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# Markets design and social interactions: how trust and reputation influence market outcome

Annick Vignes, Sylvain Mignot

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## To cite this version:

Annick Vignes, Sylvain Mignot. Markets design and social interactions: how trust and reputation influence market outcome. Ninth International Conference on Complex Networks and Their Applications, Dec 2020, Madrid, Spain. 944, Springer, pp.310-321, 2021, 978-3-030-65350-7. http-05283899

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# Markets design and social interactions: how trust and reputation influence market outcome

Sylvain Mignot · Annick Vignes

the date of receipt and acceptance should be inserted later

**Abstract** This article examines the role of trust in a market for perishable goods without quality signals and under scarcity, where agents trade either through auctions or bilateral exchanges. Using data from the Boulogne-sur-Mer fish market, we propose a measure of trust based on the dynamics of repeated encounters and analyze its impact on network structures and market outcomes. We show that while auction transactions mainly reflect economic constraints, bilateral exchanges also rely on non-economic factors. The coexistence of both mechanisms, far from being paradoxical, reveals complementary logics of coordination and contributes to the debate on market efficiency.

**Keywords** market design, trust, social networks.

**JEL classification** L10, L11, L14, L15, L20, D47, D85

## Introduction

A fundamental assumption in economics is that rational individuals act in their own self interest. One implication is that, when trading, buyers are supposed to seek for the lowest price and sellers for the highest one and social interactions are not considered. In line with that, the literature has accepted for a long time the idea that centralized markets, with common information and no friction, are more efficient. Nevertheless, some recent results weaken this idea of centralized market dominance. Moreno & Wooders (2010) show that decentralized organization allows both high and low quality units trade. Moreover, when frictions are small, the surplus realized is greater than the competitive surplus. Moreno & Wooders (2016) studies non stationary dynamic decentralized markets with adverse selection. They show that when the

<footnote>Sylvain Mignot
Lille Catholic University, 60 Boulevard Vauban, 59800 Lille, France
E-mail: sylvain.mignot@univ-catholille.fr
Tel.: +33359567915</footnote>

<footnote>Annick Vignes
INRAE, LISIS and CAMS-EHESS, UMR 8557, 54 boulevard Raspail, 75006, Paris, France
E-mail: annick.vignes@inrae.fr
Tel.: +33149542032</footnote>
horizon is finite, the surplus in the equilibrium exceeds the competitive surplus. It is now largely accepted that social relationships affect the efficiency of a market structure.

This article pays a particular attention to the influence of social connections on the process of transac-
tions, whether a market is centralized or decentralized. We carry out an empirical analysis of a particular
fish market (the Boulogne s/mer fish market). This wholesale market is organized through two sub-
markets, one centralized (auctions), the other decentralized (pairwise transactions) and traders decide
each day which sub-market they will go on. We exploit this remarkable organization to analyze the influ-
ence of loyalty between traders on the market outcome and the impact of market structures on trading
relationships. In what follows, we postulate that trust is an output of loyalty that emerges from repeated
trading links. We then measure the intensity of trust between traders and its influence, comparing the
effects on centralized and decentralized markets.

The emergence and identification of the exact role of trust in economic interactions stay elusive. Does trust come from good institutions or does it help to reinforce the existing institutions? It appears that influence of trust depends on the market organization that traders operate in. When the institutions are weak, at a local or more global level, trust largely contributes to ameliorate the efficiency (Elsner & Schwardt 2014, James 2015, Aghion et al. 2010).

If it is easy to understand how trust can influence pairwise exchanges, the way it may affect a central-
ized market remains unclear. The literature is quite sparse on this subject. In a context where investors
have knowledge about trustees before transactions occur and where trustees compete with each other
for access to investors, natural selection can favor both trust and trustworthiness, even when individuals
interact through an anonymous prices mechanism. (Manapat et al. (2012)).

In the present article, we postulate that bilateral trust between individuals comes from repeated social relationships. In the line of Hernández et al. (2018), we define the level of trust between two persons by the number of encounters (number of days two persons traded together), relative to the number of encounters the same persons have with other traders: the more two persons exchange together, the higher the level of trust. We then assume that these bilateral social relationships affect the way people exchange together. This assumption implies that we consider a market where multiple couples of traders interact, as a social network.

