Trust and firm internationalization: Dark-side effects on internationalization speed and how to alleviate them

In this conceptual paper, we draw attention to the conflicting effects that trust may have on internationalization speed, exploring the fact that trust is a major component of the influential Uppsala Model of firm internation-alization and considering internationalization speed as a multidimensional phenomenon. Building on the literature on trust and international business relationships, we argue that internationalization speed is initially fostered by the bright side of trust but its dark side prevails as the firm strengthens its relationships with foreign business partners. Inspired by research on how to suppress the dark side of trust before it emerges, we identify the choice between causation and effectuation as important in alleviating the negative effects of trust on internationalization speed. Therefore, besides making explicit the role of trust in understanding internationali-zation speed, our paper contributes to the International Business literature by examining the effects of decision logic in the internationalization process.


Introduction
The speed at which firms internationalize has an impact on their performance (Hilmersson & Johanson, 2016;Mohr & Batsakis, 2017;Musteen, Francis, & Datta, 2010) and can configure important managerial challenges (Jain, Celo, & Kumar, 2019;Johanson & Kalinic, 2016).In this context, internationalization speed is the rate of change that takes place in the internationalization process over time (Chetty, Johanson, & Martín, 2014;Hilmersson, Johanson, Lundberg, & Papaioannou, 2017), such as in the firm's level of foreign commitment, its foreign sales, or the number of foreign markets that it serves.This concept of internationalization speed is what can be called post-entry speed (Zahoor & Al-Tabbaa, 2021), and differs from other types of speed addressed in internationalization research such as the time to first foreign market entry (Chetty et al., 2014) and the rhythm of foreign expansion (Vermeulen & Barkema, 2002).Following the 2009 version of the well-known Uppsala Model, the progress of internationalization over time can be related to specific levels of knowledge, trust, and commitment that firms accumulate during internationalization (Johanson & Vahlne, 2009, p. 1424).
A well-established interpretation of the Uppsala Model is that internationalization is a slow process, as the firm's entry into a foreign market results from its ability to integrate and exploit the experiential knowledge it has gained in the business network (Johanson & Vahlne, 2009).However, slow speed is not an automatic outcome.Internationalization could be fast if the firm is able to transform experience into high levels of experiential knowledge and to develop business relationships characterized by high trust (Johanson & Johanson, forthcoming).Trust, then, becomes a vital element in the model.Since the Uppsala Model argues that trust is "a prerequisite for commitment" and also a potential "substitute for knowledge" (ibid, p. 1417), trust seems to have an impact on how slow or fast the process unfolds.Usually defined in terms of a willingness to rely on and/or become vulnerable before a partner (Blois, 1999;Rousseau, Sitkin, Burt, & Camerer, 1998;Zhong, Su, Peng, & Yang, 2017), trust has continued to play an important role in more recent versions of the Uppsala Model and in the research tradition that it has inspired (Vahlne, 2020;Vahlne & Johanson, 2020).By outlining trust as a core component of the internationalization process, the Uppsala Model makes room for conflicting expectations regarding internationalization speed.On the one hand, trust can foster internationalization by reducing uncertainty and information processing costs, and increasing satisfaction (Andersson, Blankenburg Holm, & Johanson, 2005;Gulati, 1998;Hansen, 1999).This is especially important given the uncertainties to be found in foreign markets and the challenges that appear when developing foreign business relationships (Johanson & Vahlne, 2009).On the other hand, beyond a certain level, trust can also contribute to a dark side of business relationships that constrains internationalization and induces blind-faith, complacency, and resource misallocation (Gargiulo & Benassi, 1999;Gargiulo & Ertug, 2006;Uzzi, 1997).Blind faith reduces all types of suspicion, which, in turn, makes the firm vulnerable to such an extent that it can be easily cheated; it is an efficient strategy as long as the firm is not exposed to opportunistic behavior, as blind faith implies that there are no protection or monitoring costs in the network.
Scholars have been aware of such dark-side effects since the early 1990 s (e.g., Moorman, Zaltman, & Deshpande, 1992); some of the early network-based firm internationalization research also acknowledged them (e.g., Coviello & Munro, 1997).In spite of this, the research tradition that has developed out of the Uppsala Model tends to see internationalization as a process that only reflects the bright benefits that firms can gain through long-term, trust-based business relationships.
