Related papers: Identification Methods for Ordinal Potential Diffe…
In this paper, we consider a linear-quadratic-Gaussian defending assets differential game (DADG) where the attacker and the defender do not know each other's state information while they know the trajectory of a moving asset. Both players…
We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…
Many real-world decision problems involve the interaction of multiple self-interested agents with limited sensing ability. The partially observable stochastic game (POSG) provides a mathematical framework for modeling these problems,…
This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated…
Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games which involve a large number of agents that are weakly coupled via a weighted undirected graph on which each node represents an agent. The links of the graph…
In this paper, we consider a linear quadratic stochastic two-person nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are introduced. The existence of the former is characterized by the solvability of a system of…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
We present an efficient algorithm to compute the explicit open-loop solution to both finite and infinite-horizon dynamic games subject to state and input constraints. Our approach relies on a multiparametric affine variational inequality…
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
This work studies the parameter identification problem of a generalized non-cooperative game, where each player's cost function is influenced by an observable signal and some unknown parameters. We consider the scenario where equilibrium of…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
In this expository article, we give an overview of the concept of potential mean field games of first order. We give a new proof that minimizers of the potential are equilibria by using a Lagrangian formulation. We also provide criteria to…
In this paper, we revisit the two-player continuous-time infinite-horizon linear quadratic differential game problem, where one of the players can sample the state of the system only intermittently due to a sensing constraint while the…
In many problems that involve multiple decision making agents, optimal choices for each agent depend on the choices of others. Differential game theory provides a principled formalism for expressing these coupled interactions and recent…
We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in terms of a suitable criterion and derive a primal-dual…
This paper presents a novel data-driven approach for approximating the $\varepsilon$-Nash equilibrium in continuous-time linear quadratic Gaussian (LQG) games, where multiple agents interact with each other through their dynamics and…
Game theoretic methods have become popular for planning and prediction in situations involving rich multi-agent interactions. However, these methods often assume the existence of a single local Nash equilibria and are hence unable to handle…
The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…
Many real-world multi-agent interactions consider multiple distinct criteria, i.e. the payoffs are multi-objective in nature. However, the same multi-objective payoff vector may lead to different utilities for each participant. Therefore,…