The idea that social networks influence the markets functioning is not new. On markets with a high
level of uncertainty on the goods exchanged, linking is essential for trading (Kirman & Vignes 1990,
Kranton & Minehart 2000, 2001). The place occupied by an agent in the network (in terms of centrality
for example) greatly influences its surplus (Corominas-Bosch 2004, Vignes & Etienne 2011, Fafchamps
et al. 2013).

Following this train of though, we build a specific social network, based on trust relationships. We first associate a trust index to each couple of agents (a buyer and a seller). We then consider that two traders trust each other when their trust index is high (belonging to the top 10% of the trust index distribution). From these sub-set of trust index, we create a network of trust relations. This procedure is done for both sub-markets. We postulate that the influence of the trust network should be more important on the decentralized market, where search costs can be substantial, especially when there exists no quality signals, as on the fish market. On an auction market where information is full, there are no costs of searching
and no clear possibility of linking or reciprocity between buyers and sellers (at least on the sellers side).
Trust should be more difficult to build.

A main objective of this article is to measure the existence and influence of trust on a market. Our fundamental hypothesis is that trust between agents influence the price of their transactions and that this influence differs from one market organization to the other. How much trust influences the market outcomes? How much the consequences of trust differ from a market to the other? A first novelty here consists in the analysis of an original database, which allows to compare two different market organizations. We then measure trust from observed relationships instead of surveys. A first result is that trust strongly influences the negotiated market, where the information is not centralized and where there exists no signal of information concerning the quality of the goods. Unsurprisingly, we find that trust has a low influence on the auctions outcome. A second originality consists in comparing two "trust networks", one on the auction sub-market, the other on the bilateral sub-market. The bi-partite network analysis reveals that being central (having a lot of trust relations) for a seller insures higher profit when being central for a buyer (having a lot of preferred sellers) implies paying lower prices, this effect being stronger on the decentralized sub-market. A third important result is that a strong correlation exists between trust index and centrality on the auction sub-market, that doesn't exist on the bilateral one. This result can be easily explained: on auctions, where the influence of trust is lower, central traders exchange regularly between themselves (because they are more present or sells bigger quantities), while on the pairwise market there is no relation between the probability for two traders to trust each other and their centralities on the network. Big traders can be linked together but also traders of different importance and this reveals something else than a pure economic pairwise relation.

This article is organized as follows: Section 1 outlines the main characteristics of the market and describes the database. Section 2 presents the building of the links. The measure of trust is disclosed in Section 3, Section 4 presents the calcul of trust signals and Section 5 concerns the network analysis. The conclusion follows.

# 1 The main market features and the data

We present here some particular features of the Boulogne s/mer fish market, through the analysis of a detailed database, consisting of 300 000 daily transactions on the period 2006-2007.

**The market:** The Boulogne s/mer fish market is located in the North of France near Belgium. It is considered as the most important wholesale fish market in France and one of the most important in Europe, in terms of quantity. On this market, the catch becomes scarce: this is due to the rarefaction of fish and a policy of quotas decided by the Common Fisheries Policy of the European Union, to protect the resource.

This market is a daily one, open 6 days a week. Transactions begin early in the morning. Agents are heterogeneous on both sides of the market. They are or sellers or buyers. There is no possibility of arbitrage. Sellers are boats owners and their boats are of different capacities. Small boats do not go very far and intervene regularly on the market. Bigger boats, going away for longer periods are present less regularly and sell bigger quantities of fish. Buyers are restaurant owners, retail buyers and fish processors. Buyers form then an heterogeneous population, facing different budget and time constraints. They can
freely buy on both sub-markets. Most of the restaurant owners or retail buyers are present regularly when fish processors come less often. Each day, sellers have the possibility to choose how to sell their fish (auctions or pairwise exchanges). Once the sub-market chosen, they cannot change their strategy until the next day for practical reasons (costs of bringing the merchandise from one part of the market to the other are very high). Mignot et al. (2012) show the existence of two behaviors: some agents purchase most of the time on the same sub-market, when others switch regularly. Loyal sellers, the ones who change rarely, are mainly present on the bilateral market.

