The dynamics of reinforcement learning in cooperative multiagent systems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Multiagent learning using a variable learning rate
Artificial Intelligence
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Multiagent Reinforcement Learning: Theoretical Framework and an Algorithm
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Reinforcement learning of coordination in cooperative multi-agent systems
Eighteenth national conference on Artificial intelligence
A selection-mutation model for q-learning in multi-agent systems
AAMAS '03 Proceedings of the second international joint conference on Autonomous agents and multiagent systems
Nash q-learning for general-sum stochastic games
The Journal of Machine Learning Research
An Evolutionary Dynamical Analysis of Multi-Agent Learning in Iterated Games
Autonomous Agents and Multi-Agent Systems
Theoretical Advantages of Lenient Learners: An Evolutionary Game Theoretic Perspective
The Journal of Machine Learning Research
Switching dynamics of multi-agent learning
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 1
State-coupled replicator dynamics
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
A multiagent reinforcement learning algorithm with non-linear dynamics
Journal of Artificial Intelligence Research
Reinforcement learning: a survey
Journal of Artificial Intelligence Research
Learning to cooperate via policy search
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
A Comprehensive Survey of Multiagent Reinforcement Learning
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology. Most existing studies so far have been limited to discrete strategy spaces with a small number of available actions. In many cases, however, the choices available to agents are better characterized by continuous spectra. This paper suggests a generalization of the replicator framework that allows to study the adaptive dynamics of Q-learning agents with continuous strategy spaces. Instead of probability vectors, agents' strategies are now characterized by probability measures over continuous variables. As a result, the ordinary differential equations for the discrete case are replaced by a system of coupled integral-differential replicator equations that describe the mutual evolution of individual agent strategies. We derive a set of functional equations describing the steady state of the replicator dynamics, examine their solutions for several two-player games, and confirm our analytical results using simulations.