q
Most of the work reported in this paper was done while the authors were Ph.D. student and professor, respectively, at the Faculty of Management and Organization, University of Groningen, The Netherlands. For helpful comments and discussions, we are grateful to Leigh Tesfatsion, Rob Vossen, ReneH Jorna, an anonymous referee, Han La PoutreH, Maryse Brand, Michel Wedel and to seminar participants at the Research Institute and Graduate School SOM and at the Center for Mathematics and Computer Science (CWI Amsterdam).
*Corresponding author.
E-mail address:[email protected] (B. Nooteboom).
25 (2001) 503}526
Agent-based computational transaction
cost economics
qTomas B. Klos
!
, Bart Nooteboom
"
,
*
!KPN Research, Groningen, The Netherlands
"Faculty of Management and Organization, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, Netherlands
Accepted 22 February 2000
Abstract
This article explores the use of &agent-based computational economics' (ACE) for modelling the development of transactions between"rms. Transaction cost economics neglects learning and the development of trust, ignores the complexity of multiple agents, and assumes rather than investigates the e$ciency of outcomes. E$ciency here refers to minimum cost or maximum pro"t. We model how co-operation and trust emerge and shift adaptively as relations evolve in a context of multiple, interacting agents. This may open up a new area of application for the ACE methodology. A simulation model is developed in which agents make and break transaction relations on the basis of prefer-ences, based on trust and potential pro"t. Pro"t is a function of product di!erentiation, speci"city of assets, economy of scale and learning by doing in ongoing relations. Agents adapt their trust in a partner as a function of his loyalty, exhibited by his continuation of a relation. They also adapt the weight they attach to trust on the basis of realized pro"t. The model enables an assessment of the e$ciency of outcomes relative to the optimum, as
a function of trust and market conditions. We conduct a few experiments to illustrate this application of ACE. ( 2001 Elsevier Science B.V. All rights reserved.
JEL classixcation: C63; C78; D83; L22
Keywords: Inter-"rm relations; Transaction costs; Governance; Trust; Matching; Com-plex adaptive systems; Arti"cial adaptive agents; Agent-based computational economics
1. Introduction
Inter-"rm relations in general, and buyer}supplier relations in particular, have increasingly been analyzed by means of transaction cost economics (TCE). However, as has been widely acknowledged, TCE does not include any dynam-ics of learning, adaptation or innovation. Williamson himself (1985, p. 144) admitted that&the study of economic organization in a regime of rapid innova-tion poses much more di$cult issues than those addressed here'. A more fundamental problem is that as in economics more in general it is assumed rather than investigated that e$cient outcomes will arise. Here, in inter-"rm relations, it is assumed that optimal forms of organization or governance will arise, suited to characteristics of transactions such as the need for transaction-speci"c investments, frequency of transactions, and uncertainty concerning conditions that may a!ect future transactions (Williamson, 1975, 1985). Two arguments are used for this: an argument of rationality and an argument of selection.
Williamson granted that rationality is bounded and transactions are subject to radical uncertainty, which precludes complete contingent contracting. But he proceeded to assume a higher level of rationality: people can rationally, calculatively deal with conditions of bounded rationality. Aware of their bounded rationality and radical uncertainty, people rationally design governance struc-tures to deal with those conditions. However, if rationality is bounded, then rationality of dealing with bounded rationality is bounded as well. To rationally calculate economizing on bounded rationality, one would need to know the marginal (opportunity) costs and bene"ts of seeking further information and of further calculation, but for that one would need to decide upon the marginal costs and bene"ts of the e!orts to"nd that out. This yields an in"nite regress (Hodgson, 1998; Pagano, 1999). Here we accept bounded rationality more fully and deal with it on the basis of the methodology of adaptive agents.
no exception in this respect. He held that in due course, ine$cient forms of organization will be selected out by market forces. However, that argument of selection has been shown to be dubious. For example, Winter (1964) showed that in evolution it is not the best conceivable but the best that happens to be available that survives. Due to e!ects of scale a large"rm that is ine$cient for its size may win out over e$cient small"rms. Furthermore, the selection e$ciency of markets may be hampered by entry barriers. Koopmans (1957) concluded long ago that if the assumption of e$cient outcomes is based on an argument of evolutionary process, its validity should be tested by explicit modelling of that process. Then, particularly in the study of inter-"rm relations, we have to take into account the complexities and path-dependencies that may arise in the making and breaking of relations between multiple agents. That is what we aim to do in this article. As Coase (1998) recently admitted:
[t]he analysis cannot be con"ned to what happens within a single"rm. The costs of co-ordination within a"rm and the level of transaction costs that it faces are a!ected by its ability to purchase inputs from other"rms, and their ability to supply these inputs depends in part on their costs of co-ordination and the level of transaction costs that they face which are similarly a!ected by what these are in still other"rms. What we are dealing with is a complex interrelated structure.
