Evolutionary game analysis on collaborative logistics diffusion considering diminishing marginal utility under dynamic productivity

Reducing carbon emissions in the transportation sector is crucial for sustainable practices, with collaborative logistics diffusion playing a significant role in promoting energy-saving and emission-reduction strategies. This paper introduces an evolutionary game model to analyze collaboration between manufacturers and logistics service providers (LSPs), using the Hotelling quadratic curve model to measure the diminishing marginal utility of basic profits. Initially, a static strategy leads to a cyclic evolution without reaching the evolutionary stable strategy (ESS), reflecting competitive dynamics under static productivity conditions where neither party gains a lasting advantage, leading to periodic adjustments in strategies. The Cobb-Douglas function models a dynamic productivity strategy that regulates the extra benefits of collaborative logistics and penalties for 'free-riding.' This strategy demonstrates an inward spiral convergence towards the ESS, showing that adaptive mechanisms enable manufacturers and LSPs to align interests and achieve equilibrium. Enhanced benefits from collaborative logistics promote a stable and cooperative ecosystem, discouraging free-riding and enhancing cost efficiency. Moreover, increased investment by manufacturers not only strengthens their position but also fosters an environment conducive for LSP participation, expediting collaborative logistics diffusion and minimizing potential losses.