Analyzing the Evolutionary Stability for Behavior Strategies in Reverse Supply Chain

In recent years, for the purpose of solving the problem regarding environment protection and resource saving, certain measures and policies have been promoted to establish a reverse supply chains (RSCs) with material flows from collection of used products to reuse the recycled parts in production of products. It is necessary to analyze behaviors of RSC members to determine the optimal operation. This paper discusses a RSC with a retailer and a manufacturer and verifies the behavior strategies of RSC members which may change over time in response to changes parameters related to the recycling promotion activity in RSC. A retailer takes two behaviors: cooperation/non-cooperation in recycling promotion activity. A manufacturer takes two behaviors: monitoring/non-monitoring of behaviors of the retailer. Evolutionary game theory combining the evolutionary theory of Darwin with game theory is adopted to clarify analytically evolutionary outcomes driven by a change in each behavior of RSC members over time. The evolutionary stable strategies (ESSs) for RSC members' behaviors are derived by using the replicator dynamics. The analysis numerically demonstrates how parameters of the recycling promotion activity: (i) sale promotion cost, (ii) monitoring cost, (iii) compensation and (iv) penalty cost affect the judgment of ESSs of behaviors of RSC members.