Following up on Epstein and Axtell's (1996) suggestion, we let the distribution of economic activity across di!erent organizational forms emerge from processes of interaction between these agents, as they adapt future decisions to past experiences. The system may or may not settle down and if it does, the resulting equilibrium may or may not be transaction cost economic. In any case,&[i]t is the process of becoming rather than the never-reached end points that we must study if we are to gain insight'(Holland, 1992, p. 19).
The methodology of arti"cial adaptive agents, in ACE, seems just the right methodology to deal with this&complex interrelated structure'of&processes of interaction in which future decisions are adapted to past experiences'. We use that methodology to model interactions between "rms, in the making and breaking of relations on the basis of a boundedly rational, adaptive, mutual evaluation of transaction partners that takes into account trust, costs and pro"ts. We model a system of buyer}supplier relations, because that best illustrates transaction cost issues.
We focus on the role of trust, for two reasons. The"rst reason is that TCE does not incorporate trust, and this is an area where development of insight has priority. The second reason is that the central feature, in ACE, of adaptation in the light of experience seems particularly relevant to trust (Gulati, 1995; Zucker, 1986; Zand, 1972).
1http://www.econ.iastate.edu/tesfatsi/ace.htm.
opportunism. Section 4 discusses costs and pro"ts of transactions. Then we proceed to explain the design of our model. Section 5 indicates how buyers and suppliers are matched on the basis of their preferences, which include trust next to expected pro"t. Section 6 shows how we model costs and pro"ts. Section 7 shows how we model trust. Section 8 shows how we model adaptation. Section 9 summarizes the simulation model. Section 10 discusses a few illustrative experi-ments. Finally, Section 11 discusses limitations and further research.
2. Agent-based computational economics
Holland and Miller (1991) suggest to study economic systems as &complex adaptive systems'. A complex adaptive system (CAS) &is a complex system containing adaptive agents, networked so that the environment of each adaptive agent includes other agents in the system'(1991, p. 365). The method-ology of ACE is a specialization of this to economics (see the ACE website,1 maintained by Leigh Tesfatsion). This approach is used more and more often to study problems in economics, such as in the repeated prisoner's dilemma (Klos, 1999a, Miller, 1996, Stanley et al., 1994), and on "nal-goods markets (Albin and Foley, 1992; Vriend, 1995), stock markets (Arthur et al., 1997), industrial markets (PeHli and Nooteboom, 1997) and labor markets (Tesfatsion, 2000), etc.
The essence of this approach is that economic phenomena are studied as they emerge from actual (simulated) interactions between individual, boundedly rational, adaptive agents. They are not deduced from abstract models employ-ing representative agents, auctioneers or anonymous, random matchemploy-ing, etc. Rather, whether an interaction takes place between any two given agents is left for them to decide. What the agents subsequently do in that interaction is their own*possibly sub-optimal*decision, that they make on the basis of their locally available, incomplete information and as a result of their own (cognitively limited) processing of that information. Appropriate forms of rea-soning are induction and abduction, rather than deduction as used in optimiza-tion models that are solved for&never-reached end points'.
3. Opportunism and trust
information about a partner's trustworthiness, one must take the possibility of opportunism into account and construct safeguards for it. Nooteboom (1999) argued that this involves an inconsistency concerning the time dimension in TCE. Time is essential for the central notion of transaction-speci"c invest-ments. Such investments have to be made&up front', while they can be recouped only in a succession of transactions in the future. When the relation breaks prematurely, there is a loss of speci"c assets. In the course of time there may be cumulative gains of e$ciency due to learning by doing. When the relation breaks this advantage is lost. Both yield switching costs, and these create dependence, and thereby vulnerability to&hold-up'. However, if allowance thus has to be made for the passage of time, in a relation, then one should also allow for the acquisition of knowledge concerning he trustworthiness of a transaction partner.
Then the argument in TCE is that while it might be possible to gather information about a partner's trustworthiness, that is costly and it is more e$cient to accept the possibility of opportunism and construct safeguards against it. Here also an important point is assumed rather than analyzed. Safeguarding against opportunism may be more costly or di$cult than gather-ing information about trustworthiness. The assumption of opportunism signals distrust, which may engender distrust on the other side of the relation, which can yield a vicious circle of regulation and constraint which reduces the scope for collaboration (Zand, 1972).
