Adaptive Build-up and Breakdown of Trust: An Agent Based Computational Approach

Abstract

This article employs Agent-Based Computational Economics (ACE) to investigate whether, and under what conditions, trust is viable in markets. The emergence and breakdown of trust is modeled in a context of multiple buyers and suppliers. Agents develop trust in a partner as a function of observed loyalty. They select partners on the basis of their trust in the partner and potential profit, with adaptive weights. On the basis of realized profits, they adapt the weight they attach to trust relative to profitability, and their own trustworthiness, modeled as a threshold of defection. Trust and loyalty turn out to be viable under fairly general conditions.

Appendices

Appendix A: Specification of Profit

The number of general−purpose assets that a supplier j needs in order to produce for a buyer i, is equal to $(1 - d_i )(1 - e_{s,j} )$, where e _s,j is an efficiency factor (0 < e _s,j  < 1) of scale (s) in the production volume of supplier j. The number of buyer-specific assets that a supplier j needs, to produce for a buyer i, is equal to $d_i (1 - e_{l,j}^i )$, where e ⁱ _l,j is an efficiency factor (0 < e ⁱ _l,j  < 1) of learning by cooperation (l) in the relationship between buyer i and supplier j. Thus, the profit that can potentially be made in a transaction between a buyer i and a supplier j is:

$$[ p_i^{\,j} + p_j^i = (1 + d_i ) - (d_i (1 - e_{l,j}^i ) + (1 - d_i )(1 - e_{s,j} )) $$

(A1)

The first part of the formula specifies returns and the second part specifies costs. It is assumed that the agents involved share the profit equally.

Appendix B: Details of Results

B.1 High Initial Trust

First, we consider an initial situation of high, 90% trust across all agents. First, we take intermediate initial expected values for α (0.5) and τ (0.25). Next to the variation of degree of specificity (d = 0.25, 0.45, 0.65), we vary the strength of economy of scale (scale factor sf) and learning by cooperation (lf), as follows:

• both scale and learning have intermediate strength (lf = sf = 0.5, see formula (3))

• high learning (lf = 0.9), medium scale (sf = 0.5). This is expected to favour a learning by cooperation strategy, with high loyalty

• medium learning by cooperation (lf = 0.5), high scale (sf = 0.9). This is expected to favour a scale strategy, with less loyalty.

The results are given in Table B1.

Table BI Buyers’ maximum normalized profits for high initial trust, at different learn and scale factors

Table B1 supplies maximum normalized profit actually achieved in the course of time, obtained by dividing the buyers’ maximum profits by the maximum attainable (theoretical) profit they can potentially make. This is the profit a buyer makes when he has an infinite relation with a supplier who produces for the maximum of 3 buyers. Usually maximum actual profit is achieved at the last steps of simulation because of adaptation processes in relations between buyers and suppliers. At the start point normalized profit turns out to be about 52% for high d and 61% for low d. Maximum scale effect is achieved when d is low. Here, the maximum arises in a situation where 12 buyers together buy from only 4 suppliers (each, i.e. one third of all suppliers each producing for the maximum of three buyers). Because the optimal network configuration, where suppliers produce for 3 buyers, rarely emerges, buyers organize closer to the optimum when d is higher. Then, buyers are less sensitive to the optimal configuration of network between agents, having less scope for increased efficiency by getting into an arrangement of one supplier producing for him as well as two other buyers.

For all levels of asset specificity (d), in each run at least one supplier produced for the maximum of 3 buyers, on average across runs 10 % of suppliers did this, 15% of suppliers produced for 2 buyers, 40 % for 1 buyer, and 35% for 0 buyers. The results indicate that in this high-trust society buyers follow the strategy of learning by cooperation and loyalty for all d, without switching between suppliers, even for the low value d = 0.25, where only 25% of assets are subject to learning by cooperation.

Table B1 also shows the effect of different values for the strength of learning by cooperation (lf) and economy of scale (sf). Stronger learning by cooperation increases profit more for high than for low levels of specific investments, as is to be expected. A stronger scale effect, however, also increases maximum attainable profit, which is not realized, so that the ratio between actual and potential profit declines.

So far, we assumed intermediate levels for the initial weight attached to profit (α) and for the threshold of defection (τ). Now we analyze the effects of varying those values: α = 0.0 and 1.0; τ = 0.0 and 0.5. Learn and scale factors are fixed at the average level, i.e. 0.5. The results are given in Table B2. Here, we also supply the average number of suppliers per buyer, as an indicator of the extent of outsourcing.

