Related papers: Episodic Logit-Q Dynamics for Efficient Learning i…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
We provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step…
Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic…
We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…
Logit Dynamics [Blume, Games and Economic Behavior, 1993] are randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability…
We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory,…
Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the…
We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition…
Zero-sum Linear Quadratic (LQ) games are fundamental in optimal control and can be used (i)~as a dynamic game formulation for risk-sensitive or robust control and (ii)~as a benchmark setting for multi-agent reinforcement learning with two…
Analysing learning in Multi-Agent Reinforcement Learning (MARL) environments is challenging, in particular with respect to \textit{individual} decision-making. Practitioners frequently struggle to compare training runs due to the inherent…
Recent studies in the spatial prisoner's dilemma games with reinforcement learning have shown that static agents can learn to cooperate through a diverse sort of mechanisms, including noise injection, different types of learning algorithms…
Reinforcement learning in multiagent systems has been studied in the fields of economic game theory, artificial intelligence and statistical physics by developing an analytical understanding of the learning dynamics (often in relation to…
We compute equilibrium strategies in multi-stage games with continuous signal and action spaces as they are widely used in the management sciences and economics. Examples include sequential sales via auctions, multi-stage elimination…
This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…
This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual…
Logit dynamics are dynamical systems describing transitions and equilibria of actions of interacting players under uncertainty. An uncertainty is embodied in logit dynamic as a softmax type function often called a logit function originating…
Although multi-agent reinforcement learning can tackle systems of strategically interacting entities, it currently fails in scalability and lacks rigorous convergence guarantees. Crucially, learning in multi-agent systems can become…
In many multi-player interactions, players incur strictly positive costs each time they execute actions e.g. 'menu costs' or transaction costs in financial systems. Since acting at each available opportunity would accumulate prohibitively…