The models surveyed include generalized Pólya urns, reinforced random walks, interacting
urn models, and continuous reinforced processes. Emphasis is on methods and results, with …

This paper examines the convergence of payoffs and strategies in Erev and Roth's model of
reinforcement learning. When all players use this rule it eliminates iteratively dominated …

We study a generalized Pólya urn with balls of two colours and a triangular replacement
matrix; the urn is not required to be balanced. We prove limit theorems describing the …

We consider generalizations of the classical Polya urn problem: Given finitely many bins
each containing one ball, suppose that additional balls arrive one at a time. For each new …

We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the
Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1's …

This paper is concerned with a general class of self-interacting diffusions {X t} t≥ 0 living on
a compact Riemannian manifold M. These are solutions to stochastic differential equations …

This paper investigates the properties of the most common form of reinforcement learning
(the “basic model” of Erev and Roth)[Amer. Econ. Rev. 88 (1998) 848–881]. Stochastic …

We introduce range-controlled random walks with hopping rates depending on the range N,
that is, the total number of previously distinct visited sites. We analyze a one-parameter class …

This paper illustrates asymptotic properties for a response-adaptive design generated by a
two-color, randomly reinforced urn model. The design considered is optimal in the sense …

Vertex-reinforced random walk (VRRW), defined by Pemantle, is a random process in a
continuously changing environment which is more likely to visit states it has visited before …