In this conceptual paper, we investigate the following questions: How does the level of trust that a firm accumulates toward its foreign business partners affect its internationalization speed?What can be done to alleviate the dark side of trust?By focusing on internationalization as the process that unfolds after the decision to become international has been taken, we discuss the situation of firms that have some minimal level of insertion in some type of international business network.Therefore, they hold business relationships with one or more foreign partners, regardless of the development of such relationships.Given that foreign relationships are the major connections shaping what firms learn about foreign markets and how they commit resources to foreign activities (Jansson & Sandberg, 2008;Johanson & Vahlne, 2009), we focus on how such relationships and their associated trust levels affect the progression of internationalization.We look at what Zhong et al. (2017) call "unidirectional" trust: the trust that one firm in an interorganizational relationship places on its counterpart and whose level does not necessarily match the trust that this counterpart holds towards it (McEvily, Zaheer, & Kamal, 2017;Wang, Zhang, & Zhou, 2020;Zaheer & Harris, 2006).We acknowledge the dark side of trust as a potential outcome of the development of insidership in foreign business networks (Blankenburg Holm, Johanson, & Kao, 2015;Forsgren, 2016) and discuss how firms can mitigate its possibility.
Inspired by research on how to suppress the dark side of trust before it emerges (Anderson & Jap, 2005;Dant & Gleiberman, 2011), we identify the choice between planning-based decisions (also called causal decisions) and decisions that leverage available resources and emerging opportunities over planning (also called effectual decisions, from Sarasvathy (2001) Effectuation theory) as an important part of this process.Such an idea extends the understanding of firm internationalization found in the Uppsala Model, which includes some comments about Effectuation (Johanson & Vahlne, 2009, p. 1423) but does not enter into the details of the decisions that guide firms through internationalization (Coviello, Kano, & Liesch, 2017;Dow, Liesch, & Welch, 2018).In fact, from its inception the Uppsala Model has conceived internationalization as a firm-level phenomenon (Johanson & Vahlne, 1977, p. 26;Vahlne & Johanson, 2017, p. 1089).Therefore, in addition to making explicit the role of a less visible variable such as trust in understanding internationalization speed, something that has been absent in previous explanations of this concept (c.f., Chetty et al., 2014), our paper contributes to the International Business literature by examining the role of decision logic in the internationalization process.
After this introduction, we review the literature on trust in business relationships and specify how speed materializes in an internationalization process framed by the Uppsala Model.This is followed by an evaluation of the alternatives that firms may have to alleviate the liabilities arising from the dark side of trust.We finish with an analysis of our contributions, directions for future research, and some limitations.

Trust within foreign business relationships
In the research involving business relationships, the term trust is used frequently and has been conceptualized in different ways (Blois, 1999;Rousseau et al., 1998).Some authors define it as a belief or confident expectation directed toward another party, like in a "willingness to rely on an exchange partner" (Moorman et al., 1992, p. 315).Others add to this idea of trust a disposition to be vulnerable toward a partner, like in a "willingness to take risk" (Schoorman, Mayer, & Davis, 2007, p. 346).For Morgan and Hunt (1994), the willingness to act and become vulnerable is implicit in a definition of trust that emphasizes the genuine confidence of one partner with another.In this vein, we follow Zhong et al. (2017) in accepting that both belief and behavior are legitimate and logically interrelated components of trust.
We also follow authors such as McEvily et al. (2017) and Wang et al. (2020) in accepting that trust may not accumulate symmetrically on each side of an interorganizational relationship.This is the case especially in cross-border relationships, whose uncertainties can make perceptions vary widely across the dyad (Zaheer & Zaheer, 2006).Considering that each firm in an interorganizational relationship may have its own set of reasons to trust or not the other party (McEvily et al., 2017;Zaheer, McEvily, & Perrone, 1998), we focus on analyzing the "unidirectional" trust that a firm places on a foreign business partner during internationalization (Zhong et al., 2017).In a position as trustor, the firm may fall prey to the dark side of trust when trusting too much.When it comes to identifying a firm that might be too trusting, the literature offers conflicting insights.On the one hand, authors such as McEvily et al. (2017) indicate that the party that experiences lower exchange hazards and holds more power is more likely to trust its counterpart.On the other hand, authors such as Brito and Miguel (2017) suggest it is the weaker party that tends to be the one investing in trust building more than its counterpart.Although these differences prevent us from setting boundaries that could be useful to our discussion, they suggest that we should develop our theoretical reasoning by simply assuming that the firm that expands abroad may risk trusting its counterparts too much, without worrying about the causes of this behavior.We make some comments about the effects of resource availability at the end of our discussion in section 5.1, which can be related to the effects of firm size and age on our arguments.