A third argument against incorporating trust in TCE, o!ered by Williamson (1993), is that if trust does not go beyond calculative self-interest it adds nothing, and if it does it yields blind trust, which is unwise and will not survive. So trust should be left out. Against this, Nooteboom (1999) argued that trust can be real, in the sense that it goes beyond calculative self-interest, without being blind, because it is can be bounded rather than unconditional. One can assume that people will be loyal only within constraints, i.e. below some limit that represents their resistance to temptations of opportunism.
In our simulation models we take all this into account in the following manner:
1. Trust is adaptive: it is based on experience with a (potential) partner's commitment to a relation, as exhibited by his past lack of defection to more attractive alternatives.
2. Trust goes beyond expected pro"t: it is taken up, next to pro"t, as a separate criterion of merit, in the determination of a (potential) partner's attractive-ness. The weight attached to trust relative to expected pro"t is also adaptive: it depends on realized pro"ts.
4. Trustworthiness also is adaptive: the threshold of defection is adjusted as a function of realized pro"ts. In the present,"rst version of the model this feature has not yet been implemented.
This approach allows us to experiment with the development of trust and trustworthiness, the role this plays in making and breaking of relations, the resulting durability or volatility of relations and the outcome regarding e$ -ciency, in terms of realized pro"ts. These experiments are conducted under dif-ferent conditions concerning costs and pro"ts that are relevant for transaction cost analysis. These are discussed in the next section.
4. Costs and pro5ts
A central concept in transaction cost analysis is the notion of &transaction speci"c investments'. These yield pro"ts as well as costs. The pro"t lies in di!erentiated products, which yield a higher pro"t than standardized products. With standardized products one can compete only on price, and under free and costless entry to the market this will erode price down to marginal cost, as proposed in standard micro-economics. In contrast, di!erentiated products allow for a pro"t margin. One way to model this is to locate products and users in anN-dimensional product characteristics space (Lancaster, 1966). The loca-tion of a product represents the bundle of characteristics it o!ers and the location of a user represents his&ideal product'. The distance between the two represents the opportunity cost a user incurs when buying the product. A prod-uct can exact a pro"t margin, over and above marginal costs, to the extent that it is closer to the user than the nearest competing product (Eaton and Lipsey, 1989).
To the extent that assets are not speci"c, they may be used for alternative partners and generate economy of scale. When production technology and/or marketing are in#exible, so that a speci"c product entails a speci"c investment, di!erentiated products entail speci"c investments (Nooteboom, 1993). This entails loss of economy of scale. As analyzed in TCE, a speci"c investment has to be made&up front'and is recouped only after repeated transactions, while it has less or no value in other applications, in transactions with another partner. Thus, it entails switching costs in the form of loss of investment (and the need to make new investments for a new partner). This makes one dependent on the commitment of the partner to continue the relation until the investment is recouped. That yields the&hold-up'problem. Ongoing relations allow for
speci-"c investments to be recouped, and they may yield economies of experience (or
2See Roth and Sotomayor (1990) for an excellent introduction to and overview of matching theory.
These features of pro"t from di!erentiated products, economy of scale, econ-omy of experience and switching costs are incorporated in the simulation model. This enables us to explore the advantages and disadvantages of exclusive, durable relations versus non-exclusive, volatile ones. In a few illustrative experi-ments with the model we vary the degree to which investment in any given buyer}supplier relation is speci"c, and we test hypotheses concerning the e!ects on the&make or buy'decision. Our hypothesis, taken directly from TCE, is that more product di!erentiation will favor&make'over&buy'. Another is that, to the extent that the advantages of durable &buy' relations are higher, trust and trustworthiness, in terms of commitment to an ongoing relationship in spite of more attractive alternatives, matter more. We would expect that adaptive agents then evolve to relatively high levels of trustworthiness, less frequent switching, higher perceived commitment and hence trust, and a high weight attached to trust in the evaluation of partners. We also investigate the e!ect on outcomes in terms of cumulative pro"t, to see to what extent optimal pro"ts are indeed realized, and how this varies across runs of the model. Lack of optimal outcomes and a variety of outcomes would form an illustration of path-dependence in the formation of relations among multiple agents. The next section introduces how partners are matched on the basis of preferences.
5. Preferences and matching
Rather than rely on standard, anonymous random matching devices, the choice of partners is explicitly incorporated in the model. Agents are assumed to have di!erential preferences for di!erent potential trading partners (cf. Weis-buch et al. (2000)). On the basis of preferences, buyers are assigned to suppliers or to themselves, respectively (see Fig. 1). When a buyer is assigned to himself this means that he&makes rather than buys'. In other words: we endogenize the
&make or buy decision'. This process is generated by a so-called matching algorithm.2The current section describes the algorithm in some detail.
