Related papers: Limiting dynamics for Q-learning with memory one i…
We consider a class of two-player zero-sum stochastic games with finite state and compact control spaces, which we call stochastic shortest path (SSP) games. They are undiscounted total cost stochastic dynamic games that have a cost-free…
Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been…
An interesting iterative procedure is proposed to solve a two-player zero-sum Markov games. Under suitable assumption, the boundedness of the proposed iterates is obtained theoretically. Using results from stochastic approximation, the…
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…
Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm…
This paper combines ideas from Q-learning and fictitious play to define three reinforcement learning procedures which converge to the set of stationary mixed Nash equilibria in identical interest discounted stochastic games. First, we…
In the literature on game-theoretic equilibrium finding, focus has mainly been on solving a single game in isolation. In practice, however, strategic interactions -- ranging from routing problems to online advertising auctions -- evolve…
Recently, the eco-evolutionary game theory which describes the coupled dynamics of strategies and environment have attracted great attention. At the same time, most of the current work is focused on the classic two-player two-strategy game.…
Memory-one strategies are a set of Iterated Prisoner's Dilemma strategies that have been praised for their mathematical tractability and performance against single opponents. This manuscript investigates best response memory-one strategies…
In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…
Mutual relationships, such as cooperation and exploitation, are the basis of human and other biological societies. The foundations of these relationships are rooted in the decision making of individuals, and whether they choose to be…
Achieving convergence of multiple learning agents in general $N$-player games is imperative for the development of safe and reliable machine learning (ML) algorithms and their application to autonomous systems. Yet it is known that, outside…
Learning in games discusses the processes where multiple players learn their optimal strategies through the repetition of game plays. The dynamics of learning between two players in zero-sum games, such as Matching Pennies, where their…
Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum…
Reinforcement learning has been successful both empirically and theoretically in single-agent settings, but extending these results to multi-agent reinforcement learning in general-sum Markov games remains challenging. This paper studies…
Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some…
Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice.…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…
Although learning has found wide application in multi-agent systems, its effects on the temporal evolution of a system are far from understood. This paper focuses on the dynamics of Q-learning in large-scale multi-agent systems modeled as…