Tag Archives: Game Theory

The seminal work on the “firstly cooperate, then repeat other’s actions” strategy in game theory

September 19, 2024 15:36 ,

Robert Axelrod; William D. Hamilton, The Evolution of Cooperation, Science, New Series, Vol. 211, No. 4489. (Mar. 27, 1981), pp. 1390-1396 https://ee.stanford.edu/~hellman/Breakthrough/book/pdfs/axelrod.pdf.

Cooperation in organisms, whether bacteria or primates, has been a
difficulty for evolutionary theory since Darwin. On the assumption that interactions
between pairs of individuals occur on a probabilistic basis, a model is developed
based on the concept of an evolutionarily stable strategy in the context of the
Prisoner’s Dilemma game. Deductions from the model, and the results of a computer
tournament show how cooperation based on reciprocity can get started in an asocial
world, can thrive while interacting with a wide range of other strategies, and can resist
invasion once fully established. Potential applications include specific aspects of
territoriality, mating, and disease.

Posted in: Psycho-physiological bases of engineering , Tagged:

Nice summary of reinforcement learning in control (Adaptive Dynamic Programming) and the use of Q-learning plus NN approximators for solving a control problem under a game theory framework

October 19, 2015 11:04 ,

Kyriakos G. Vamvoudakis, Non-zero sum Nash Q-learning for unknown deterministic continuous-time linear systems, Automatica, Volume 61, November 2015, Pages 274-281, ISSN 0005-1098, DOI: 10.1016/j.automatica.2015.08.017.

This work proposes a novel Q-learning algorithm to solve the problem of non-zero sum Nash games of linear time invariant systems with N -players (control inputs) and centralized uncertain/unknown dynamics. We first formulate the Q-function of each player as a parametrization of the state and all other the control inputs or players. An integral reinforcement learning approach is used to develop a model-free structure of N -actors/ N -critics to estimate the parameters of the N -coupled Q-functions online while also guaranteeing closed-loop stability and convergence of the control policies to a Nash equilibrium. A 4th order, simulation example with five players is presented to show the efficacy of the proposed approach.

Posted in: Applications of reinforcement learning to control engineering , Tagged: , , , ,