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Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…
In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…
We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…
We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…
Smart metering infrastructure allows for two-way communication and power transfer. Based on this promising technology, we propose a demand-side management (DSM) scheme for a residential neighbourhood of prosumers. Its core is a discrete…
Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…
This paper studies singular mean field control problems and singular mean field stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some…
Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…
Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…
This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by…
In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…
In this paper, we investigate a distributed Nash equilibrium computation problem for a time-varying multi-agent network consisting of two subnetworks, where the two subnetworks share the same objective function. We first propose a…
In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification…
This paper proposes a new method for finding closed-loop saddle points in zero-sum linear-quadratic stochastic differential games by decoupling their inherent structure. Specifically, we develop a nested iterative scheme that constructs a…
A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems…
This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen…
We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE seeking algorithm for monotone games that requires one…
This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information…