From a relational perspective1 , trust embodies noneconomic factors that complement transactional mechanisms in the governance of exchange relationships (Dyer & Singh, 1998;Kingshott, 2006;Zaheer & Venkatraman, 1995).This is the case with norms of reciprocity and cooperation, which lead firms to act in good faith and make long-term commitments toward their counterparts without fearing opportunistic behavior.In general, trust-building takes time and tends to require relationship-specific investments that can make it quite costly (Adobor, 2005;Blois, 1999).This is because trust accumulates gradually over the history of repeated exchanges between two partners, which signal to each other how reliable their partner is and whether they intend a longterm relationship.Such signals of reliability and loyalty are particularly important in the context of international business relationships, which are affected by the additional challenges of foreign market uncertainty and cultural distance between home and host markets (Leonidou, Aykol, Fotiadis, Christodoulides, & Zeriti, 2017;Malik, Ngo, & Kingshott, 2018).
In this way, trust is seen both as an element that facilitates foreign business relationships and as a product of foreign relationship development (Boersma, Buckley, & Ghauri, 2003;Madhok, 2006).This idea reflects the dynamic of trust in interfirm relationships in general, starting with the greater openness about sharing strategic knowledge that exists when business partners trust one another (Gulati & Gargiulo, 1999;Uzzi, 1996).This may include sensitive knowledge about market opportunities or other firms, lessons learned from past experiences, or proprietary product knowledge.Such knowledge sharing makes collaboration and joint problem solving possible (Ring & Van de Ven, 1994).In addition, trust can be a powerful driver behind the willingness to make the extra commitments necessary for relationship-specific investments (Gounaris, 2005;Morgan & Hunt, 1994).With trust, firms are likely to be more inclined to make the investments necessary to address the needs of trusted partners and show more flexibility toward them (Mooi & Frambach, 2012).A process of mutual adaptation takes place when both partners make additional commitments to each other.
Besides developing out of experience accumulated within the dyadic business relationship, the trust that one firm has in another may also be based on the counterpart's past performance, which is transformed into reputation and distributed throughout the network.This is especially important at the beginning of a business relationship, when the firm may trust its counterpart because other firms have vouched for its reliability.In other words, the network surrounding the business relationship is not decoupled from the trust prevailing between the counterparts.In a similar way, the network can also be a source for information that a potential or existing counterpart does not deserve to be trusted.Rumors and reputation can prevent a firm that is not trustworthy from building relationships in a network, making it stigmatized.If such a situation occurs, a significant amount of resources committed to the network may be required to demonstrate that the firm deserves to be trusted once more.
Some researchers have argued that firms may experience several liabilities when they develop too much trust in a business partner.One such liability is network rigidity, a term which represents how difficult it can be for firms to coordinate a network of relationships, cut old linkages, and enter new ones (Gargiulo & Benassi, 2000;Thorgren & Wincent, 2011).Rigidity may emerge from the pressure to correspond to partners' reciprocity expectations or when firms experience relational inertia (Gargiulo & Benassi, 1999;Gargiulo & Ertug, 2006).These problems can lock firms into questionable exchanges that lack timely and accurate feedback, thereby compromising their performance (Villena, Revilla, & Choi, 2011).Another problem of excessive trust is the potential for resource misallocation, which can take the form of unnecessary obligations or a sense of reciprocity toward a partner beyond what could be considered efficient (Gargiulo & Ertug, 2006;Wicks, Berman, & Jones, 1999).Coupled with network rigidity, these effects suggest that high trust in existing relationships can become a trap for firms.