## 2 Intensity of social links

Let's estimate now the intensity of social links for the different agents. Equation 1 represents, for an agent $i$, the ratio $\alpha_i$ of the number of transactions carried out by a trader divided by the number of agents he traded with on the whole period. This ratio should give a first estimation of the intensity of links for each agent. A high value should indicate an agent involved in loyal relationships.

$$ \alpha_i = \frac{\text{number of transactions}}{\text{number of traders}} \qquad (1) $$

The aggregate descriptive statistics are summarized in Tab.1.

<table><caption>Table 1: Mean and Median for buyers and sellers ratio distributions on both markets.</caption><thead><tr><th>α<sub>i</sub> buyers side</th><th>Auction</th><th>Negotiated</th></tr></thead><tbody><tr><td>Mean</td><td>13.51</td><td>19.63</td></tr><tr><td>Median</td><td>6.31</td><td>12.17</td></tr></tbody><thead><tr><th>α<sub>i</sub> sellers side</th><th>Auction</th><th>Negotiated</th></tr></thead><tbody><tr><td>Mean</td><td>16.77</td><td>23.15</td></tr><tr><td>Median</td><td>4.77</td><td>19.61</td></tr></tbody></table>

The mean and the median of $\alpha_i$ are higher on the bilateral market than on the auction one (for both buyers and sellers). For a given number of transactions, a buyer (respect. seller) trades with less sellers (respect. buyers) on the bilateral market than on the auction one. We observe a large difference between the mean and the median on the auction market and this can be due to a large number of people, coming rarely and buying at random. When looking at the data, we observe a high number of buyers coming rarely on auction market, while on the decentralized market, traders are present more regularly.

These first results suggest that the bilateral market is more risky, and that on this sub-market traders seem to choose their partners more carefully. Empirical evidence suggests the existence of loyal behavior on the decentralized market, which could help to mitigate the risk.
## 3 A measure of trust

Let's do now the hypothesis that auctions do not facilitate loyal strategies, while on the bilateral market people can choose with whom they exchange. Once on the decentralized market, people can either exchange with someone they trust or exchange at random. Because people are not present every day, it can happen that a very loyal agent has no other choice than exchanging with a non-usual suspect.

Consider now a bilateral market, where there is no arbitrage, composed by N buyers $i$, and M sellers $j$, who buy and sell regularly during $\tau$ periods, $\tau=1...T$. At each period $\tau$, a buyer (seller) can be present or not. When present, he can exchange with one or more sellers (buyers). In each matching, players trade with a partner they trust or with somebody else.

## 4 Looking for a signal of trust

Let's now measure trust by the intensity of the matching. Do buyers and sellers match at random, following the opportunity of common presence or do they strategically choose their partners ? We first look at the correlation between $M_{i,j}$ the number of days a couple (buyer $i$ and seller $j$) is present on each sub-market, and $B_{i,j}$ the number of encounters. From Figure ??, we compute $M_{i,j} = \sum_{\tau=1}^{T} P_{i,j,\tau}$ and $B_{i,j} = \sum_{\tau=1}^{T} L_{i,j,\tau}$. Figure 1a and Figure 1b represent the relation between $M_{i,j}$ "being present at the same time" and $B_{i,j}$ "trading together" for each market.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Comparison of $B_{i,j}$ and $M_{i,j}$ across markets.</figcaption></figure>

Looking at the correlation between $B_{i,j}$ and $M_{i,j}$ (cf. Figure 1a and 1b), we observe a stronger correlation between these two values when exchanges are centralized. The value is higher on the auction market than on the bilateral one (0.77 vs 0.58). Looking at the scatter-plot between these two variables (Figure 1a and Figure 1b), we observe that two agents present at the same time on the auction market are more likely to exchange together than on the bilateral market. The linear regression of $B_{i,j}$ on $M_{i,j}$ (Table 2) shows that the $R^2$ of the linear fit is at 0.60 for the auction versus 0.35 for the decentralized market.

