Effect name (Additional description) | Mathematical formula | Graphical representation | |
---|---|---|---|

1. Network dynamics
| |||

1.1. Endogenous trade network interdependencies
Network → network | |||

Reciprocity (Favor firms that buy something from our firm) | \( {\displaystyle \sum_j{x}_{ij}{x}_{j i}} \) | ||

Preference for firms with partners in common (i.e., firms within the same trading group) |
Transitive triplets (Hierarchical cliques) | \( {\displaystyle \sum_{j, h}{x}_{ij}{x}_{j h}{x}_{hi}} \) | |

Three-cycles (Non-hierarchical cliques) | \( {\displaystyle \sum_{j, h}{x}_{j i}{x}_{ih}{x}_{j h}} \) | ||

Common suppliers (Connect with firms that use the same suppliers) | \( {\displaystyle \sum_j{x}_{ij}}{\displaystyle \sum_{\begin{array}{c}\hfill h\hfill \\ {}\hfill h\ne i, j\hfill \end{array}}\left({b}_0 x-\left|{x}_{ih}-{x}_{j h}\right|\right)} \) | ||

Number of second-tier suppliers (Connect with multiple primary suppliers through intermediaries) |
# [j|x
_{
ij
} = 0, max(x
_{
ih
}
x
_{
hj
}) > 0]
| ||

Indegree popularity (Seek the most popular suppliers) | \( {\displaystyle \sum_j{x}_{ij}}{\displaystyle {\sum}_h{x}_{h j}} \) | ||

Outdegree (Control for network density) | \( {\displaystyle \sum_j{x}_{ij}} \) | ||

1.2. Effects of firms’ performance z on supply network structures
Performance → network | |||

Client’s performance (High-performing firms connect with more suppliers) | \( {\displaystyle \sum_j{x}_{i j}{z}_i} \) | ||

Supplier’s performance (Selecting high-performing firms as suppliers) | \( {\displaystyle \sum_j{x}_{ij}{z}_j} \) | ||

Similarity of performance (Preference for firms with similar performance) | \( {\displaystyle \sum_j{x}_{ij}\left( si{m}_{ij}^z-\overline{si{m}^z}\right)} \) | ||

2. Performance dynamics
| |||

Linear performance trend (Baseline revenue trend) |
z
_{
i
}
| ||

Performance → revenues | |||

Quadratic performance trend (The effect of current performance on the future performance trend) | \( {z}_i^2 \) | ||

Network → performance | |||

(A) Topology: The effect of the number of suppliers on the future performance trend | \( {z}_i{\displaystyle \sum_j{x}_{i j}} \) | ||

B Flow: The effect of the suppliers’ performance on the performance trend | \( {\displaystyle \sum_j{x}_{ij}\left( si{m}_{ij}^z - \overline{si{m}^z}\ \right)} \) |