Seminar by M.D. Sams Afif Nirjhor from Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University, Japan
26 November 2025
KST 09:00
The Seminar is being held in Room 1010 (Jasmin) – Integrated mechanical engineering building. Click here for the campus map.
When a large task is divided into several smaller subtasks, and these subtasks are allocated to different people or groups, then the system is called a division of labour. Division of labour can have complex network structures, an arbitrary number of subtasks, and asymmetric interactions among the subtask-holder groups which consists of the experts on that particular subtask. Cooperation among the subtask-holders is essential in division of labour. Our studies are the first to consider the evolution of cooperation in the division of labour considering it as a network of groups having assymetric interaction [1][2][3][4]. Here, we discuss 3 studies on the evolution of cooperation in the division of labour. Each subsequent study generalizes the previous one by relaxing structural constraints on the network of division of labour. These studies present a hierarchical generalization of network complexity: beginning with a unidirectional linear finite network, extending to a unidirectional tree network and finally a general complex network with a single output. In all of these 3 studies we consider subtask-holder groups to be initially made of players whose strategies are cooperation or defection, called cooperators or defectors respectively, and the group sizes are infinite.
Firstly, we consider that a defector stops the process of the division of labour on the way when sub-task holder groups are either on the unidirectional linear network or on the general tree network. For a subtask holder group, a player is randomly chosen from each group, who can be either a cooperator or a defector. Cooperators pay the cost of cooperation for performing the task by improving or modifying a product or service. The cooperator in the subtask passes the product to a player chosen from the immediate downstream group/groups. The downstream player receives the benefit from the upstream cooperator, which can be considered as salaries or product values based on the division of labour. A defector neither pays anything nor passes the product or service to the downstream player, thus the subtask is not done, and the process of the division of labour is stopped. As a result, all players are damaged by the stop. The players in each sub-task holder group compare their payoffs, and update their strategy, so that the strategy with a higher payoff is more chosen with time. Here, the evolution of cooperation means that cooperators increase in number in the sub-task holder groups and take over all sub-task holder groups with enough time. We consider the effect of sanctioning the defectors on the evolution of cooperation. We consider two types of sanction system, one in which the defector is found with a probability and punished, and another where the players from the first sub-task holder group are punished in the case of any defection, representing the case of punishing a leader or scapegoat. The dynamics is modeled by the replicator equations, and we develop a novel method to analyse the local stability in the general tree network. We find that not the benefit of the product but the cost of cooperation matters to the evolutionary dynamics and that the probability of finding a defector determines which sanction system promotes the evolution of cooperation or the coexistence of cooperator and defector groups.
Secondly, we consider that the process of the division of labour is not stopped by defectors; defectors neither improve the product or service nor pay a cost for it, and pass the product to a player in the immediate downstream sub-task holder group. Therefore, the quality of the final product or service depends on the number of cooperators chosen in the sub-task holder groups. If the number of cooperators in the division of labour increases, the bonus for all players increases. This is modeled by the replicator equations, showing that the benefit from cooperators is cancelled out, and then any network structure can be adopted to this model if the network has a single output. Sanction on the defectors induces the evolution of cooperation and co-existences of cooperator and defector groups. Whether or not the length of the division of labour influences the evolution of cooperation is determined by the bonus functions.
In sum, we find that the benefits from cooperation do not, but the costs of cooperation influence the evolution of cooperation. Sanction always promotes cooperation. When defection stops the division of labour, we find that the structure of the network influences the evolutionary dynamics particularly in the case of the finite tree network. However, the network structure does not influence the evolutionary dynamics when the defection does not stop the division of labour, under some bonus functions. The scope for stable co-existence of cooperators and defectors is more, when the division of labour does not stop with defection.