On the auction market, the only fact of being both present can explain most of the exchanges. When it comes to pairwise exchanges, the only fact of being present at the same time do not imply common trades. We conclude that pairwise trading depends on something more than random meeting. Our hypothesis is
<table><caption>Table 2: *Strength of the relation between B<sub>i,j</sub> and M<sub>i,j</sub> on the negotiated and the auction market.*</caption><thead><tr><th></th><th>auction</th><th>negotiated</th></tr></thead><tbody><tr><td>R<sup>2</sup></td><td>0.60</td><td>0.35</td></tr><tr><td>Coef</td><td>0.32</td><td>0.16</td></tr><tr><td>std dev</td><td>0.002</td><td>0.002</td></tr><tr><td>Pr &gt; t</td><td>&lt;0.0001</td><td>&lt;0.0001</td></tr><tr><td>Correlation</td><td>0.77</td><td>0.58</td></tr></tbody></table>

that exchanges on the bilateral market are conditioned to loyal relationships and trust behaviors.

Let's now the assumption that the more people exchange together, the more they trust each other. It allows to define a trust index $R_{i,j}$ (Eq. 2) for each possible couple $i, j$ by a ratio of the total number of common encounters on the sum of the total encounters for $i$ and the total encounters for $j$.

$$R_{i,j} = \frac{2 * B_{i,j}}{S_i + S_j} \qquad (2)$$

With $S_i = \sum_j B_{i,j}$ and $S_j = \sum_i B_{i,j}$

Calculating a trust index (values between 0 and 1) allows to measure the difference in agents' behaviors on both sub-markets. We seek to verify if agents are more strategic on the negotiated market. Furthermore, looking at the distributions of trust index allows to pinpoint differences in trust level between the two market organizations. An index equal to 1 corresponds to the situation where two agents trade exclusively together. An index equal to 0.5 corresponds to a couple for which, for each partner, the mutual transactions represent half of their total number of transactions. A couple of agents who never trade together will have a null trust index. We then consider that the higher the value, the more they trust each other.

Figure 2 displays the distribution of trust index (equation 2) on the negotiated and on the auction market. For sake of clarity, the graph only displays the strictly positive values of $R_{i,j}$.

To estimate the difference between the two distributions (auctions market and pairwise exchanges), we compute in Table (3) the observed value of $R_{i,j}$ of transacting couples for the two sub-markets. We also compute the values for all the possible pairs, including the ones that never transacted together, corresponding to null values. Observe that the main differences between the two $R_{i,j}$ distributions come from the shape of the distributions, with higher kurtosis and skewness on the pairwise market, which suggests highly heterogeneous linking behaviors on this sub-market.
<figure><img src="image_4.png" /><figcaption>Fig. 2: Distribution of trust index on the bilateral (left) and the auction (right) sub-markets (for active pairs)</figcaption></figure>

<table><caption>Table 3: *Trust index distributions on the bilateral and the auction market: for active pairs (strictly positive values) on the left side and all the possible pairs (total distribution) on the right side.*</caption><thead><tr><th rowspan="2">market</th><th colspan="2">Distribution of positive values<br>R<sub>i,j</sub> > 0</th><th colspan="2">Total distribution<br>R<sub>i,j</sub> ≥ 0</th></tr><tr><th>auction</th><th>negotiated</th><th>auction</th><th>negotiated</th></tr></thead><tbody><tr><td>Mean</td><td>0.0082</td><td>0.0076</td><td>0.003</td><td>0.004</td></tr><tr><td>Median</td><td>0.0049</td><td>0.0052</td><td>0</td><td>0.001</td></tr><tr><td>Q1</td><td>0.0021</td><td>0.0022</td><td>0</td><td>0</td></tr><tr><td>Q3</td><td>0.0115</td><td>0.0104</td><td>0.0034</td><td>0.0056</td></tr><tr><td>D9</td><td>0.0217</td><td>0.0168</td><td>0.0115</td><td>0.0123</td></tr><tr><td>Max</td><td>0.069</td><td>0.12</td><td>0.069</td><td>0.12</td></tr><tr><td>Std Dev</td><td>0.0082</td><td>0.0081</td><td>0.0066</td><td>0.007</td></tr><tr><td>Kurtosis</td><td>1.99</td><td>23.34</td><td>7.60</td><td>28.95</td></tr><tr><td>Skewness</td><td>1.49</td><td>3.45</td><td>2.66</td><td>3.89</td></tr><tr><td>Number of pairs</td><td>7843</td><td>10126</td><td>19500</td><td>19251</td></tr></tbody></table>

The two distributions are strongly different. The percentage of active pairs of traders (compare to the all possible pairs) is higher on the bilateral market (52%) than on the auction market (40%). The graph of exchanges is more dense on the bilateral market than on the centralized one.

