The evolution of cooperation is an unsolved research topic and has been investigated from the viewpoint of not only biology and other natural sciences but also social sciences. Much extant research has focused on the evolution of cooperation among peers. While, different players belonging to different organizations play different social roles, and players playing different social roles cooperate together to achieve their goals. We focus on the evolution of cooperation in linear division of labor that is defined as follows: a player in the i-th role interacts with a player in the i + 1-th role, and a player in the n-th role achieves their goal (1 ≤ i < n) if there are n roles in the division of labor. We take the industrial waste treatment process as an example for illustration. We consider three organizational roles and B is the i-th role. The player of B can choose two strategies: legal treatment or illegal dumping, which can be interpreted as cooperation or defection (i = 1-3). With legally required treatment, the player of B pays a cost to ask the player of B to treat the waste (j = 1, 2). Then, the cooperator of B pays a cost to treat the waste properly. With illegal dumping, the player of B dumps the waste and does not pay any cost (i = 1-3). However, the waste dumped by the defector has negative environmental consequences, which all players in all roles suffer from. This situation is equivalent to a social dilemma encountered in common-pool resource management contexts. The administrative organ in Japan introduces two sanction systems to address the illegal dumping problem: the actor responsibility system and the producer responsibility system. In the actor responsibility system, if players in any role who choose defection are monitored and discovered, they are penalized via a fine. However, it is difficult to monitor and detect the violators, and this system does not work well. While, in the producer responsibility system, the player in B is fined if the player cannot hand the manifest to the local administrative organ because the players of B (i = 1-3) who choose defection do not hand the manifest to the player of B. We analyze this situation using the replicator equation. We reveal that (1) the three-role model has more empirical credibility than the two-role model including B and B, and (2) the producer responsibility system promotes the evolution of cooperation more than the system without sanctioning. (3) the actor responsibility system does not promote the evolution of cooperation if monitoring and detecting defectors is unsuccessful.

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