In an internationalization context, Forsgren (2016) expressed similar ideas using the concept of liability of insidership.He meant that the firms' embeddedness in foreign business networksits development of strong, trust-based relationships with foreign business partnerscould actually create rigidities and inefficient obligations.Over-embeddedness may occur when a web of strongly connected and inter-connected relationships surrounds the firm, forming a network that is likely to prevent change and development in general, and thus limiting the firm's room for maneuver.This situation is critical to the extent that the Uppsala Model has made insidership synonymous with successful internationalization and has characterized foreign expansion as a process of overcoming outsidership, the lack of connections within foreign business networks (Johanson & Vahlne, 2009).Insidership starts to develop when the firm establishes its first relationship with a partner in a foreign business network and evolves as the firm enters new relationships in the same network or strengthens its existing ones (Blankenburg Holm et al., 2015;Hilmersson & Jansson, 2012).If the negative consequences of building too much trust within business relationships are acknowledged, higher insidership may in fact be perceived as a constraint on further internationalization.

The speed of the internationalization process
Before discussing how the bright and dark sides of trust may affect internationalization speed, we must first specify how internationalization speed materializes in a process like the one outlined by the Uppsala Model.The modern Uppsala Model was introduced in 2009 and characterizes internationalization as a process that takes place in the context of networks of business relationships (Johanson & Vahlne, 2009).This view updated the original model, introduced in 1977, which described internationalization as a sequential process through which firms grew their commitment to increasingly distant markets as they learned more about them.The 2009 model, rather, describes the state of a firm's internationalization at any given moment in terms of its network position and its knowledge of opportunities, capabilities, and resources.According to the revised model, such variables affect how internationalization evolves through subsequent resource commitment, learning, knowledge-creation, and trust-building (Fig. 1).
The change variables relationship commitment decisions, learning, and trust-building, highlighted in bold, will be closely discussed throughout this paper.The Uppsala Model assumes that all of the learning about foreign markets and opportunities, as well as all of the commitment that firms undergo, occur mostly within relationships."There is nothing outside relationships", as Johanson and Vahlne (2003, p. 93) have established.
Although the Uppsala Model features no explicit temporal concepts, its representation as a recurring loop involving state variables and change processes suggests time as an implicit dimension that accumulates as internationalization unfolds.Such a materialization of time does not set a deterministic flow of events although it continues to follow a forward progression shaped by specific causal relationships (George & Jones, 2000;Hurmerinta-Peltomäki, 2003).Time in the Uppsala Model can also be regarded as objectively measurable rather than subjectively perceived by individuals (Ancona, Okhuysen, & Perlow, 2001;Hurmerinta-Peltomäki, 2003), given that individual actors are only implicitly included in the model and all of the model's arguments refer to firm behavior (Johanson & Vahlne, 2009).From that, the flow of time can be objectively verified in the succession of observable events that change the state of firm internationalization (Johanson & Johanson, forthcoming).
Among the change variables affecting firm internationalization, the only change forces that Johanson and Vahlne described as being visible to external observers are relationship commitment decisions.In other words, despite the prominent role of trust and learning in the Uppsala Model, relationship commitment decisions must be examined to see the L. Oliveira and M. Johanson internationalization process unfolding objectively.These decisions may manifest in "changes in entry modes, the size of investments, organizational changes, and definitely in the level of dependence" (Johanson & Vahlne, 2009, p. 1424).The Uppsala Model further establishes that commitment decisions may appear either in the development of new foreign business relationships or investments in the existing ones.If the firm expands its internationalization by investing in new business relationships, it can, in addition, choose between establishing new relationships within the same market or approaching business networks in new locations (Andersen & Buvik, 2002).This suggests that one visible dimension where changes in firm internationalization result from commitment decisions is the number of countries that the firm serves.

State Change
While investments in existing relationships do not change the number of countries in the firm's international profile, they may still lead to distinct international footprints, given that certain commitment decisions may result in different operation modes and largely distinct commercial outcomes.Indeed, the share of foreign sales and the share of foreign assets represent, respectively, performance and structural indexes for the degree of firm internationalization (Sullivan, 1994).Altogether it seems reasonable that a temporal analysis of the internationalization process described in the Uppsala Model incorporates not only changes in firms' dispersion of international markets (that is, the number of countries they serve) but also changes in international commercial intensity (that is, their exporting intensity or percentage of foreign sales) and commitment of foreign resources (that is, the percentage of their assets located abroad).These are the same dimensions that Casillas and Acedo (2013) considered in their multidimensional view of internationalization speed.
