[C17] Evolution and Genetics & Interdisciplinary Studies

[C17-03] The evolution of cooperation in the generalized supply chain on a network with a single output

*MD Sams Afif Nirjhor^1,2,3, Fangyue Liu³, Mayuko Nakamaru^2,3 (1. Meiji University (Japan), 2. Institute of Science Tokyo (Japan), 3. Tokyo Institute of Technology (Japan))

Keywords:

Evolution of Cooperation,Supply chain on networks,Asymmetric interaction,Replicator equation,Sanction

Division of labor is an existential part of human society, and cooperation makes it sustainable. This study considers a finite supply chain as an example of division of labor, where a finite number of groups initially composed of cooperators and defectors are in an arbitrary network leading into a single output, and the divided subtasks of the supply chain are allocated to the groups. Cooperation is needed to sustain supply chain; defectors deteriorate the final product or service provided by supply chain. The players from different groups with different economic or social roles asymmetrically interact with each other and imitate the strategy of a player with a higher payoff in the same group. If cooperators can take over with time, we call it the evolution of cooperation. Similar previous studies by Nirjhor and Nakamaru (2023a and 2023b) considered that the task immediately stops, once a defector is chosen in any chain. However, in some supply chains, one or several defections often do not stop the chain, as faulty products are possible. This study investigates the evolution of cooperation in the supply chain, where continuation is possible even after defection/defections. A player from each group is randomly selected who buys product/products with a cost from some group/groups and gains profit by selling it to some other group/groups. In addition, each of the chosen players may develop or modify the product with a cost of cooperation. If the selected player from a group is a cooperator, s/he pays the cost of cooperation; if s/he is a defector s/he does not pay it. After every round of supply, a bonus is given to everyone based on the total number of cooperations, making this bonus a function of the total number of cooperators in each round. It is found that bonus functions need to be strictly increasing functions to satisfy social dilemma. We introduce a sanction system, where the exact defector is found and punished. We model the system with replicator equations of asymmetric games. Our findings are as follows; (i) Network structures do not matter. (ii) The evolution of cooperation does not depend on the profit in any network with a single output. (iii) Sanction promotes cooperation and the coexistence of the cooperator and defector groups. (iv) For a linear bonus function, there is no bistability of equilibria, no effect of the number of groups on the evolution of cooperation. If the cost of cooperation is the same for all groups, coexistence of cooperators and defectors cannot be locally stable. However, when different groups have different costs of cooperation, coexistence is locally stable.