"Imitator-Experimenter Dynamics: A Complete Characterization" (with Robert Rosenthal)
 

Abstract: Gale and Rosenthal (1999) study a model of boundedly rational agents repeatedly playing a simple game. Some agents are experimenters (they search randomly for better strategies); others are imitators (they adapt their strategies towards what they see other agents doing). Gale and Rosenthal analyze the dynamic properties of this model and show that (a) the model is stable in the large unless strategies are very strong strategic complements; (b) if strategies were strategic complements, but not too strong, the model is asymptotically stable; (c) if strategies are sufficiently strong strategic substitutes, the model is unstable in the small but "not too unstable". This characterization leaves a gap: it does not say what happens in the case where strategies are strategic substitutes, but not "sufficiently strong" to satisfy the conditions of (c). This paper completes the characterization by filling that gap. We find a critical parameter value measuring the strength of strategic substitutes such that (c.1) for strategic substitutes weaker than this critical level the model is asymptotically stable and (c.2) for strategic substitutes stronger than the critical level the model is unstable in the small but "not too unstable".