## 4.1 Influence of the trust index on prices

Do personal links affect the trading outcome? The following GLM model (see equation 3), seeks to evaluate the influence of the trust index on the formation of transaction prices. Because of the heterogeneity of the variables, different dummies are included in the model <fnref n="1" />. The explained variable is the log of the price of each transaction. Dummies allow to take into account the weekday ("weekday" variable), the month

<footnote n="1">¹ Regression of quantity on price per kilo being the regression of a choice variable on another choice variable, there exist risks of lack of identification or simultaneity bias. We choose not to include transactions quantities as explanatory variables in this paper. Including them doesn't change significantly any of our results.</footnote>
("month") and the year ("year") effects, as well as the species ("Specie" variable) effect. The results are given in Table 4.

$$P_{i,j,\tau,t} = \beta_1 + \beta_2 \cdot R_{i,j} + \beta_3 \cdot \text{Weekday}_\tau + \beta_4 \cdot \text{year}_k + \beta_5 \cdot \text{month}_k + \beta_6 \cdot \text{Specie}_k + v_{i,j,\tau,t} \quad (3)$$

<table><caption>Table 4: Log-level estimation results (Eq. 3) for both sub-markets.</caption><thead><tr><th rowspan="2">Price</th><th colspan="3">Auction</th><th colspan="3">Pairwise</th></tr><tr><th>Coef</th><th>Std Dev</th><th>Pr > t</th><th>Coef</th><th>Std Dev</th><th>Pr > t</th></tr></thead><tbody><tr><td>Intercept</td><td>-0.07</td><td>0.12</td><td>0.56</td><td>0.73</td><td>0.08</td><td>&lt;.0001</td></tr><tr><td>R<sub>i,j</sub></td><td>0.62</td><td>0.13</td><td>&lt;0.0001</td><td>2.99</td><td>0.06</td><td>&lt;.0001</td></tr><tr><td>R squared</td><td colspan="3">0.73</td><td colspan="3">0.78</td></tr><tr><td>nb observations</td><td colspan="3">201047</td><td colspan="3">279219</td></tr></tbody></table>

Clearly, for a given weekday, month, year and specie, the trust index positively influences the price of transactions, and this influence is higher on the bilateral market than on the auctions. If the trust index between two persons would increase of 0.1 (the two persons reinforce their mutual trades), the price of their transactions would increase of nearly 30 percent through pairwise transactions. The increase through auctions should be lower even if significant. We obtain here two important results, which are that trust influences more the prices when transactions are bilateral and that this influence is positive. When a buyer trusts a seller, he/she agrees to pay a higher price. On a market with no quality signals and scarce resource, the risk (of getting no fish or getting fish of poor quality) is on the buyer side. Agreeing to pay a higher price to some particular sellers can be viewed as an insurance.

The fact that trust has a higher influence when the price results from bilateral negotiation, implies that the influence of trust on the negotiated market can't be fully explained by a simple reputation effect, as same traders exchange on both sub markets.

Considering this result, we suppose now that the structure of the exchanges network must exhibit significant differences on both sub-markets, differences we highlight in the following section.

## 5 Bipartite trust network

Our definition of a link is based on the trust index (equation 2) as defined in Section 3. We then consider the entire distribution of trust index, including the null value (associated to couples with no trades). We have already explained that there is a possibility of random matching on this market. We assume now that trust indexes belonging to the D9 ninth decile of the total distribution of trust (as displayed in Table 3) have a higher probability to result from strategical behaviors. In other words, we analyze the graph of the 10% strongest bilateral relations on each sub-market.
$$ Link_{i,j} = \begin{cases} 1 & \text{if } R_{j,i} \ge D9 \\ 0 & \text{else} \end{cases} \qquad (4) $$

The descriptive statistics (see Table 5) display more information.

