Regret-Based Continuous-Time Dynamics
Sergiu Hart and Andreu Mas-Colell
Abstract
Regret-based dynamics have been introduced and studied in the context of
discrete-time repeated play. Here we carry out the corresponding analysis in
continuous time. We observe that, in contrast to (smooth) fictitious play or
to evolutionary models, the appropriate state space for this analysis is the
space of distributions on the product of the players' pure action spaces
(rather than the product of their mixed action spaces). We obtain relatively
simple proofs for some results known in the discrete case (related to
"no-regret" and correlated equilibria), and also a new result on
two-person potential games (for this result we also provide a discrete-time
proof).
Journal of Economic Literature Classification Numbers: C7, D7, C6