This article models the learning process of a population of randomly rematched tabula rasa neural network agents playing randomly generated 3 × 3 normal form games of all strategic types. Evidence was found of the endogenous emergence of a similarity measure of games based on the number and types of Nash equilibria, and of heuristics that have been found effective in describing human behavior in experimental one-shot games. The neural network agents were found to approximate experimental human behavior very well across various dimensions such as convergence to Nash equilibria, equilibrium selection, and adherence to principles of dominance and iterated dominance. This is corroborated by evidence from five studies of experimental one-shot games, because the Spearman correlation coefficients of the probability distribution over the neural networks’ and human subjects’ actions ranged from 0.49 to 0.89.
CheungY. W.FriedmanD. (1997). Individual learning in normal form games: Some laboratory results. Games and Economic Behavior, 19, 46–76.
4.
ChoI. K.SargentT. J. (1996). Neural networks for encoding and adapting in dynamic economies. In AmmanH. M.KendrickD. A.RustJ. (Eds.), Handbook of computational economics, Vol 1 (pp. 441–470). Amsterdam: Elsevier.
5.
CooperR. W.DeJongD. V.ForsytheR.RossT. W. (1990). Selection criteria in coordination games: Some experimental results. The American Economic Review, 80(1), 218–233.
6.
Costa-GomesM.CrawfordV. P.BrosetaB. (2001). Cognition and behavior in normal-form games: An experimental study. Econometrica, 69(5), 1193–1236.
7.
CybenkoG. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems, 2, 303–314.
8.
DrorI. E.GalloglyD. P. (1999). Computational analyses in cognitive neuroscience: In defense of biological implausibility. Psychonomic Bulletin & Review, 6(2), 173–182.
9.
ErevI.RothA. E. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. American Economic Review, 88(4), 848–881.
10.
FukumizuK.AmariS. (2000). Local minima and plateaus in hierarchical structures of multilayer perceptrons. Neural Networks, 13(3), 317–327.
11.
FunahashiK. (1989). On the approximate realization of continuous mappings by neural networks. Neural Networks, 2, 183–192.
12.
GermanoF. (2007). Stochastic evolution of rules for playing finite normal form games. Theory and Decision, 62(4), 311–333.
13.
GigerenzerG.SeltenR. (Eds.) (2001). Bounded rationality: The adaptive toolbox. Cambridge, MA: MIT Press.
14.
GilboaI.SchmeidlerD. (1995). Case-based decision theory. The Quarterly Journal of Economics, 110(3), 605–639.
15.
GilboaI.ZemelE. (1989). Nash and correlated equilibria: Some complexity considerations. Games and Economic Behavior, 1(1), 80–93.
16.
HarsanyiJ. C.SeltenR. (1988). A general theory of equilibirum selection in games. Cambridge, MA: MIT Press.
17.
HaruvyE.StahlD. (2004). Deductive versus inductive equilibrium selection: experimental results. Journal of Economic Behavior and Organization, 53(3), 319–331.
18.
HensherD.JohnsonL. (1981). Applied discrete-choice modelling. New York: Wiley.
HosmerD.LemeshowS. (1989). Applied logistic regression. New York: John Wiley & Sons.
21.
IvanovA. (2008). Strategic play and risk aversion in one-shot normal-form games: An experimental study (Tech. Rep.). Virginia Commonwealth University, School of Business, Department of Economics.
22.
JuddJ. (1990). Neural network design and the complexity of learning. Cambridge, MA: MIT Press.
23.
KahnemanD.TverskyA. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–292.
24.
KatzK. (1996). Three applications of game theory. Unpublished doctoral dissertation, University of Pennsylvania.
25.
KettnerR.MarcarioJ.PortN. (1993). A neural network model of cortical activity during reaching. Journal of Cognitive Neuroscience, 5, 14–33.
26.
LeakeD. (Ed.) (1996). Case-based reasoning: Experiences, lessons, and future directions. Menlo Park, CA: AAAI/MIT Press.
27.
LeCunY.BottouL.OrrG. B.MullerK.-R. (1998). Efficient backprop. In: OrrGMüllerK.-R. (Eds.), Neural networks: Tricks of the trade (pp. 9–50). Berlin/Heidelberg: Springer.
28.
LehkyS. R.SejnowskiT. J. (1988). Network model of shape-from-shading: Neural function arises from both receptive and projective fields. Nature, 333, 452–454.
29.
LemkeC. E.HowsonJ. T. (1964). Equilibrium points of bimatrix games. Journal of the Society for Industrial and Applied Mathematics, 12(2), 413–423.
30.
LiCalziM. (1995). Fictitious play by cases. Games and Economic Behavior, 11, 64–89.
31.
LouviereJ.HensherD.SwaitJ. (2000). Stated choice methods. New York: Cambridge University Press.
32.
MathWorks (2007). MATLAB. Natick, MA: MathWorks.
