# Stubborn learning

## Author

Listed:
• Jean-François Laslier

()

• Bernard Walliser

()

## Abstract

The paper studies a specific adaptive learning rule when each player faces a unidimensional strategy set. The rule states that a player keeps on incrementing her strategy in the same direction if her utility increased and reverses direction if it decreased. The paper concentrates on games on the square $$[0,1]\times [0,1]$$ [ 0 , 1 ] × [ 0 , 1 ] as mixed extensions of $$2\times 2$$ 2 × 2 games. We study in general the behavior of the system in the interior as well as on the borders of the strategy space. We then describe the system asymptotic behavior for symmetric, zero-sum, and twin games. Original patterns emerge. For instance, for the “prisoner’s dilemma” with symmetric initial conditions, the system goes directly to the symmetric Pareto optimum. For “matching pennies,” the system follows slowly expanding cycles around the mixed strategy equilibrium. Copyright Springer Science+Business Media New York 2015

## Suggested Citation

• Jean-François Laslier & Bernard Walliser, 2015. "Stubborn learning," Theory and Decision, Springer, vol. 79(1), pages 51-93, July.
• Handle: RePEc:kap:theord:v:79:y:2015:i:1:p:51-93
DOI: 10.1007/s11238-014-9450-3
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File URL: http://hdl.handle.net/10.1007/s11238-014-9450-3

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## References listed on IDEAS

as
1. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
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12. V. P. Crawford., 2014. "Boundedly Rational versus Optimization-Based Models of Strategic Thinking and Learning in Games," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
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## Citations

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Cited by:

1. Drew Fudenberg & Kevin He, 2018. "Learning and Type Compatibility in Signaling Games," Econometrica, Econometric Society, vol. 86(4), pages 1215-1255, July.

### Keywords

Games; Behavior; Learning; Dynamics;

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