A two-stage feasible directions algorithm for nonlinear constrained optimization
Mathematical Programming: Series A and B
Competitive Markov decision processes
Competitive Markov decision processes
Multiagent Reinforcement Learning: Theoretical Framework and an Algorithm
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Nash convergence of gradient dynamics in general-sum games
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
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Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair.