exogenous system that can be controlled with the proposed method, and assuming only that the agents' learning rule satisfies positive correlation, Nash stationarity, and δ-passivity.
We show that the result can be applied to previous work on epidemic population games, and also to other exogenous systems such as the Leslie-Gower model for the interaction between populations of hosts and parasites. Like in the second problem, we proved convergence to a desired equilibrium 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. (b) We remove the assumption that the agents' learning rule satisfies δ-passivity and consider the agents' learning rule to satisfy only positive correlation and Nash stationarity. We design a dynamic incentive and a memoryless incentive that guide a population to a desirable equilibrium. For the memoryless incentive, we prove convergence using a Lyapunov function, that can also be used to obtain anytime bound on the states of the exogenous system and of the population.
The interaction between the two dynamical systems makes it difficult to design incentives that can change their choices of strategy while satisfying requirements, such as constraints on the trajectory of the exogenous system.
Evolutionary game theory is a natural framework for studying the strategic choices of agents and their learning that determines their strategy revisions.
When a large number of agents noncooperatively select strategies from a common set, the framework of population games allows for amenable design and analysis.
We investigate the following three problems related to incentive design for a large number of agents whose choices influence the evolution of an exogenous system:
Problem 1: We consider populations of agents whose learning rule combines characteristics of several learning rules that were previously studied individually. We refer to such previously studied rules as canonical rules and as hybrid rules the ones that combine characteristics of the canonical rules. We show that the conic combination of all sensible δ-passive canonical rules will result in a δ-passive hybrid rule.
Problem 2: We consider agents during an epidemic outbreak scenario and design incentives to guide them into using strategies that mitigate the transmission of the disease. 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 an 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.
Problem 3: (a) We generalize the design concept from the second problem to obtain a more general incentive design method for populations coupled to an exogenous system, with explicit constraints for the type of exogenous system that can be controlled with the proposed method, and assuming only that the agents' learning rule satisfies positive correlation, Nash stationarity, and δ-passivity.
We show that the result can be applied to previous work on epidemic population games, and also to other exogenous systems such as the Leslie-Gower model for the interaction between populations of hosts and parasites. Like in the second problem, we proved convergence to a desired equilibrium 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. (b) We remove the assumption that the agents' learning rule satisfies δ-passivity and consider the agents' learning rule to satisfy only positive correlation and Nash stationarity. We design a dynamic incentive and a memoryless incentive that guide a population to a desirable equilibrium. For the memoryless incentive, we prove convergence using a Lyapunov function, that can also be used to obtain anytime bound on the states of the exogenous system and of the population.