Fig. 1. Buyers are assigned to suppliers or to themselves.
3To be precise, the DCR algorithm allows both sides of the market to be coincident, overlapping or disjoint, and it also allows arbitrarily speci"ed o!er and acceptance quota. This algorithm produces stable matchings. These are matchings that have no blocking (pairs of ) agents, i.e. (pairs of ) agents who can (bi- or) unilaterally improve upon their actual situation under the matching by *rather than to their actual match*being matched to (each other or) themselves. The DCR algorithm was used because it provides a way of assigning agents to each other, not because it produces stable matchings; in the current application, stability is just a side-e!ect.
speci"cation of potential pro"t and trust, to express that they interact: the score must be zero if either trust or potential pro"t is zero. The product of potential pro"tability and trust interpreted as a probability of realization would consti-tute expected pro"t. In order to allow agents to attach varying weights to pro"tability versus trust, instead of simple multiplication of the two we employ a Cobb}Douglas functional form
score
ij"pro"tabilityaiji trust1~ij ai, (1)
where score
ijis the scoreiassigns toj, pro"tabilityijis the pro"tican potentially make&through'j, trust
ijisi's trust injandai3[0, 1] is the importanceiattaches to pro"tability relative to trust, i.e. the &pro"t-elasticity' of the scores that
i assigns; i may adapt the value ofai from each timestep to the next. Later sections describe how pro"tability and trust are determined, and how adapta-tion takes place.
4For the moment, we assume that all buyers are acceptable to the suppliers; suppliers do not, like the buyers, have any alternative, so they will rather supply to any buyer than remain single. quali"cations. First of all, and most importantly, unlike the DCR algorithm we do allow buyers to be matched to themselves, in which case they are their own supplier. Secondly, only disjoint sets of buyers and suppliers are allowed, so that there are no agents that can be buyer as well as supplier. So, although buyers may be their own supplier, they can not supply to other buyers. Finally, we allow di!erent agents to have di!erent quotas*i.e. di!erent maximum num-bers of matches allowed at any moment in time*because di!erent buyers and suppliers are likely to want di!erent numbers of partners. Each buyer includes itself as one of the alternatives in its preference ranking, and suppliers not ranking higher than the buyer are unacceptable. In other words: a buyer prefers to remain single (and&make') rather than&buy'from an unacceptable supplier. Determining whether the buyer-"rm should or should not perform a function itself is at the heart of transaction cost economic reasoning.
The matching algorithm proceeds as follows. Buyers may have one or more suppliers and suppliers may have one or more buyers; each buyerihas an o!er quotao
i (51) and each supplierjhas an acceptance quotaaj (51). Before the matching, all buyers and suppliers establish a strict preference ranking over all their alternatives. The algorithm then proceeds in a"nite number of steps.
1. In the "rst step, each buyer sends a maximum of o
i requests to its most preferred, acceptable suppliers. The algorithm structurally favors the agents that send the requests; it is plausible that buyers do this. Because the buyers typically have di!erent preference rankings, the various suppliers will receive di!erent numbers of requests.
2. The suppliers "rst reject all requests received from unacceptable buyers.4 Then, each supplier&provisionally accepts'a maximum ofa
jrequests from its most preferred acceptable buyers and rejects the rest (if any).
3. Each buyer that was rejected in any step"lls its quotao
i in the next step by sending requests to (o
i minus the number of outstanding, provisionally accepted, requests) next-most-preferred, acceptable suppliers that it has not yet sent a request to.
4. Each supplier again rejects requests received from unacceptable buyers and provisionally accepts the requests from up to a maximum ofa
jmost prefer-red, acceptable buyers from among newly received and previously provis-ionally accepted requests and rejects the rest. As long as one or more buyers have been rejected, the algorithms goes back to step 3.
5Remember that overlap between both sides of the market is not allowed, which takes away the possibility for buyers to produce for themselves as well as for their competitors.