33.
MazzoniP.AndersenR. A.JordanM. I. (1991). A more biologically plausible learning rule than backpropagation applied to a network model of cortical area 7a. Cerebral Cortex, 1, 293–307.
34.
McFaddenD. (1973). Conditional logit analysis of qualitative choice behavior. Frontiers in Econometrics, 105–142. Massachusetts: Academic Press.
35.
MookherjeeD.SopherB. (1997). Learning and decision costs in experimental constant sum games. Games and Economic Behavior, 19(1), 97–132.
36.
MyersR. (1986). Classical and modern regression with applications. Boston, MA: Duxbury Press.
37.
NagelR. (1995). Unraveling in guessing games: An experimental study. The American Economic Review, 85(5), 1313–1326.
38.
NguyenD.WidrowB. (1990). Improving the learning speed of 2-layer neural network by choosing initial values of the adaptive weights. In IEEE First International Joint Conference on Neural Networks (pp. 21–26) San Diego, CA.
39.
OckenfelsA.SeltenR. (2005). Impulse balance equilibrium and feedback in first price auctions. Games and Economic Behavior, 51, 155–170.
Rey-BielP. (2009). Equilibrium play and best response to (stated) beliefs in normal form games. Games and Economic Behavior, 65(2), 572–585.
42.
RieskampJ.BusemeyerJ.LaineT. (2003). How do people learn to allocate resources? Comparing two learning theories. Journal of Experimental Psychology. Learning, Memory, and Cognition, 29(6), 1066–1081.
43.
RobinsonT. (2000). Biologically plausible back-propagation (Tech. Rep.). Victoria University of Wellington.
44.
RumelhartD.HintontG.WilliamsR. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533–536.
45.
SargentT. S. (1993). Bounded rationality in macroeconomics. New York: Oxford University Press.
46.
SarkarD. (1995). Methods to speed up error back-propagation learning algorithm. ACM Computing Surveys, 27(4), 519–544.
47.
SarleW. (1994). Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Group International Conference (pp. 1538–1550). Cary, NC: SAS Institute Inc.
48.
SchotterA.WeigeltK.WilsonC. (1994). A laboratory investigation of multiperson rationality and presentation effects. Games and Economic Behavior, 6(3), 445–468.
49.
SeltenR. (1998). Features of experimentally observed bounded rationality. European Economic Review, 42(3–5), 413–436.
50.
SeltenR.AbbinkK.BuchtaJ.SadriehA. (2003). How to play 3 x 3 games: A strategy method experiment. Games and Economic Behavior, 45(1), 19–37.
51.
SeltenR.AbbinkK.CoxR. (2005). Learning direction theory and the Winner’s Curse. Experimental Economics, 8(1), 5–20.
52.
SgroiD. (2005). Using neural networks to model bounded rationality in interactive decision-making. In: ZizzoD. (Ed.), Transfer of knowledge in economic decision-making (pp. 128–147). London: Palgrave Macmillan.
53.
SgroiD.ZizzoD. (2009). Learning to play 3 x 3 games: neural networks as bounded-rational players. Journal of Economic Behavior and Organization, 69(1), 27–38.
54.
SgroiD.ZizzoD. J. (2007). Neural networks and bounded rationality. Physica A: Statistical Mechanics and its Applications, 375(2), 717–725.
55.
SontagE.SussmannH. (1989). Backpropagation can give rise to spurious local minima even for networks without hidden layers. Complex Systems, 3(1), 91–106.
56.
StahlD.HaruvyE. (2004). Rule learning across dissimilar symmetric normal-form games (Tech. Rep.). University of Texas.
57.
StahlD. O.WilsonP. W. (1995). On players’ models of other players: Theory and experimental evidence. Games and Economic Behavior, 10(1), 218–254.
58.
SteinerJ.StewartC. (2008). Contagion through learning. Theoretical Economics, 3(4), 431–458.
59.
TangF. F. (2001). Anticipatory learning in two-person games: Some experimental results. Journal of Economic Behavior & Organization, 44(2), 221–232.
60.
TesfatsionL. (2002). Agent-based computational economics: Growing economies from the bottom up. Artificial Life, 8(1), 55–82.
61.
TesfatsionL.JuddK. L. (2006). Handbook of computational economics, Vol. 2. Amsterdam: Elsevier.
62.
van OoyenA.RoelfsemaP. (2003). A biologically plausible implementation of error-backpropagation for classification tasks. In KaynakO.AlpaydinE.OjaE.XuL., (Eds.), Artificial Neural Networks and Neural Information Processing Supplementary Proceedings ICANN/ICONIP 2003 (pp. 442–444). Istanbul.
63.
WaldropM. (1992). Complexity: The emerging science at the edge of order and chaos. New York: Simon and Schuster.
64.
ZipserD.AndersenR. A. (1988). A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons. Nature, 331, 679–684.
