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Dynamic Games and Applications
Published in: Dynamic Games and Applications 2/2021

13-10-2020

Aspiration Can Promote Cooperation in Well-Mixed Populations As in Regular Graphs

Author: Dhaker Kroumi

Published in: Dynamic Games and Applications | Issue 2/2021

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Abstract

Classical studies on aspiration-based dynamics suggest that dissatisfied individuals switch their strategies without taking into account the success of others. The imitation-based dynamics allow individuals to imitate successful strategies without taking into account their own-satisfactions. In this article, we propose to study a dynamic based on aspiration, which takes into account imitation of successful strategies for dissatisfied individuals. Individuals compare their success to their aspired levels. This mechanism helps individuals with a minimum of self-satisfaction to maintain their strategies. Dissatisfied individuals will learn from their neighbors by choosing the successful strategies. We derive an exact expression of the fixation probability in well-mixed populations as in graph-structured populations. As a result, we show that weak selection favors the evolution of cooperation if the difference in aspired level exceeds some crucial value. Increasing the aspired level of cooperation should oppose cooperative behavior while increasing the aspired level of defection should promote cooperative behavior. We show that the cooperation level decreases as the connectivity increases. The best scenario for the cooperative evolution is a graph with a small connectivity, while the worst scenario is a well-mixed population.
previous article Correction to: Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information
next article An Update on Continuous-Time Stochastic Games of Fixed Duration

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Appendix
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Metadata
Title
Aspiration Can Promote Cooperation in Well-Mixed Populations As in Regular Graphs
Author
Dhaker Kroumi
Publication date
13-10-2020
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 2/2021
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-020-00368-7

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