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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
They show that even the simplest NN, a single perceptron, is capable of implementing trigger strategies in a repeated prisoner’s dilemma game and of supporting all subgame perfect payoffs. They also prove that only a slightly more complicated network is capable of supporting all equilibrium payoffs in a general 2 ×2 game.
- 2.
The Nash equilibrium is the set of strategies for which neither player has an incentive to unilaterally change strategy.
- 3.
For simplicity, the network presented has only one hidden layer however some of the NNs in this paper will employ more than one hidden layer, each with identical structural and functional properties.
- 4.
Simulations of neural networks with more neurons were at best not found to significantly improve performance, and often degraded performance due to overfitting.
- 5.
Note that this is a stricter prediction criterion than asking the neural network to simply play the NE strategy.
References
Binmore K, McCarthy J, Ponti G, Samuelson L, Shaked A (2002) A backward induction experiment. J Econ Theory 104(1):48–88
Cho I, Sargent T (1996) Neural networks for encoding and adapting in dynamic economies. Handb Comput Econ 1:441–470
Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Contr Signals Syst 2:303–314
Dror IE, Gallogly DP (1999) Computational analyses in cognitive neuroscience: in defense of biological implausibility. Psychon Bull Rev 6(2):173–182
Funahashi K (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192
Gigerenzer G (2000) Adaptive thinking: rationality in the real world. Oxford University Press, New York
Gigerenzer G, Selten R (eds) (2001) Bounded rationality: the adaptive toolbox. MIT Press, Cambridge, MA
Harsanyi JC, Selten R (1988) A general theory of equilibirum selection in games. MIT Press, Cambridge, MA
Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251–257
Johnson EJ, Camerer CF, Sen S, Rymon T (2002) Detecting failures of backward induction: monitoring information search in sequential bargaining experiments. J Econ Theory 104:16–47
Kettner R, Marcario J, Port N (1993) A neural network model of cortical activity during reaching. J Cogn Neurosci 5:14–33
Lehky SR, Sejnowski TJ (1988) Network model of shape-from-shading: neural function arises from both receptive and projective fields. Nature 333:452–454
Mazzoni P, Andersen RA, Jordan MI (1991) A more biologically plausible learning rule than backpropagation applied to a network model of cortical area 7a. Cereb Cortex 1:293–307
Robinson T (2000) Biologically plausible back-propagation. Tech. rep., Victoria University of Wellington
Sgroi D, Zizzo D (2009) Learning to play 3 ×3 games: neural networks as bounded-rational players. J Econ Behav Organ 69(1):27–38
Spiliopoulos L (2009) Neural networks as a learning paradigm for general normal form games. SSRN eLibrary. http://ssrn.com/paper=1447968
Zipser D, Andersen RA (1988) A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons. Nature 331:679–684
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer
About this paper
Cite this paper
Spiliopoulos, L. (2011). Learning Backward Induction: A Neural Network Agent Approach. In: Chen, SH., Terano, T., Yamamoto, R. (eds) Agent-Based Approaches in Economic and Social Complex Systems VI. Agent-Based Social Systems, vol 8. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53907-0_5
Download citation
DOI: https://doi.org/10.1007/978-4-431-53907-0_5
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-53906-3
Online ISBN: 978-4-431-53907-0
eBook Packages: Humanities, Social Sciences and LawSocial Sciences (R0)