6. Modelling potential pro5t
A buyer's potential to generate pro"ts for a supplier is a function of the buyer's position on the"nal market*where he is a seller*as expressed in the degree of product di!erentiation. A supplier's potential to generate pro"ts for a buyer is determined by the supplier's e$ciency in producing for the buyer. The model allows for varying degrees of product di!erentiation. As indicated before, a more di!erentiated product yields a higher pro"t margin. This is expressed in a buyer-speci"c variabled
i3[0, 1] that determines the pro"t the buyer will make when selling his products. We will be experimenting with di!erent values for
d
iProduction, whether conducted by a supplier or by the buyer himself, requiresto see how they a!ect the choices that agents make. investments in assets. One unit of asset is normally required to produce one product, but increasing e$ciency may decrease this amount. Assuming the production technology is more or less rigid (di!erentiated products require specialized assets), we assume a connection between the di!erentiation of a buyer's product and the speci"city of the assets required to produce it. To the extent that assets are speci"c, they entail switching costs. On the other hand, if products are not di!erentiated, investments to produce the product for one buyer can easily be switched to producing the product for other buyers. The simplest way to model this relation is to assume that asset speci"city is equal to product di!erentiation, i.e. the proportion of the asset that is speci"c to a buyer is equal to the extent to which that buyer's product is di!erentiated. If a buyer produces for himself, it makes no sense to distinguish between buyer-speci"c and non-speci"c assets.5A buyer's minimum acceptance level of suppliers is the score that the buyer would attach to himself. Since it is plausible that he completely trusts himself, trust is set at its maximum of 1, and the role of trust in the score is disregarded:a"1.
If a supplier produces for one or more buyers, then his investments are split into two categories: buyer-speci"c and non-speci"c*i.e. general purpose*assets. As explained above, the percentage of investment that is speci"c to that buyer is the same as the extent to which that buyer's product is di!erentiated. The supplier adds the remaining, general-purpose investment for each buyer over all the buyers he is matched to. The corresponding volume of production is subject to economy of scale. The utilization of speci"c assets is subject to experience e!ects: uninter-rupted use for the buyer involved yields learning by doing.
The number of general-purpose assets that supplier j needs in order to produce for buyeri, is equal to (1!d
i)(1!es,j), wherediis the di!erentiation of buyer i's products and e
Table 1
Renormalization constant,C S0,2T 20
BaseTrust,b S0, 1] 0.3
Renormalization constant,C S0,2T 20
BaseTrust,b S0, 1] 0.3
InitTrust(subject) S0, 1] 0.75
TrustFactor [0, 1] 0.5
buyer-speci"c assets that a supplierjneeds to produce for a buyeriis equal to
d
i(1!eil,j), whereeil,jis supplierj's&learning e$ciency'(e$ciency due to learning by doing) for buyeri.
Both economy of scale and experience e!ects are modelled with the following function:
y"max
C
0, 1! 1fx#1!fD, (2)
where
f for the scale e!ect,f"scaleFactor(see Table 1), the horizontal axis measures
general-purpose assets of supplier j summed over all his buyers, and the vertical axis measures the scale e$ciencye
s,j of the supplier.
f for the experience e!ect, f"learnFactor (see Table 1), the horizontal axis
measures the total of consecutive periods of supply by supplierjto a given buyeri, and the vertical axis measures the suppliers learning by doingeil
,jwith respect to that buyer.
Fig. 2. E$ciency of scale and of learning-by-doing.
di!erent values off. The graph shows positive values along the vertical axis only for more than 1 general purpose asset. This expresses that a supplier can be more scale-e$cient than a buyer producing for himself only if the scale at which he produces is larger than the maximum scale at which a buyer might produce for himself. Furthermore, a supplier's buyer-speci"c e$ciency is 0 in their "rst transaction, and only starts to increase if the number of transactions is larger than 1. The way pro"ts are made, then, is that suppliers may reduce costs by generating e$ciencies for buyers, while buyers may increase returns by selling more di!erentiated products. It is assumed that the pro"t that is made resulting from both partners'contributions is shared equally between the buyer and the supplier involved.
7. Modelling trust
Fig. 3. Trust.
in-house production as an alternative to engaging a supplier, we assume max-imum trust, and the weight attached to trust (1!a) is zero. In other words trust is 100%, but it is not relevant. Evaluating himself, the producer looks only at potential pro"t. In other words, we assume that"rms will not be opportunistic to themselves.
Following Gulati (1995), we also assume that trust increases with the duration of a relation. As a relation lasts longer, one starts to take the partner's behavior for granted, and to assume the same behavior (i.e. commitment, rather than breaking the relation) for the future (cf. the notion of &habituation' in Nooteboom et al., 1997). Like e!ects of scale and experience, we assume that this is subject to decreasing returns to scale, and we use the same basic functional form employed before. However, here we add an additional, base level of trust. This re#ects the notion, discussed by Nooteboom (1999), that trust has several foundations. One is basic, ex ante trust as an institutional feature of a society. It may be interpreted as the expected percentage of non-opportunistic people, or as some standard of elementary decency that is assumed to prevail. On top of that basic level of trust one can develop partner-speci"c trust on the basis of experience in dealings with him. This yields the following speci"cation, to re#ect the increase of trust with the duration of an ongoing relation
y"b#(1!b)
A
1! 1fx#1!f
B
, (3)wherebis the base-level of trust andxis the number of consecutive matches the agents have been involved in. Here, for the parameter f we substitute trustFactor(see Table 1).
