Using evolutionary game theory to study governments and logistics companies’ strategies for avoiding broken cold chains

Abstract

Cold chain brokenness is a source of safety problems related to cool cargos. The cold chain logistics companies (CCLCs) can share their logistics information with governments to provide cold chain transparency, traceability, and brokenness proofs. The governments administrate the information sharing of the companies to prevent social loss and recovery costs when disastrous events happen. In this research, we apply the evolutionary game theory to examine the mutual interactions between the CCLCs (whose behavioral space consists of two strategies, information sharing and not) and the governments (whose behavioral space consists of two strategies, administration and not). First, we formulate the interactions as an evolutionary game model considering the governments and CCLCs as two interacted populations, whose dynamics are impacted by some parameters (including administration cost, penalty, subsidy, revenues, and logistics costs). Second, we devise eight propositions to examine the parameter impacts, the equilibrium points, and the evolutionary stable strategies (ESSs). Third, eight propositions, the effects of critical parameters on the ESSs, their dynamics and sensitivities are then simulated and investigated numerically. As results in theoretical and numerical analysis, high administration cost is harmful to advocate long-term information sharing strategy; subsidization is useful to encourage the companies for adopting information sharing strategy but is absent for long-term impacts; penalty cost is critical to administrate the CCLCs; high revenue of the CCLCs without information sharing strategy will challenge the governments’ administration mechanism. We finally discuss the contributions of information sharing to avoiding cold chain brokenness, as well as the future research directions considering the three pillars of sustainability for cold chains.

Appendix: Proofs of Proposition 3 and 8

Proof of Proposition 3

If and only if $\det J > 0$ and ${\text{tr J}} < 0$, the EPs of the evolutionary theory model (9) are ESSs. According to the local stability analysis method of the Jacobian matrix, we analyze the local stability of five equilibrium points obtained from Proposition 1 under different constraints. Table 12 presents the analysis results. □

Table 12 Local stability analysis of the evolutionary game between governments and CCLCs

Proof of Proposition 8

The analysis processes are given in Table 11 when $A_{g} > P_{ns}$. We conduct local stability analysis by adjusting the parameters’ ranges. At the EP (0,0), we can derive four ESSs, as shown in Table 13. When the governments give up the penalty cost that is the most crucial instrument to administrate the CCLCs, the CCLCs will give up the information sharing strategy gradually because they cannot observe administration strengths from the governments.

Table 13 Local stability with no penalty in administration

Further, because the governments lose this vital administration instrument, they will adopt (NA) and let the CCLCs out of control. In summary, the penalty is an essential means of administration. Table 13 summarizes the analysis results. □