| PhD Viva

Name of the Speaker: Mr. Partha Sarathi Mohapatra (EE18D703)
Guide: Dr. Puduru Viswanadha Reddy
Online meeting link: https://meet.google.com/ics-mczn-ttg
Date/Time: 16th June 2025 (Monday), 10:00 AM
Title: Dynamic Games with Coupled Inequality Constraints

Abstract :

Multi-agent systems and their control architectures have evolved significantly in recent years, becoming integral to many modern engineering applications. These systems are characterized by heterogeneous interacting agents with interdependent objectives and action sets. Dynamic game theory provides a powerful mathematical framework for modeling and analyzing these multi-agent decision-making processes that evolve over time. Despite substantial progress, the current dynamic game literature faces two major limitations. First, it often assumes independent action sets, overlooking real-world couplings due to constraints like budgets, capacities, and emissions, which result in non-rectangular action spaces. Second, existing dynamic game models typically restrict interactions to purely simultaneous or sequential forms, failing to capture hybrid interactions observed in real-world systems.

This work addresses these limitations in the existing literature on dynamic games. In the first part, we analyze discrete-time dynamic games, also referred to as difference games, under stage-wise mixed coupled inequality constraints. We derive both necessary and sufficient conditions for the existence of generalized Nash equilibria in this class of coupled constrained difference games, under both open-loop and feedback information structures. In the second part, we introduce a new class of difference games, termed quasi-hierarchical games, which incorporate a combination of sequential and simultaneous player interactions. For this class, we propose a new solution concept called the feedback Stackelberg–Nash equilibrium and analyze its existence in the presence of coupled constraints. In both parts, for linear-quadratic games with affine constraints, we reformulate the existence conditions as large-scale linear complementarity problems, for numerical computation of the equilibrium.