Fig. 3 shows the relation between the past duration of a relation and agents'
6This form of adaptation is called reinforcement learning. A classi"er system is used to implement it. See Arthur (1991, 1993), Kirman and Vriend (2000) and Lane (1993) for discussions and other applications in economic models; good general introductions to classi"er systems are Booker et al. (1989), Goldberg (1989) and Holland et al. (1986).
7This works as follows: the agent adds the pro"t obtained during timesteptto the strength of the value that was used fora. Then, all strengths are renormalized to sum toCagain (see Arthur (1993) for a discussion of this learning mechanism). This is done by multiplying each of them with the ratio C/(C#n
t), wherentis the pro"tc realized in timestept.
agent, trust starts out at a certain starting value that is set exogenously, and is adapted to experience with the loyalty of partners. If an agent i, involved in a relation with an agentj&breaks'their relation, thenj's trust inidecreases; in e!ect,j's trust drops by a percentage of the distance between the current level and the base-line level of trust; it stays there until the next time j and i are matched, after which is starts to increase again for as long as the relation lasts without interruption.
8. Adaptation
An agent in a CAS is adaptive if&the actions of the agent in its environment can be assigned a value (performance, utility, payo!,"tness, or the like); and the agent behaves in such a way as to improve this value over time'(Holland and Miller, 1991, p. 365). The adaptive character of the arti"cial agents in the present model refers to the possibility for the agents to change the value they use for
afrom each timestep to the next. As discussed,ais the pro"t elasticity of the preference score (1!ais the elasticity with respect to trust). This contributes to a change in the scores they assign to di!erent agents. Each agent has several possible values fora3[0, 1]; the number is a parameter in the simulation. To each value, each agent assigns a strength.6This expresses the agent's con"dence in the success of using that particular value; the various strengths always add up to a constantC. At the beginning of each timestep each agent chooses a value of
a. The choice between the di!erent possible values for a is probabilistic
*a simple roulette wheel selection* with each value's selection probability equal to its relative strength, i.e. its strength divided byC. The strength of the value that was chosen foraat the start of a particular timestep, is updated at the end of that timestep, on the basis of the agent's performance during that timestep, in terms of realized pro"t.7As an output of the simulation, each agent
i's weighted average value forai is calculated:
+
ai/0,2,1
8The simulation was developed in the general-purpose, object-oriented programming language SIMULA (Birtwistle et al., 1973). The object-oriented paradigm is very well suited for agent-based modelling (see McFadzean and Tesfatsion, 1999; Epstein and Axtell, 1996). The program and the source-code are available upon request.
This indicates where i's emphasis lies: because the value with the highest strength pulls the weighted average in its direction, the emphasis lies on low values foraif the weighted averagea
i is low and vice versa.
9. The simulation model
The simulation proceeds in a sequence of time steps, called a &run'. Each simulation experiment may be replicated several times (multiple runs), to reduce the in#uence of draws from random distributions on the results. At the begin-ning of a simulation starting values are set for certain model parameters. The user is prompted to supply the number of buyers and suppliers, as well as the number of runs, and the number of timesteps in each run.8 The program's random number generator is seeded and"nally, the agents are instantiated and given a number for identi"cation. At the start of each run, each of the agents is initialized. For example, the agents'pro"ts (from the previous run) are re-set to zero and the agents'trust in other agents is re-set. The simulation is described in more detail in Klos (1999b). The#ow diagram in Fig. 4 gives an overview.
In each timestep, before matching takes place, each agent calculates scores and ranks potential partners accordingly. Random draws are used to settle the ranking of alternatives with equal scores. To calculate scores each agent chooses a value fora: the elasticity of the score with respect to potential pro"t. Potential pro"tability depends on pro"t margin, related to the degree of product di! eren-tiation, economies of scale and economies of experience. As discussed before, suppliers enjoy scale-economies in the total of general purpose assets used in the production for multiple buyers. Furthermore, as a supply relation lasts, the supplier accumulates experience and e$ciency at using speci"c assets in the production for a particular buyer. Suppliers'scale-e$ciency is inferred from the outcome of the previous timestep. Only after the matching does it become clear to how many and which buyers each supplier is actually matched, and what the real extent of his scale-e$ciency is. Expectations of the supplier's position on each buyer-speci"c experience curve, on the other hand, will already be accurate before the matching*assuming, of course, that the relation makes it through the matching.
