Learning by Distributed Automata

We introduce a slightly modiied version of a standard learning automaton and show that this`responsive' learning automata eliminates dominated strategies when playing against an unknown environment. This new automaton has strong convergence properties that are easily analyzed, allowing us to compute explicit bounds for convergence rates. Groups of such automata, interacting via a general game, are then studied. We show that synchronous groups of automata converge to the serially undominated set. We then show that, in contrast, asynchronous automata do not necessarily converge to the serially undominated set. However, these asynchronous automata do converge to the serially set-undominated set, which we deene.