| PhD Seminar

Name of the Speaker: Mr. Partha Sarathi Mohapatra (EE18D703)
Guide: Dr. Puduru Viswanadha Reddy
Venue: ESB 234 (Malaviya Hall)
Date/Time: 19th September 2024 (Thursday), 2:00 PM
Title: Feedback Stackelberg-Nash equilibria in quasi-hierarchical difference games with inequality constraints

Abstract :

Dynamic game theory (DGT) provides a mathematical framework for analyzing multi-agent decision processes evolving over time. DGT has been applied effectively in engineering, management science, and economics, where dynamic multi-agent decision problems naturally arise. Notable engineering applications include cyber-physical systems, communication networks, and smart grids. Most existing DGT models are formulated in unconstrained settings. However, real-world multi-agent decisions often involve constraints, such as saturation limits, bandwidth restrictions, production capacities, budgets, and emission limits. These factors introduce equality and inequality constraints into the dynamic game model, linking each player's decisions to the others at every stage. As a result, players' decision sets are interdependent, or coupled.

In Seminar 1, we considered a class of linear-quadratic difference games with coupled affine inequality constraints. We presented both necessary and sufficient conditions for the existence of generalized open-loop Nash equilibria for this class of games.

In this seminar, we study a class of two-player deterministic finite-horizon difference games with coupled inequality constraints, where both players have two types of decision variables. In one type, players interact sequentially; in the other, they interact simultaneously. We refer to this class of games as quasi-hierarchical dynamic games and define a solution concept called feedback Stackelberg-Nash (FSN) equilibrium. Under the separability assumption of the cost functions, we provide a recursive formulation of the FSN solutions using dynamic programming. Furthermore, the FSN solution for this class of constrained games is obtained using the parametric feedback Stackelberg solution of an associated unconstrained parametric game, which involves only sequential interactions, with a specific choice of parameters that satisfy certain implicit complementarity conditions. For the linear-quadratic case, we demonstrate that the FSN solutions can be obtained by reformulating these implicit complementarity conditions as a single large-scale linear-complementarity problem. Finally, we illustrate our results using a dynamic duopoly game with production constraints.