Fig. 4. A#ow diagram of the simulation.
9A di!erent seed was used for the random number generator in each timestep, but the same seed was used in each"rst, second, etc., run of each experiment.
Table 2
Di!erence between suppliers'initial scores and a buyer's own score ("d) for di!erent values of di!erentiation and of the buyer'sa
a
d 0 0.25 0.5 0.75 1
0.25 0.50 0.23 0.06 !0.05 !0.13 0.35 0.40 0.17 0.01 !0.10 !0.18
0.45 0.30 0.11 !0.04 !0.15 !0.23
0.55 0.20 0.03 !0.10 !0.20 !0.28
0.65 0.10 !0.04 !0.16 !0.25 !0.33
0.75 0.00 !0.12 !0.22 !0.30 !0.38
timesteps realized pro"ts are accumulated for all buyers and suppliers, and all the relevant parameters are tracked.
10. Experiments
Experiments were run with the parameters and variables as shown in the right-most column of Table 1. The degree of product di!erentiation was varied in six experiments, each of which was run for 250 timesteps and replicated 25 times: results are typically presented as averages over those 25 runs.9 Before going to the results, it is useful to consider what may be expected from the simulations. The experimental variable&di!erentiation'of the buyers'products is tied to the speci"city of the assets that suppliers invest in to support their production for those buyers. Initially, therefore, the buyers are confronted with the score-di!erentials given in Table 2.
The values in Table 2 are calculated as follows. The score that a buyer
iassigns to a supplierj, is
score
i,j"(0.5di#0.5dieil,j#0.5(1!di)es,j)atj (1~a)
i , (5)
where the supplier's initial learning-e$ciency for buyeri,eil
,j"0, the supplier's initial e$ciency of scale,e
s,j"0 and buyeri's initial trust in supplierj,tji"0.75. The score that buyeriassigns to himself is equal tod
i, because that is his pro"t when he makes and he usesa"1 to calculate his own score. The values in the
Fig. 5. Proportion&made'(as opposed to&bought').
10This is corrected for the fact that the suppliers' scale-e$ciency is limited because their acceptance quota is set to 3; if it is unlimited, the system quickly settles in a state where all buyers buy from the same supplier.
need for buyers to consider them acceptable*decreases. Ifd"0.75, there is no value forathat gives suppliers a net advantage so we may expect no outsourcing at all in that case. Notice that for anyd(0.75, no matter how much smaller, the suppliers do have a net advantage, which, furthermore, if matches do occur, increases over time with suppliers'increasing learning e$ciency and also when suppliers are matched to more than 1 buyer. The situation in Table 2, therefore, is likely to shift in favor of suppliers as time progresses. In general, then, we would expect more making (and less buying) when di!erentiation increases. This is in accordance with expectations from TCE.
The proportion of economic activity under&hierarchy', i.e.&make'rather than
&buy', in the di!erent experiments, is shown in Fig. 5. This shows that, as expected, the proportion made is higher when di!erentiation is high than when it is low, and if d"0.75, nothing is bought; the buyers make everything themselves (the plot for d"0.75 coincides with the top border of the graph). Notice however, that in all experiments, the proportion made decreases during approximately the"rst 20 timesteps, after which it increases and more strongly so, whendis higher.
Fig. 6. Buyers'normalized pro"ts.
initial decrease in&proportion made'(see Fig. 5) is good for the buyers, in terms of pro"t, when di!erentiation is low (their normalized pro"t increases during this initial period), but&bad'when di!erentiation is high, since the theoretically most appropriate choice is to make when di!erentiation is high. Eventually, this is also what the agents learn.
Furthermore, in several of the experiments, the agents are performing more poorly than they could. This is because&performance as it could be'is based on pro"t made in a relation with a supplier with maximum scale- and learning-e$ciency. Since each supplier can have a maximum of 3 buyers, this requires that the 12 buyers together buy from only 4 suppliers. That this network con"guration does not always emerge, is shown in Fig. 7, which depicts the buyers'average normalized pro"ts in each of the 25 individual runs of
experi-mentd"0.35. In this experiment, there are three levels at which average pro"ts
&stabilize'; almost 1 (6 runs), and approximately 0.9 (15 runs) and 0.8 (4 runs). The
"rst of these levels corresponds to the situation where the 12 buyers buy from 4 suppliers (with their maximum of 3 buyers each) and no buyer makes anything. The second level corresponds to the situation where 9 buyers are consistently matched to 3 suppliers and the other three buyers are either making or buying, but not all three from the same supplier at the same time. Also, there is much switching between suppliers in this case, so these three buyers form no long-lasting relations. The "nal level (0.8) corresponds to the situation when even more buyers are not consistently buying from the same supplier who is matched to his maximum number of buyers. If the simulation is re-run with 12 buyers but only 4 suppliers, most of the runs quickly lock in to the "rst level described above.