It is worth noting that internationalization speed can be negative, leading to a retraction in the state of a firm's internationalization.Such retractions may result, for instance, from reductions in firms' commitment to foreign markets as a product of either strategic intent or external shocks (Benito, 2005;Benito & Welch, 1997).Nevertheless, the outcomes of these decisions are still compatible with the dimensions outlined above.

Effects of trust on internationalization speed
While the product of commitment decisions is observable and gives form to internationalization speed, less visible change variables in the Uppsala Model can be used to explain the mechanisms associated with perceived levels of speed.As previously mentioned, trust, knowledge, and commitment represent the basic elements behind the internationalization process that Johanson and Vahlne (2009) have outlined.Considering that the relationships between these elements can be mapped in the same way the processes of trust-building, knowledge accumulation, and commitment building can be seen to interact, the outcomes of these relationships, over time, define internationalization speed.One such interaction configures the direct effects of trust on commitment and another one reports the indirect relationships between these variables, mediated by knowledge accumulation (Fig. 2).In both cases, internationalization speed is initially fostered by the bright side of trust but, as the firm strengthens its foreign business relationships, the dark side comes increasingly to prevail.Johanson and Vahlne (2006, p. 172) have already indicated that "cooperation breeds trust and trust breeds cooperation".This suggests that the relationship between trust and commitment in foreign business relationships forms a potentially reinforcing cycle.When a firm accumulates trust toward a foreign business partner, it is likely to dedicate more time and resources to them as a signal of its long-term commitment to the relationship or its expectation of future reciprocity from it (Cropanzano & Mitchell, 2005;Hallén, Johanson, & Seyed-Mohamed, 1991).The more time and resources a firm puts into a relationship, the more repeated interactions it is likely to have with its partner, and the better will be the conditions for further trust-building and additional commitment toward that relationship.

Direct effects of trust on internationalization speed
As the firm dedicates more time and resources to particular foreign relationships, one can also expect that it will be able to sell more of its products and services abroad.This should happen because the firm may become a more capable supplier over time, developing solutions that fit the particular needs of its foreign partners and receiving a larger share of their orders.The firm may enter new markets as a result of this process, like when foreign partners ask it to be their supplier across various countries in order to prioritize efficiency gains and take advantage of the benefits of the mutual adaptation between them.The firm may also proactively seek additional opportunities in markets adjoining those of its foreign partners in order to gain economies of scale that justify its additional commitment, such as setting up a local manufacturing plant or distribution center.Finally, existing relationships may facilitate the emergence of new relationships due to the transitivity of trust: if a potential new partner is trusted by one of the firm's existing partners, it becomes easier for that firm to trust and do business with this new firm (Gulati, 1995;McEvily & Zaheer, 1999).This means that trusted foreign partners may, through expansion in existing foreign markets or new foreign market entries, facilitate further internationalization.
In spite of that, excessive trust in a business partner will probably lead the firm to focus its commitments on existing markets and

Internationalization Speed
-Commitment of foreign resources -Dispersion of international markets -International commercial intensity

Trust accumulated in foreign business relationships
Market-Specific Knowledge Fig. 2. Relationships between trust and internationalization speed.
L. Oliveira and M. Johanson relationships beyond efficient levels instead of concentrating on new relationships and entering new territories.This effect happens because, as it strengthens existing relationships, the firm's capacity to divert its attention to new relationships becomes compromised.As Forsgren (2016Forsgren ( , p. 1142) points out, "if this were to mean that old relationships must be abandoned for new ones", the firm may hesitate.Strong foreign business relationships can also drain significant resources if they require excessive relationship-specific assets or if the firm engages in progressively costlier attempts to make them efficient, resulting in an escalation of commitment (Brockner, 1992;Staw, 1981).The more commitment is accumulated in a given course of action, the more likely the firm will find itself pursuing paths of self-justification and ignoring negative feedback from inefficient relationships.Under this disproportional and inefficient evolution of commitment toward specific business relationships, the firm is likely to reduce its speed of new market entry and the commercial viability of its existing foreign activities is likely to deteriorate, impacting the development of its foreign sales.Each business relationship requires time and resources to prosper; but it is also necessary that the firm focuses its strategy on the relationships, which is especially the case when trust emerges.Gaining a strong insidership in a business network may lead to a lack of acquisition of new competences as most activities will be performed in the existing relationships, locked into the requirements of the same business partners.A too strong relationship, with too strong trust, is thus likely to eventually slow a firm's learning and flatten the curve of its skills acquisition.When the relationship reaches such a situation it is likely to contribute to making internationalization speed approach a threshold after which speed begins to decelerate.A consolidation phase begins, where the firm has to concentrate on existing relationships rather than to keep a high internationalization speed.The internationalization may continue but will do so at a slower speed.
