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Games 2017, 8(1), 1; doi:10.3390/g8010001

Cognitive Hierarchy Theory and Two-Person Games

1
Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
2
Departamento de Física de la Materia Condensada, University of Zaragoza, 50009 Zaragoza, Spain
3
Departamento de Física Teórica, University of Zaragoza, 50009 Zaragoza, Spain
*
Author to whom correspondence should be addressed.
Academic Editors: Attila Szolnoki and Ulrich Berger
Received: 30 November 2016 / Accepted: 14 December 2016 / Published: 3 January 2017
(This article belongs to the Special Issue Evolutionary Games and Statistical Physics of Social Networks)
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Abstract

The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory. View Full-Text
Keywords: social dilemmas; game theory; cognitive theory social dilemmas; game theory; cognitive theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gracia-Lázaro, C.; Floría, L.M.; Moreno, Y. Cognitive Hierarchy Theory and Two-Person Games. Games 2017, 8, 1.

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