Table BII Buyers’ maximum normalized profits for different α and τ

When α = 0, agents put their emphasis on trust and follow the strategy of learning by cooperation for all d. The distribution of suppliers between buyers in this case is the same as before (Table B2). Each buyer has ongoing transactions with the same supplier but when loyalty is equal to zero (τ = 0) buyers sometimes break relations with suppliers for high d because then profit doesn’t exceed the level of when they make. These buyers try to switch to other suppliers but they don’t succeed because all agents are concentrated on trust built up in the past of their current relation. Opportunistic buyers then return to their initial partners and as a result they lose in profit slightly, for high d, because of switching costs. If loyalty is high (τ = 0.5) there is no switching for any level of d, and agents try to generate as much profit as possible in stable relations by using the advantage of loyalty and trust, in learning by cooperation.

When α = 1, agents focus on profitability rather than on trust, and buyers follow two strategies simultaneously: some of them buy from suppliers and others make themselves.

When τ = 0.0 approximately half of buyers have suppliers for d = 0.25 and these buyers follow the scale strategy, seeking a supplier who already serves two buyers, and trying to match with him. As a result, in this case 17% of all suppliers produce for three buyers. For d = 0.45 and d = 0.65 buyers prefer to make themselves, mostly because outsourcing is only preferred as relations with suppliers last longer and generate economies of learning, but this is unlikely to happen at zero loyalty. However, because of high initial trust buyers try to reach suppliers sometimes and then lose profit a little because of switching costs. If τ = 0.5 the proportion of buyers who have suppliers increases for all d: 60 % of buyers have suppliers for d = 0.25, 40% for d = 0.45 and 30 % for d = 0.65. However, the distribution of suppliers over buyers is different for different d. When d = 0.25 approximately 20% of suppliers produce for three buyers and therefore profit is higher than in the case with τ = 0.0. When d = 0.45 about 12% of suppliers produce for three buyers and 5% of suppliers produce for one buyer and when d = 0.65 suppliers produce only for one buyer and it is about 30% of them. Therefore, for low and average d more buyers follow the scale strategy because high loyalty allows them to keep stable relations with matched suppliers and generate higher profit than in the case with zero loyalty. For high d one part of buyers (70%) produce themselves and other part (30%) follow the strategy learning by cooperation because economies of learning are more important than scale effect.

B.2 Average And Low Initial Trust

Now we turn to ‘societies’ with an average (50%) and lower level (10%) of initial trust. Learn and scale factors are again fixed at the average level, i.e. 0.5. The main outcome here is that buyers make for high and average levels of specific assets (d), and buy only for low levels. The results are specified in Tables B3 and B4.

Table BIII Buyers’ maximum normalized profits for average initial trust

At a medium level of initial trust, under low specific assets (d = 0.25) trust increases from an average to the highest level. This may seem surprising, since then the effect of learning by cooperation is lowest, so that the rewards of a trust strategy seem lowest. The explanation is as follows. Under average trust, suppliers are more attractive than buyers consider themselves to be only for low d, because potential losses in case of switching are smaller for low d than for high d. For high levels of specificity, buyers never enter into relations with outside suppliers, and thus never profit from collaboration and forego opportunities for the build-up of trust. For low specificity, the risk of outsourcing is less, and outsourcing occurs even if trust is not high. Then, advantages of learning by doing, even though limited by low d, set in, and advantages of loyalty are experienced, yielding an increase of trust.

Compared with the corresponding case in the high trust world (first column, Table B1), normalized profits are the same for high and low values of d, but lower for intermediate values. The network configuration of suppliers and buyers for low d is the same as in the case of high initial trust: 10% of suppliers produce for 3 buyers, 15% of suppliers produce for 2 buyers, 40 % for 1 buyer, 35% for 0 buyers. Buyers follow the learning by cooperation strategy in ongoing relations without switching.

In the case of low initial trust, see Table B4, buyers produce themselves (have no suppliers) even for a low level of specific assets. The result is a drop of normalized profits for low d, compared to the medium and high trust cases. All opportunities for learning by cooperation in collaboration are foregone.

Table BIV Buyers’ maximum normalized profits for low initial trust