CONVERGENCE: AN EXPERIMENTAL STUDY OF TEACHING AND LEARNING IN REPEATED GAMES

Nash equilibrium can be interpreted as a steady state where players hold correct beliefs about the other players’ behavior and act rationally. We experimentally examine the process that leads to this steady state. Our results indicate that some players emerge as teachers—those subjects who, by their actions, try to influence the beliefs of their opponent and lead the way to a more favorable outcome—and that the presence of teachers appears to facilitate convergence to Nash equilibrium. In addition to our experiments, we examine games, with different properties, from other experiments and show that teaching plays an important role in these games. We also report results from treatments in which teaching is made more difficult. In these treatments, convergence rates go down and any convergence that does occur is delayed. (JEL: C70, C91, D83, D84)

[1]  Theo Offerman,et al.  Is the Quadratic Scoring Rule Behaviorally Incentive Compatible , 2001 .

[2]  Colin Camerer,et al.  Experienced-Weighted Attraction Learning in Normal Form Games , 2007 .

[3]  L. Samuelson Evolutionary Games and Equilibrium Selection , 1997 .

[4]  Andrew Schotter,et al.  Does Game Theory Predict Well for the Wrong Reasons: An Experimental Investigation , 1993 .

[5]  Vincent P. Crawford,et al.  Introduction to Experimental Game Theory , 2002, J. Econ. Theory.

[6]  Martin Dufwenberg,et al.  Measuring Beliefs in an Experimental Lost Wallet Game , 2000, Games Econ. Behav..

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

[8]  Urs Fischbacher,et al.  z-Tree - Zurich toolbox for readymade economic experiments: experimenter's manual , 1999 .

[9]  Charles R. Plott,et al.  The Groves-Ledyard mechanism: An experimental study of institutional design , 1996 .

[10]  H. Peyton Young,et al.  Strategic Learning and Its Limits , 2004 .

[11]  E. Hopkins Two Competing Models of How People Learn in Games (first version) , 1999 .

[12]  R. Selten,et al.  Experimental Sealed Bid First Price Auctions with Directly Observed Bid Functions , 1994 .

[13]  Kyle Hyndman,et al.  Learning and sophistication in coordination games , 2009 .

[14]  T. Sargent,et al.  Escaping Nash Inflation , 2000, SSRN Electronic Journal.

[15]  Steffen Huck,et al.  Do players correctly estimate what others do?: Evidence of conservatism in beliefs , 2002 .

[16]  S. Hart,et al.  Uncoupled Dynamics Do Not Lead to Nash Equilibrium , 2003 .

[17]  J. Sonnemans,et al.  Value Orientations, Expectations and Voluntary Contributions in Public Goods. , 1996 .

[18]  N. Wilcox,et al.  Learning and Belief Elicitation : Observer Effects by , 2004 .

[19]  R. Selten,et al.  End behavior in sequences of finite prisoner's dilemma supergames , 1986 .

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

[21]  V. Crawford Adaptive dynamics in coordination games , 1995 .

[22]  Yan Chen,et al.  When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting ⁄ , 2004 .

[23]  E. Elisabet Rutström,et al.  Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test , 2009, Games Econ. Behav..

[24]  A. Schotter,et al.  An Experimental Study of Belief Learning Using Elicited Beliefs , 2002 .

[25]  Miguel A. Costa-Gomes,et al.  Stated Beliefs and Play in Normal-Form Games , 2007 .

[26]  Teck-Hua Ho,et al.  Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games , 2002, J. Econ. Theory.

[27]  Timothy N. Cason,et al.  Learning, teaching, and turn taking in the repeated assignment game , 2012, Economic Theory.

[28]  Owen R. Phillips,et al.  Dynamic Learning in a Two-Person Experimental Game , 2001 .

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

[30]  John Conlisk Adaptive tactics in games: Further solutions to the Crawford puzzle , 1993 .

[31]  U. Fischbacher z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[32]  E. Haruvy Identification and testing of modes in beliefs , 2002 .

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

[34]  Dilip Mookherjee,et al.  Learning behavior in an experimental matching pennies game , 1994 .

[35]  A. Terracol,et al.  Dumbing down rational players: Learning and teaching in an experimental game , 2009 .

[36]  D. Stahl,et al.  On Players' Models of Other Players: Theory and Experimental Evidence , 1995 .

[37]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

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

[39]  Joep Sonnemans,et al.  UvA-DARE (Digital Academic Repository) Price stability and volatility in markets with positive and negative expectations feedback: an experimental investigation , 2007 .

[40]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Two-Person Guessing Games: An Experimental Study , 2003 .

[41]  Nick Feltovich,et al.  Thinking Like a Game Theorist: Comment , 2000 .

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

[43]  Glenn Ellison,et al.  Learning from Personal Experience: One Rational Guy and the Justification of Myopia , 1997 .

[44]  T. Sargent,et al.  Self-confirming equilibrium , 2008 .

[45]  Ramón Cobo-Reyes,et al.  The dark side of friendship: ‘envy’ , 2012 .

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

[47]  H. Peyton Young,et al.  The Possible and the Impossible in Multi-Agent Learning , 2007, Artif. Intell..

[48]  Georg Weizsäcker Ignoring the Rationality of Others: Evidence from Experimental Normal-form Games , 2001 .

[49]  Paul R. Milgrom,et al.  Adaptive and sophisticated learning in normal form games , 1991 .

[50]  Richard T. Boylan,et al.  Fictitious Play: A Statistical Study of Multiple Economic Experiments , 1993 .

[51]  Andrew Schotter,et al.  An experimental study of belief learning using real beliefs , 1998 .

[52]  Colin Camerer,et al.  Sophisticated EWA Learning and Strategic Teaching in Repeated Games , 2000 .

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

[54]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

[55]  T. Sargent,et al.  Convergence of Least Squares Learning Mechanisms in Self- Referential Linear Stochastic Models* , 1989 .

[56]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[57]  John Conlisk,et al.  Adaptation in games: Two solutions to the Crawford puzzle , 1993 .

[58]  Timothy C. Salmon An Evaluation of Econometric Models of Adaptive Learning , 2001 .

[59]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[60]  Bogaçhan Çelen,et al.  Introduction to a festschrift for Andrew Schotter , 2012 .