<table><caption>Table 5: Networks statistics.</caption><thead><tr><th></th><th>Auction</th><th>Bilateral</th></tr></thead><tbody><tr><td>Nodes</td><td>295</td><td>300</td></tr><tr><td>buyers</td><td>100</td><td>93</td></tr><tr><td>sellers</td><td>195</td><td>207</td></tr><tr><td>Links</td><td>1950</td><td>1925</td></tr><tr><td>Density</td><td>0.1</td><td>0.1</td></tr><tr><td>Clustering(reinforcement)</td><td>0.71</td><td>0.39</td></tr></tbody></table>

The density of a network corresponds to the ratio between the number of existing links and the number of total possible links. The density value is between 0 and 1. A density close to 1 reflects a dense network with an important number of links while a density close to 0 corresponds to sparse links. Both sub-markets have a similar density equal to 0.1 because of the choice of the thresholds.

The clustering coefficient we use here, as defined in Robins & Alexander (2004) is an indicator of inter-sellers and inter-buyers closeness. It measures the reinforcement between two individuals rather than the clustering of a group of individuals.

In other words, consider that two sellers $S_i$ and $S_j$ trust the same buyer $B_k$. The probability for $S_j$ to trust a buyer $B_l$, $l \neq k$, is higher if $S_i$ trusts $B_l$. We observe from Table 5 that this coefficient is higher on the auction market (71%) compared to the bilateral market (39%). This suggests a higher specialization on the auction market (specific groups of buyers trust or regularly exchange with specific groups of sellers). This could be due to the diversity of the fish sold. Some sellers are specialized in particular varieties of fish and we can imagine that groups of buyers, with similar characteristics (restaurant owners or wholesalers) share the same preferences or the same constraints.

When it comes to the bilateral market this phenomenon is really weaker (the clustering coefficient is much lower), each buyer trusts a specific group of sellers. Loyalty links seem based on something else than economic specialization.

## 5.1 The advantage of being central

Let's attribute now a vector or trust indexes and a coefficient of centrality to each agent. The centrality we use is defined by the number of trust ties that a node has, divided by the maximum number of ties he could have.
The networks structures are different and it is now important to evaluate the consequences of these differences on the individual strategies. It is commonly accepted that, in social networks, actors who have more ties (i.e. are more linked to other actors) benefit from a favorable position. They may have alternative ways to satisfy their needs, and hence are less dependent on particular relationships. Similarly, a trader who has invested in creating only few links may have little bargaining power in that relationship, since he has no alternative partners with which to profitably trade. It is advantageous to be connected to those who have few options (the advantage of monopoly position); being connected to buyers (or sellers) who have many potential trading partners reduces one's bargaining power over the trade surplus.

We now analyze the effects of buyers' and sellers' centrality on prices. We use normalized degree centrality and measure its influence for both buyers and sellers ($deg_i$ and $deg_j$).

$$P_{i,j,\tau,t} = \beta_1 + \beta_2 \cdot deg_i + \beta_3 \cdot deg_j + \beta_4 \cdot Species_t + \beta_5 \cdot Weekday_{\tau} + \beta_6 \cdot Month_{\tau} + v_{i,j,\tau,t} \quad (5)$$

<table><caption>Table 6: Influence of centrality on prices for both sub-markets (log level estimation, Eq. 5).</caption><thead><tr><th rowspan="2">Parameter</th><th colspan="3">Auction</th><th colspan="3">Pairwise</th></tr><tr><th>coefficients</th><th>Std err</th><th>Pr > |t|</th><th>coefficient</th><th>Std err</th><th>Pr > |t|</th></tr></thead><tbody><tr><td>Intercept</td><td>0.03</td><td>0.12</td><td>0.76</td><td>0.87</td><td>0.08</td><td>&lt;0.0001</td></tr><tr><td>centrality buyer</td><td>-0.41</td><td>0.01</td><td>&lt;0.0001</td><td>-0.59</td><td>0.01</td><td>&lt;0.0001</td></tr><tr><td>centrality seller</td><td>0.49</td><td>0.03</td><td>&lt;0.0001</td><td>0.78</td><td>0.02</td><td>&lt;0.0001</td></tr><tr><td>R squared</td><td>0.74</td><td></td><td></td><td>0.79</td><td></td><td></td></tr></tbody></table>

