Table 2 Symbols and descriptions.

\({p}_{i}^{j}\)

The price of the manufacturer i's product, \({p}_{i}^{j}\,>\,0\).

\({q}_{i}^{j}\)

The output of the manufacturer i's product, \({q}_{i}^{j}\,>\,0\).

\({\theta }_{i}^{j}\)

The degree of the manufacturer i's DX, \(0\,\le\, {\theta }_{i}^{j}\,\le\, 1\).

\({\pi }_{i}^{j}\)

The profits of the manufacturer i, \({\pi}_{i}^{j}\,\ge\, 0\).

Q

Potential market demand, \(Q\,>\,0\).

c

The unit cost of the product, \(c\,>\,0\).

α

Production cost saving coefficient, \(0\,<\,\alpha \,<\, c\).

φ

Demand increment coefficient, \(\varphi \,>\, 0\).

λ

Technology spillover coefficient, \(0\,\le\, \lambda \,<\, \varphi\).

C_i

Investment cost of the manufacturer i's DX, \({c}_{i}\,\ge\, 0\).

m

Cost coefficient of manufacturer’s DX, \(m \,>\, 0\).

e

Unit carbon emissions, \(e \,>\, 0\).

β

Carbon emission saving coefficient, \(0\, <\, \beta\, <\, e\).

p_e

CTP of per unit carbon emissions, \({p}_{e} \,>\, 0\).

R_i

Carbon quota allocated by the government to manufacturer i, \({R}_{i}\,\ge\, 0\).