## 3 Evolutionary Game Model for Carbon Emission Reduction
### Managerial Insights
Namely, this ESS exists if one of the following three conditions remains: (1) For manufacturer, his/her profit under his/her unilateral emission-reduction is greater than that in the setting without emission reduction, while conversely the retailer's profit under his/her unilateral emission reduction is less; moreover, for the manufacturer, his/her total profit under emission-reduction cooperation between two parties is more than that in the setting where there exists the free-riding behavior, while conversely the retailer's profit under emission reduction cooperation is less ((i) \(c_{M}<u_{M}q_{2}\), \(u_{M}q_{1}>u_{M}q_{3}+c_{M}\) and \(u_{R}q_{3}<c_{R}\), \(u_{R}q_{1}<u_{R}q_{2}+c_{R}\)); (2) for either manufacturer or retailer, the profit under unilateral emission reduction is greater than that without emission reduction; moreover, for the manufacturer, her total profit under emission-reduction cooperation between two parties is more than that in the setting where there exists the free-riding behavior, while conversely the retailer's profit under emission reduction cooperation is less ((ii) \(c_{M}<u_{M}q_{2}\), \(u_{M}q_{1}>u_{M}q_{3}+c_{M}\) and \(c_{R}<u_{R}q_{3}<u_{R}q_{1}<u_{R}q_{2}+c_{R}\)); (3) Comparing with no emission reduction cooperation, the manufacturer's unilateral involvement definitely increases his/her profit, whereas the retailer's unilateral involvement definitely decreases his/her profit; moreover, for either manufacturer or retailer, the unilateral free-ridingbehavior will increase the firm's profit, comparing with emission-reduction cooperation between two parties ((iii) \(c_{M}<u_{M}q_{2}<u_{M}q_{1}<u_{M}q_{3}+c_{M}\) and \(u_{R}q_{3}<c_{R}\), \(u_{R}q_{1}<u_{R}q_{2}+c_{R}\)). The above Observation implies that manufacturers can gain bonus from emission reduction, that is, the higher the investment efficiency of emission reduction is, the more profit the emission reduction strategy can bring. We can attribute this phenomenon to two reasons: First, manufacturers' investment for low-carbon emission reduction in the earlier stage can substantially decrease the carbon footprint of products (since emission-reducing efficiency follows the principle of diminishing marginal utility). Second, there is steadily increasing demand that is ascribed to the growing of consumers' low-carbon awareness. However, it will be ineffective but cost inefficient to conduct low-carbon promotion when consumers' low-carbon awareness is high. Taking home appliance sales market as an example, manufacturers will strengthen technological innovation to launch products since consumers realize that products with low-energy consumption are more environment-friendly. **Observation 3** For manufacturers and retailers, the system evolutionary actions will converge to \(E_{3}(0,1)\) with evolutionary stable equilibrium \((M_{L},R_{H})\) in case that one of three conditions holds, (i) \(u_{M}q_{2}<c_{M}\), \(u_{M}q_{1}<u_{M}q_{3}+c_{M}\) and \(u_{R}q_{3}>c_{R}\), \(u_{R}q_{1}>u_{R}q_{2}+c_{R}\), or (ii) \(c_{M}<u_{M}q_{2}<u_{M}q_{1}<u_{M}q_{3}+c_{M}\) and \(u_{R}q_{3}>c_{R}\), \(u_{R}q_{1}>u_{R}q_{2}+c_{R}\), or (iii) \(u_{M}q_{2}<c_{M}\), \(u_{M}q_{1}<u_{M}q_{3}+c_{M}\) and \(c_{R}<u_{R}q_{3}<u_{R}q_{1}<u_{R}q_{2}+c_{R}\).