Transient and asymptotic dynamics of reinforcement learning in games

Learning and risk aversion

“…Such rules satisfy the above condition in a trivial manner because the expected distribution tomorrow is the same as today. 19 We conclude, therefore, that such a property is too restrictive. Restricting the set of environments on which the improvement is required would lead us to identify a larger class of learning rules.…”

“…Hence, our analysis provides a similar level of generality 18 See Claim 1 in the Appendix for the proof. 19 It can also be shown that unbiased learning rules are the only learning rules which are continuous in x for all a, a ∈ A and satisfy a (α a (s) + f a (s)) F a sosd a α a (s)F a in every environment. For details, see Claim 2 in the Appendix.…”

Individual Strategy Update and Emergence of Cooperation in Social Networks

“…However, very different update rules, with a clear learning interpretation, lead to other outcomes. It is worth quoting work in progress by Galán, Izquierdo, Santos, and Sánchez (2010), who elaborate on previous research on two-player games (Izquierdo, Izquierdo, Gotts, & Polhill, 2007;Izquierdo, Izquierdo, & Gotts, 2008) with reinforcement learning dynamics as used by Macy and Flache (2002). Using the Prisoner's Dilemma as an example, they observe that the asymptotic state of a two-player game with this dynamics is full cooperation for both players with transients around a mixed strategy equilibrium.…”

Modelado de sistemas complejos mediante simulación basada en agentes y mediante dinámica de sistemas

“…Polhill et al, 2001;Gotts et al, 2003), teoría de procesos estocásticos (Izquierdo et al, 2008a), aproximaciones de campo medio (ver p. ej. Galán & Izquierdo, 2005;Izquierdo et al, 2007), visualizaciones de datos interactivas (ver p. ej. Izquierdo et al, 2008a;Izquierdo et al, 2008b), o simple inspección.…”