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Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate…

The paper investigates the long-time behavior of zero-sum linear-quadratic stochastic differential games, aiming to demonstrate that, under appropriate conditions, both the saddle strategy and the optimal state process exhibit the…

This paper considers a zero-sum two-player asymmetric information stochastic game where only one player knows the system state, and the transition law is controlled by the informed player only. For the informed player, it has been shown…

This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time…

Game theory provides essential analysis in many applications of strategic interactions. However, the question of how to construct a game model and what is its fidelity is seldom addressed. In this work, we consider learning in a class of…

The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this…

Safety is a critical feature of controller design for physical systems. When designing control policies, several approaches to guarantee this aspect of autonomy have been proposed, such as robust controllers or control barrier functions.…

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

Reinforcement learning is one of the most popular approaches for automated game playing. This method allows an agent to estimate the expected utility of its state in order to make optimal actions in an unknown environment. We seek to apply…

In this paper, for POMDPs, we provide the convergence of a Q learning algorithm for control policies using a finite history of past observations and control actions, and, consequentially, we establish near optimality of such limit Q…

Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modeling the costs of spending time in a state and executing an action, respectively). The goals of the…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

In this note, we consider repeated play of a finite game using learning rules whose period-by-period behavior probabilities or empirical distributions converge to some notion of equilibria of the stage game. Our primary focus is on…

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…

A key task in Artificial Intelligence is learning effective policies for controlling agents in unknown environments to optimize performance measures. Off-policy learning methods, like Q-learning, allow learners to make optimal decisions…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can…

This paper introduces a multi-agent approach to adjust traffic lights based on traffic situation in order to reduce average delay time. In the traffic model, lights of each intersection are controlled by an autonomous agent. Since decision…