Two Competing Models of How People Learn in Games (first version)

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimisation. This paper compares their properties and finds that they are far more similar than were thought. In particular, exponential fictitious play and suitably perturbed reinforcement model have the same expected motion and therefore will have the same asymptotic behaviour. It is also shown that more general models of stochastic fictitious play and perturbed reinforcement between the two models is speed: stochastic fictitious play gives rise to faster learning.

[1]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[2]  W. Brian Arthur,et al.  On designing economic agents that behave like human agents , 1993 .

[3]  David M. Kreps,et al.  Learning Mixed Equilibria , 1993 .

[4]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[5]  Ken Binmore,et al.  Learning to be imperfect: The ultimatum game , 1995 .

[6]  J. Hofbauer,et al.  Fictitious Play, Shapley Polygons and the Replicator Equation , 1995 .

[7]  A. Roth,et al.  Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term* , 1995 .

[8]  J. Ochs.  Games with Unique, Mixed Strategy Equilibria: An Experimental Study , 1995 .

[9]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[10]  E. Hopkins.  Learning, Matching and Aggregation , 1995 .

[11]  L. Samuelson,et al.  Evolutionary Drift and Equilibrium Selection , 2010 .

[12]  Daniel Friedman,et al.  Individual Learning in Normal Form Games: Some Laboratory Results☆☆☆ , 1997 .

[13]  Martin Posch,et al.  Cycling in a stochastic learning algorithm for normal form games , 1997 .

[14]  Frederick W. Rankin,et al.  On the Origin of Convention: Evidence from Coordination Games , 1997 .

[15]  John H. Kagel,et al.  Signalling and Adaptive Learning in an Entry Limit Pricing Game , 1997 .

[16]  Tilman Börgers,et al.  Learning Through Reinforcement and Replicator Dynamics , 1997 .

[17]  S. Huck,et al.  Learning in Cournot Oligopoly - An Experiment , 1999 .

[18]  Nicolaas J. Vriend,et al.  Will reasoning improve learning , 1997 .

[19]  A. Roth,et al.  Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria , 1998 .

[20]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[21]  Drew Fudenberg,et al.  Learning in Games , 1998 .

[22]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[23]  John Duffy,et al.  Does observation of others affect learning in strategic environments? An experimental study , 1999, Int. J. Game Theory.

[24]  D. Fudenberg,et al.  Payoff Information and Self-Confirming Equilibrium , 1999 .

[25]  E. Hopkins.  A Note on Best Response Dynamics , 1999 .

[26]  Colin Camerer,et al.  Experience‐weighted Attraction Learning in Normal Form Games , 1999 .

[27]  A. Rustichini.  Optimal Properties of Stimulus-Response Learning Models* , 1999 .

[28]  M. Hirsch,et al.  Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games , 1999 .

[29]  Nick Feltovich,et al.  Reinforcement-based vs. Belief-based Learning Models in Experimental Asymmetric-information Games , 2000 .

[30]  Andreas Blume,et al.  Learning and communication in sender-receiver games: an econometric investigation , 2002 .

[31]  Drew Fudenberg,et al.  Learning Purified Mixed Equilibria , 2000, J. Econ. Theory.

[32]  An Insatiable Appetite for Ideas , 2001 .

[33]  Jean-François Laslier,et al.  A Behavioral Learning Process in Games , 2001, Games Econ. Behav..

[34]  J. Hofbauer.  From Nash and Brown to Maynard Smith: Equilibria, Dynamics and ESS , 2001 .

[35]  Farshid Vahid,et al.  Predicting How People Play Games: A Simple Dynamic Model of Choice , 2001, Games Econ. Behav..