The results are indicated in Table 6. The usual causalities (dummies variables as year, month or day...) are not displayed. We observe that the position of an agent has a significant influence on the transactions prices on both sub-markets, and that this influence is higher on the bilateral market (higher R squared and higher coefficients). This influence is positive for sellers and negative for buyers and this is in line with previous results on markets. On a market with frictions (search costs, private information), it is advantageous for a seller to establish links with a large number of potential buyers. On the auction market, the information is centralized and there is no search costs. Prices result from the competition between buyers. Partnerships cannot help.

On the buyers side, the coefficient is higher (in absolute value) on the pairwise market. More central buyers pay cheaper prices and this reflects a higher bargaining power (due to the higher number of potential sellers).

From these results, we can deduce two things. First that traders have an interest to establish as many trust links as they can. Second, it is clear that each trader has interest to build strong relationships with lonely traders. It seems that there is a competition among traders that trust a same partner.
## 5.2 Trust and centrality

Let's add $R_{i,j}$ in the regression in order to control for the bilateral trust effect and isolate the influence of the position in the trust network. But an important question remains: what is the intensity of the correlation between traders trust indexes and their centralities? Do these two variables represent two different phenomena? To answer this question we measure the correlation between the trust index and traders centrality on each market (Tab.7).

<table><caption>Table 7: Correlation between traders trust indexes and centralities.</caption><thead><tr><th></th><th>Auction</th><th>Pairwise</th></tr></thead><tbody><tr><td>Correlation for sellers</td><td>0.62</td><td>0.26</td></tr><tr><td>Correlation for buyers</td><td>0.39</td><td>-0.19</td></tr></tbody></table>

Concerning the auction market, we observe a high correlation between the bilateral trust index of traders, and their respective centralities. Without surprise, we can conclude that interlinks on auctions result from the competition mechanism, more than from trust strategies. This is in line with the results in Section 5, Table 5, that exhibits a high clustering on the centralized market.

Meanwhile, the correlations are weak on the pairwise market. Agents with high trust indexes are not always central agents. Being central or trusting partners correspond to two different strategies.

While the correlation is high between trust and centrality on the auction market, it seems that two different effects correspond to these two different variables on the pairwise market. In what follows, we measure (cf. Eq. 6) the respective effects of centrality and trust on the decentralized market.

$$P_{i,j,\tau,t} = \beta_1 + \beta_2 \cdot R_{i,j} + \beta_3 \cdot \text{deg}_i + \beta_4 \cdot \text{deg}_j + \beta_5 \cdot \text{Species}_t + \beta_6 \cdot \text{Weekday}_\tau + \beta_7 \cdot \text{month}_\tau + v_{i,j,\tau,t} \quad (6)$$

The results are displayed in Table 8.

<table><caption>Table 8: Influence of trust and centrality on prices (log level estimation, Eq. 6).</caption><thead><tr><th rowspan="2">Parameter</th><th colspan="3">Pairwise</th></tr><tr><th>coefficients</th><th>Std err</th><th>Pr > |t|</th></tr></thead><tbody><tr><td>Intercept</td><td>0.82</td><td>0.08</td><td>&lt;0.0001</td></tr><tr><td>centrality buyer</td><td>-0.56</td><td>0.01</td><td>&lt;0.0001</td></tr><tr><td>centrality seller</td><td>0.67</td><td>0.02</td><td>&lt;0.0001</td></tr><tr><td>R<sub>i,j</sub></td><td>1.34</td><td>0.07</td><td>&lt;0.0001</td></tr><tr><td>R squared</td><td>0.79</td><td></td><td></td></tr></tbody></table>

The stable co-existence of these two sub-markets where the same types of goods are traded by the same agents can seem paradoxical. Our analysis of the trust relationships help to resolve this paradox.
The auction mechanism is an efficient one when people have no time for linking. They then trust the
competitive market mechanism to insure an efficient redistribution of resources. But when they have time
for linking, or exchanges involve rare goods, trusting some few partners can be optimal and the pairwise
market mechanism allows this.

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