Figure 3 presents the giant component of the firm–firm co-bidding network. Using the Louvain algorithm (Blondel et al. 2008) we identified 22 communities with a modularity of 0.66. We refer to these communities as \(C_1\), \(C_2,\ldots ,C_{22}\), and they are indexed in descending order in respect to their size. For readability, we have colored the eight largest communities in Fig. 3. However, the high modularity of the network is unsurprisingly and can be explained by the fact that the network primarily represents competing firms that are specialized in supplying different services–works, goods, services, etc–in different regions. Hence, the most prominent communities divide the network into two major groups of firms that operate mainly in the northern (Red, Blue, and Green) and southern (Purple and Yellow) regions of the state of Ceará, but also on contracts that supply Food services (Blue and Purple) or construction works (Red and Yellow). Interestingly, the remaining communities operate at a state-wide level (Pink and light Blue), and there is one particular community (Violet) that operates exclusively in the mesoregion of Jaguaribe only supplies Food services.
In some cases, firms form densely connected sub-graphs (e.g., \(C_{14}\)). These structures can be a first indicator to flag groups of firms that present a high risk of collusion and procurement manipulation. As such, next, we explore possible additional metrics to classify each community of firms through their activity in order to further narrow which groups of firms might deserve a more profound investigation by audit officials.
Activities diversity
We started by looking at the regional diversity on which firms performed their activities (e.g., bid on tenders in order to supply services) and the diversity of the type of contracts for which they bid. While a firm with low diversity in both regional reach and contract-type can simply indicate a firm that is narrow in both scope and domain; the existence of groups of connected firms (i.e., a community of firms) that share a low diversity in both dimensions can highlight a more troublesome scenario. In particular, it can indicate the conditions for firms to coordinate and cooperate to control a specific market and regional context, and should be investigated with further discernment.
To that end, we estimate the Simpson’s diversity indexFootnote 1 for each community. The Simpson’s diversity index (\(\lambda\)) measures the probability that two randomly sampled elements from a set share a given characteristic in common. In that sense, \(\lambda = 0\) is associated with the highest diversity possible, and \(\lambda = 1\) with the lowest diversity. Formally we estimate the Simpson’s index for each community as
$$\begin{aligned} \lambda ^{C_i}_{\mathrm{cat}} = \sum _{t \in \gamma } (p_{C_i}^t)^2 \end{aligned}$$
(2)
where \(p_{C_i}^t\) corresponds to the fraction of bids done in a procurement contract type \(\gamma :\){Consumables Health, Services, Construction, Events, Food, Fuel,…} or mesoregion \(\gamma :\){Metropolinana, Norte, Sul, Noroeste,…} by the firms in community \(C_i\), \(\forall i \in \{1,2,\ldots ,21,22\}\). The quantity \(p_{C_i}^t\) is normalized per community, so that \(\sum _{t} p_{C_i}^t = 1.0\). We estimated \(\lambda ^{C_i}_{\mathrm{cat}}\) independently for each community (\(C_i\)), and for contracts according to the region that issue the tender and the tender contract type (e.g., services, food, tenancy, construction, etc). Our choice of the Simpson’s index over other alternatives (e.g., entropy) is due to its straightforward interpretation in our context: the probability that two bids made by firms within the same community share the same characteristic (e.g., region or contract type).
Figure 4a illustrates the empirical distributions (\(p_{C_i}^t\)) of procurement activity for the ten most prominent communities. We show the results for both the Regional distribution of activities and by Contract Type. Blue colors denote a low relative frequency of bids, while red identifies a high frequency. These indicators allowed us to infer the degree of specialization and agglomeration of a community. In particular, we found that Community 8 (\(C_8\)) activities are agglomerated in a single region (Jaguaribe) and firms specialize in one type of contract (Food). The same conclusion can also be inferred from the high levels of \(\lambda ^{C_8}_{\mathrm{cat}}\), which means that Community 8 has low diversity of activity distribution. Figure 4b compares all the 22 communities in terms of the two diversity indicators defined above. We find a clustering of communities in the bottom left quadrant—a low level of agglomeration and specialization—that we associate with healthy markets composed of firms that, on average, have a diversified portfolio of activities and regional distribution. In contrast, in the top right quadrant, we found communities that relied on procurement contracts of a single type and agglomerated in a small number of regions.
The combination of these two diversity indicators, at the community level, provides a powerful feature to identify groups of firms that can dominate over a niche market or, in the worst case, develop undesirable leverage, as a group, in negotiating procurement contracts. Hence, lowering the desirable efficiency that public procurement aims at achieving in the tendering process. However, it is important to stress that these metrics are just indicative of potential problems, and thus the true nature of the activities of the firms in each community should be carefully investigated by the corresponding local authorities.
Bidding coordination
To further investigate the risk/susceptibility of market manipulation by firms, we next looked at the propensity that each community has in participating in “single bidder” contracts. Another pattern often associated with corruption and loss of efficiency. Hence, what is the susceptibility of each community to such practice? To answer this question, we started by investigating the average number of times, per community, that a firm is the single bidder of a tender. Figure 5a shows the results for all 22 communities in the most significant component of the Firm–Firm network. Traditionally, a high level of single bids can be an indicator of firms acting with some level of informal advantage in the tendering process or due to lack of competition in a specific market. At the community level, such an indicator can be indicative of unusual activity from a group of firms. Hence, low levels of single bidding indicate the risk of coordination (e.g., firms participating coherently in the same contracts) while high levels can sign the prevalence of less competitive markets or informal advantage in the tendering process. Overall, of the largest ten communities, only Community 8 exhibits low levels of single bidders, a pattern that extends to Communities 14 and 21 as well. In contrast, we saw that community 12 strongly deviates from the baseline with an average value of single bidding that is roughly four times that of a typical firm.
In addition, we looked at the average number of bidders per tender in order to assess the potential existence of coherent behavior, that is, coordination between the firms in a community. To that end, we estimated the average number of bidders per tender for each community, which we normalized by the size of the community (i.e., the number of firms in a community). Interestingly, Fig. 5b shows that in Community 8, firms tend to participate in tenders with several firms that match almost exactly the community’s size. While, in some cases—Communities 14 and 19—firms tend to bid to tenders that are several times larger than their communities. Noteworthy to mention that this analysis is biased by the size of the communities, so the expectation would be to see a smoothly increasing relationship, with the largest community achieving the smallest value, and in the limiting case of a community with a single firm we would obtain the maximum. However, it is clear that in some cases—Communities 8, 14, and 19—there are apparent deviations.