  We consider a prospect theoretic version of the classical Q-learning
algorithm for discounted reward Markov decision processes, wherein the
controller perceives a distorted and noisy future reward, modeled by a
nonlinearity that accentuates gains and underrepresents losses relative to a
reference point. We analyze the asymptotic behavior of the scheme by analyzing
its limiting differential equation and using the theory of monotone dynamical
systems to infer its asymptotic behavior. Specifically, we show convergence to
equilibria, and establish some qualitative facts about the equilibria
themselves.
