Math. Model. Nat. Phenom.
Volume 18, 2023
|Number of page(s)||23|
|Section||Population dynamics and epidemiology|
|Published online||28 April 2023|
Analysis of dynamic evolution process of the N-player division of labor game model
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China
2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
* Corresponding author: firstname.lastname@example.org
Accepted: 16 March 2023
This paper investigates a three-strategy (cooperators, toxin producers, and cheaters) N-player division of labor game in bacterial populations. We construct the replicator equation to discuss the evolution of the frequency of the three strategies. Firstly, we prove that the interior equilibrium is always unstable, the three strategies cannot coexist. Secondly, according to Sotomayor’s theorem, the system undergoes transcritical bifurcation. Furthermore, the sensitivity of the two-dimensional evolutionary state diagrams to the third parameter (toxin rate, absorption rate, toxin quantity, etc) is analyzed. In summary, high toxicity rates, high levels of toxins, and low levels of competition tend to promote cooperation. All players choose to perform the task, and the cheater disappears. When the absorption rate of cooperators is high enough, only cooperators exist in the population over time. When the absorption rate of the cooperator is low, and the absorption rate of the toxin producer is greater than the threshold, the cooperator and the toxin producer coexist. All players perform the task. Finally, the triangle diagrams and three-dimensional diagrams are presented, which show the initial conditions of the three strategies also affect the dynamic results. As the amount of toxin increases, the range of players who choose to perform tasks widens.
Mathematics Subject Classification: 91A06 / 91A80 / 34K18 / 93A30
Key words: Replicator dynamics / Ar-player division of labor game / transcritical bifurcation / evolutionary game theory / toxin production
© The authors. Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.