Asynchronous Decision-Making Dynamics Under Best-Response Update Rule in Finite Heterogeneous Populations

To study how sustainable cooperation might emerge among self-interested interacting individuals, we investigate the long-run behavior of the decision-making dynamics in a finite, well-mixed population of individuals, who play collectively over time a population game. Repeatedly each individual is ac...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 63; no. 3; pp. 742 - 751
Main Authors Ramazi, Pouria, Cao, Ming
Format Journal Article
LanguageEnglish
Published IEEE 01.03.2018
Subjects
Benchmark testing
Best-response dynamics
Convergence
convergence analysis
Decision making
evolutionary game theory
Games
Silicon
Sociology
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Summary:To study how sustainable cooperation might emerge among self-interested interacting individuals, we investigate the long-run behavior of the decision-making dynamics in a finite, well-mixed population of individuals, who play collectively over time a population game. Repeatedly each individual is activated asynchronously to update her decision to either cooperate or defect according to the myopic best-response rule. The game's payoff matrices, chosen to be those of either prisoner's dilemma or snowdrift games to underscore cooperation-centered social dilemmas, are fixed, but can be distinct for different individuals. So, the overall population is heterogeneous. We first classify such heterogeneous individuals into different types according to their cooperating tendencies stipulated by their payoff matrices. Then, we show that no matter what initial strategies the individuals decide to use, surprisingly one can always identify one type of individuals as a benchmark such that after a sufficiently long but finite time, individuals more cooperative compared to the benchmark always cooperate, while those less cooperative compared to the benchmark defect. When such fixation takes place, the total number of cooperators in the population either becomes fixed or fluctuates at most by one. Such insight provides theoretical explanation for some complex behavior recently reported in simulation studies that highlight the puzzling effect of individuals' heterogeneity on collective decision-making dynamics.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2737142