Effect name (Additional description) | Mathematical formula | Graphical representation | |
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1. Network dynamics | |||
1.1. Endogenous trade network interdependencies Network → network | |||
Reciprocity (Favor firms that buy something from our firm) | \( {\displaystyle \sum_j{x}_{ij}{x}_{j i}} \) |
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Preference for firms with partners in common (i.e., firms within the same trading group) | Transitive triplets (Hierarchical cliques) | \( {\displaystyle \sum_{j, h}{x}_{ij}{x}_{j h}{x}_{hi}} \) |
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Three-cycles (Non-hierarchical cliques) | \( {\displaystyle \sum_{j, h}{x}_{j i}{x}_{ih}{x}_{j h}} \) |
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Common suppliers (Connect with firms that use the same suppliers) | \( {\displaystyle \sum_j{x}_{ij}}{\displaystyle \sum_{\begin{array}{c}\hfill h\hfill \\ {}\hfill h\ne i, j\hfill \end{array}}\left({b}_0 x-\left|{x}_{ih}-{x}_{j h}\right|\right)} \) |
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Number of second-tier suppliers (Connect with multiple primary suppliers through intermediaries) | # [j|x ij = 0, max(x ih x hj ) > 0] |
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Indegree popularity (Seek the most popular suppliers) | \( {\displaystyle \sum_j{x}_{ij}}{\displaystyle {\sum}_h{x}_{h j}} \) |
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Outdegree (Control for network density) | \( {\displaystyle \sum_j{x}_{ij}} \) |
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1.2. Effects of firms’ performance z on supply network structures Performance → network | |||
Client’s performance (High-performing firms connect with more suppliers) | \( {\displaystyle \sum_j{x}_{i j}{z}_i} \) |
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Supplier’s performance (Selecting high-performing firms as suppliers) | \( {\displaystyle \sum_j{x}_{ij}{z}_j} \) |
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Similarity of performance (Preference for firms with similar performance) | \( {\displaystyle \sum_j{x}_{ij}\left( si{m}_{ij}^z-\overline{si{m}^z}\right)} \) |
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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 | \( {z}_i{\displaystyle \sum_j{x}_{i j}} \) |
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B Flow: The effect of the suppliers’ performance on the performance trend | \( {\displaystyle \sum_j{x}_{ij}\left( si{m}_{ij}^z - \overline{si{m}^z}\ \right)} \) |
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