Learning backward induction: a neural network agent approach

Leonidas, Spiliopoulos (2009): Learning backward induction: a neural network agent approach.

Abstract

This paper addresses the question of whether neural networks (NNs), a realistic cognitive model of human information processing, can learn to backward induce in a two-stage game with a unique subgame-perfect Nash equilibrium. The NNs were found to predict the Nash equilibrium approximately 70% of the time in new games. Similarly to humans, the neural network agents are also found to suffer from subgame and truncation inconsistency, supporting the contention that they are appropriate models of general learning in humans. The agents were found to behave in a bounded rational manner as a result of the endogenous emergence of decision heuristics. In particular a very simple heuristic socialmax, that chooses the cell with the highest social payoff explains their behavior approximately 60% of the time, whereas the ownmax heuristic that simply chooses the cell with the maximum payoff for that agent fares worse explaining behavior roughly 38%, albeit still significantly better than chance. These two heuristics were found to be ecologically valid for the backward induction problem as they predicted the Nash equilibrium in 67% and 50% of the games respectively. Compared to various standard classification algorithms, the NNs were found to be only slightly more accurate than standard discriminant analyses. However, the latter do not model the dynamic learning process and have an ad hoc postulated functional form. In contrast, a NN agent’s behavior evolves with experience and is capable of taking on any functional form according to the universal approximation theorem.

• Item Type: MPRA Paper
• Language: English
• Keywords: Agent based computational economics; Backward induction; Learning models; Behavioral game theory; Simulations; Complex adaptive systems; Artificial intelligence; Neural networks
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

K. Binmore, et al. (2002). ‘A Backward Induction Experiment’. Journal of Economic Theory 104(1):48–88.

I. Cho & T. Sargent (1996). ‘Neural Networks for Encoding and Adapting in Dynamic Economies’. Handbook of Computational Economics 1:441–470.

G. Cybenko (1989). ‘Approximation by superpositions of a sigmoidal function’. Mathematics of Control, Signals and Systems 2:303–314.

I. E. Dror & D. P. Gallogly (1999). ‘Computational analyses in cognitive neuroscience: In defense of biological implausibility’. Psychonomic Bulletin & Review 6(2):173–182.

K. Funahashi (1989). ‘On the approximate realization of continuous mappings by neural networks’. Neural Networks 2:183–192.

G. Gigerenzer (2000). Adaptive thinking: Rationality in the real world. Oxford University Press, New York.

G. Gigerenzer & R. Selten (eds.) (2001). Bounded rationality: The adaptive toolbox. MIT Press, Cambridge, MA.

J. C. Harsanyi & R. Selten (1988). A General Theory of Equilibirum Selection in Games. MIT Press, Cambridge, MA.

K. Hornik (1991). ‘Approximation capabilities of multilayer feedforward networks’. Neural Networks 4:251–257.

E. J. Johnson, et al. (2002). ‘Detecting failures of backward induction: Monitoring information search in sequential bargaining experiments’. Journal of Economic Theory 104:16–47.

R. Kettner, et al. (1993). ‘A neural network model of cortical activity during reaching’. Journal of Cognitive Neuroscience 5:14–33.

S. R. Lehky & T. J. Sejnowski (1988). ‘Network model of shape-from-shading: Neural function arises from both receptive and projective fields’. Nature 333:452–454.

P. Mazzoni, et al. (1991). ‘A more biologically plausible learning rule than backpropagation applied to a network model of cortical area 7a’. Cerebral Cortex 1:293–307.

T. Robinson (2000). ‘Biologically Plausible Back-Propagation’. Tech. rep., Victoria University of Wellington.

D. Sgroi & D. J. Zizzo (2007). ‘Neural networks and bounded rationality’. Physica A: Statistical Mechanics and its Applications 375(2):717–725.

L. Spiliopoulos (2009). ‘Neural Networks as a Learning Paradigm for General Normal Form Games’. SSRN eLibrary - http://ssrn.com/paper=1447968.

D. Zipser & R. A. Andersen (1988). ‘A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons’. Nature 331:679–684.