Learning in experimental 2×2 games

In this paper, we introduce two new learning models: action-sampling learning and impulse-matching learning. These two models, together with the models of self-tuning EWA and reinforcement learning, are applied to 12 different 2×2 games and their results are compared with the results from experimental data. We test whether the models are capable of replicating the aggregate distribution of behavior, as well as correctly predicting individualsʼ round-by-round behavior. Our results are two-fold: while the simulations with impulse-matching and action-sampling learning successfully replicate the experimental data on the aggregate level, individual behavior is best described by self-tuning EWA. Nevertheless, impulse-matching learning has the second-highest score for the individual data. In addition, only self-tuning EWA and impulse-matching learning lead to better round-by-round predictions than the aggregate frequencies, which means they adjust their predictions correctly over time.

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

[2]  Sebastian J. Goerg,et al.  Stationary Concepts for Experimental 2 X 2 Games: Reply , 2011 .

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

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

[5]  Ben Polak,et al.  Fictitious play in 2×2 games: A geometric proof of convergence , 1994 .

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

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

[8]  Klaus Abbink,et al.  RatImage - research Assistance Toolbox for Computer-Aided Human Behavior Experiments , 1995 .

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

[10]  Alvin E. Roth,et al.  A Choice Prediction Competition for Market Entry Games: An Introduction , 2010, Games.

[11]  R. Selten,et al.  Stationary Concepts for Experimental 2x2 Games , 2008 .

[12]  C. Harley Learning the evolutionarily stable strategy. , 1981, Journal of theoretical biology.

[13]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[14]  R. Selten,et al.  Learning Direction Theory and the Winner’s Curse , 2005 .

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

[16]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[17]  Alan W. Beggs,et al.  On the convergence of reinforcement learning , 2005, J. Econ. Theory.

[18]  Robert W. Rosenthal,et al.  Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment , 1990 .

[19]  Ido Erev,et al.  Generality, repetition, and the role of descriptive learning models , 2005 .

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

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

[22]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[23]  A. Rubinstein,et al.  Games with Procedurally Rational Players , 1997 .

[24]  G. Brier VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

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

[26]  E. Kalai,et al.  Rational Learning Leads to Nash Equilibrium , 1993 .

[27]  D. Marchiori,et al.  Predicting Human Interactive Learning by Regret-Driven Neural Networks , 2008, Science.

[28]  R. Selten Axiomatic Characterization of the Quadratic Scoring Rule , 1998 .

[29]  Teck-Hua Ho,et al.  Self-tuning experience weighted attraction learning in games , 2007, J. Econ. Theory.

[30]  Colin Camerer,et al.  Stationary Concepts for Experimental 2 X 2 Games: Comment , 2011 .

[31]  Sebastian J. Goerg,et al.  Experimental investigation of stationary concepts in cyclic duopoly games , 2009 .

[32]  Wei Chen,et al.  Bounded Memory, Inertia, Sampling and Weighting Model for Market Entry Games , 2011, Games.