arXiv subjects

Partha Sarathi Mohapatra

Publications and source records attributed to Partha Sarathi Mohapatra.

4 recordsLinked to original sources

arXiv2026

Infinite-Horizon Linear-Quadratic Difference Games with Coupled Affine Inequality Constraints: Open-Loop Generalized Nash Equilibria

In this technical note, we study a class of infinite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We derive necessary conditions for the existence of open-loop generalized Nash equilibria and establish their sufficiency under additional assumptions. Sufficient conditions are characterized in terms of the existence of square-summable solutions to associated infinite-horizon linear complementarity systems. We further reformulate these conditions and show that computing open-loop generalized Nash equilibria reduces to solving a large-scale linear complementarity problem together with verifying additional conditions. Finally, we illustrate our results using a vehicle platooning example with constraints.

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arXiv2025

Feedback Stackelberg-Nash equilibria in difference games with quasi-hierarchical interactions and inequality constraints

In this paper, we study a class of two-player deterministic finite-horizon difference games with coupled inequality constraints, where each player has two types of decision variables: one involving sequential interactions and the other simultaneous interactions. We refer to this class of games as quasi-hierarchical dynamic games and define a solution concept called the feedback Stackelberg-Nash (FSN) equilibrium. Under separability assumption on cost functions, we provide a recursive formulation of the FSN solution using dynamic programming. We show that the FSN solution can be derived from the parametric feedback Stackelberg solution of an associated unconstrained game involving only sequential interactions, with a specific choice of the parameters that satisfy certain implicit complementarity conditions. For the linear-quadratic case, we show that an FSN solution is obtained by reformulating these complementarity conditions as a single large-scale linear complementarity problem. Finally, we illustrate our results using a dynamic duopoly game with production constraints.

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arXiv2025

Linear-quadratic mean-field-type difference games with coupled affine inequality constraints

In this letter, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-field-type equilibrium can be characterized by the existence of a multiplier process which satisfies some implicit complementarity conditions. Further, we show that the equilibrium strategies can be computed by reformulating these conditions as a single large-scale linear complementarity problem. We illustrate our results with an energy storage problem arising in the management of microgrids.

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arXiv2025

Generalized open-loop Nash equilibria in linear-quadratic difference games with coupled-affine inequality constraints

In this note, we study a class of deterministic finite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We show that the necessary conditions for the existence of generalized open-loop Nash equilibria in this game class lead to two strongly coupled discrete-time linear complementarity systems. Subsequently, we derive sufficient conditions by establishing an equivalence between the solutions of these systems and convexity of the players' objective functions. These conditions are then reformulated as a solution to a linear complementarity problem, providing a numerical method to compute these equilibria. We illustrate our results using a network flow game with constraints.

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