Fig. 7. Buyers'normalized pro"ts in 25 runs of experimentd"0.35.
Fig. 8. Buyers'weighted averagea.
and more strongly when di!erentiation is higher. Whend"0.75, there is hardly any e!ect on this variable: because there is no outsourcing at all in this case, the pro"t that is made is the same no matter which value was used fora, so no one value is better than the rest in this sense. Because the buyers do attain maximum normalized pro"t when di!erentiation is higher, the higher weighted average
relatively high pro"ts are correlated with&no making'(only buying), and a rela-tively low weighted averagea! This seems to imply that the individual agents are often not able to learn what is best for them, due to the interactions they have with other agents and due to the fact that, collectively, they create a situation that they adapt to, while the situation is changingbecausethey are all adapting to it. Further research will be done to investigate this correlation in more detail.
11. Discussion
This study aimed to explore and illustrate the use of the methodology of agent-based computational economics (ACE) for modelling the emergence of inter-"rm co-operation and trust. When the full implications of bounded ra-tionality are accepted, we need such a process-based approach. Rather than knowing in advance what is optimal, agents need to adapt perceptions and evaluations on the basis of experience. Perceptions and evaluations of pro" tabil-ity and trustworthiness depend on experience in the sometimes chaotic and generally unpredictable making and breaking of relations among multiple agents. Whether this yields e$cient outcomes is not to be assumed but to be investigated. In view of uncertainties and path dependencies that arise in the making and breaking of relations, optimal outcomes are not guaranteed.
As the central challenge we took the modelling of adaptive trust: its adapta-tion in view of perceived loyalty, its role next to pro"t in the choice of partners, and adaptation of the weight attached to trust in view of realized pro"ts. The main conclusion is that such a model is feasible, in a form that reproduces the core issues of transaction cost economics. The model endogenizes the&make or buy' issue. It incorporates the positive e!ect of di!erentiated products on pro"t as well as the associated problem of switching costs. It incorporates the trade-o!between the higher pro"tability of di!erentiated products and the scale advantages of a standard product. The model allows us to track how trust and its role in partner evaluation evolve under di!erent conditions, such as the degree and pro"tability of product di!erentiation, strength of economy of scale, opportunities for learning by doing, and basic levels of trust that prevail in a society.
after adaptation settles down in a stable outcome, and that this outcome varies between runs. This re#ects the path dependency that arises in the making and breaking of relations: paths to optimal results can get blocked.
We have hardly scratched the surface of experimentation. We can investigate the e!ects of di!erent initial conditions concerning the level and weight of trust, and the level of basic trust, re#ecting di!erences in institutional environment. We can test the robustness of outcomes, e.g. under the invasion of opportunists into a setting with high levels and weights of trust. Or vice versa: the perspectives for altruists in an opportunistic setting.
The model is also amenable to important extensions. We aim to extend the model with a threshold of resistance to opportunistic temptation of switching to more attractive partners. An agent will defect from an existing relation only when the gain in expected pro"t exceeds the threshold. We can then compare the e!ects of di!erent levels of such a threshold of loyalty. We can build in an adaptation mechanism of that threshold, similar to the current adaptation of the weight attached to trust, and observe how loyalty develops under di!erent conditions and starting values. We feel that this extension should be made before we proceed to more extensive and systematic testing and experimentation with the model.
In the current set-up switching costs arise only due to loss of learning by doing. We also intend to implement switching costs in the form of loss of speci"c assets. A technical complication is that the switching cost depends on the residual value of the asset after N periods of utilization, and this allows for a wide variety of speci"cations. When we add loss of speci"c assets, we can compare di!erent forms of governance, such as di!erent distributions of switch-ing costs between partners: the cost is shared equally, or the one who makes the investment pays, or the one who breaks the relation pays.
While the adaptation process (of the pro"t elasticity of preference scores) operates only on the experience of the agent himself, in contrast with genetic algorithms, the process is rather blind, or at least non-cognitive. Another extension of the model would be to delve more deeply into cognitive processes involved in adaptation.
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