Altogether, we expect that the trust accumulated toward foreign business partners initially benefits firm internationalization by fostering commitment and, with that, new market entries and superior foreign sales.However, as that level of trust toward foreign partners becomes higher, commitment levels may escalate while the remaining indicators reverse their trends: the rate of new market entries may decrease and foreign sales may suffer.Both market entries and foreign sales to customers in business networks abroad require market-specific and relationship-specific commitment.As the firm's resources and capacity to learn are limited, the firm may face the need to exclude alternatives, that is other customers and business networks.An increase in trust is thus likely to positively influence internationalization speed through faster commitment, but only to a specific point before the effect fades and eventually decreases.This is because further increases of speed are constrained by the additional consolidation and management effort required.Firms generally find it more important to take care of existing investments rather than continually pursuing internationalization speed.Moreover, too much trust tends to limit further learning that could come from diversifying business partners, thereby creating a spiral of increasing dependency in relation to existing, highly trusted relationships.When trust becomes too strong, therefore, firms need to consolidate their existing business, an action that can be expected to decrease speed of entry into new foreign markets and speed of commercial intensity.Hence: • P1a.There is an upward curvilinear relationship between the level of trust that a firm accumulates toward a foreign business partner and the speed of its resource commitment to the relationship with that partner.• P1b.There is an inverted U-shaped relationship between the level of trust that a firm accumulates toward its more trusted foreign business partners and the speed at which it enters new foreign markets over time.• P1c.There is an inverted U-shaped relationship between the level of trust that a firm accumulates toward its more trusted foreign business partners and the speed at which it expands its international commercial intensity over time.
Since trust usually accumulates over time, depending on relationship commitment, the more trusted foreign business partners mentioned in P1b and P1c should be those with whom the firm has lengthier relationships or who account for a larger share of its relationship-specific investments.

Indirect effects of trust on internationalization speed
The idea that firms tend to increase their foreign commitment over time after learning from trusted partners has been central to the evolution of the Uppsala Model (Johanson & Vahlne, 1977, 2009).In fact, learning from the experience of foreign partners can be an important source of market-specific knowledge, which is knowledge that is specific to particular social, political, and economic contexts (Eriksson, Johanson, Majkgard, & Sharma, 1997;Hilmersson, 2014).Firms can then use this knowledge to inform their operations within the host market, helping them to identify suppliers and clients and understand their preferences.Although business networks can stretch beyond national borders, market-specific knowledge conveys the unique features of business actors, cultures, and formal institutions in individual country markets (Sandberg, 2014).It is normally acquired through direct activities in a host market, although this process can be accelerated when firms draw on the experience of foreign partners (Barkema, Bell, & Pennings, 1996;Makino & Delios, 1996).
Market-specific knowledge can facilitate the expansion of business activities in the countries where that knowledge is relevant and in those considered similar to them (Johanson & Vahlne, 1977).It can reduce perceived uncertainty, thus opening the way for additional commitment and increase the relevance of foreign operations, expanding foreign sales.Therefore, besides its direct effects, one can also expect that trust promotes internationalization speed along its various dimensions through knowledge accumulation: increased commitment abroad, additional market entries, and larger foreign sales (Johanson & Johanson, forthcoming).However, limitations to these effects may exist when trust assumes too high levels.One such limitation refers to the scope of the market-specific knowledge that the firm can access through trustbased relationships.Another limitation regards the extent to which learning from trusted partners can be considered beneficial in the first place.
In terms of the first limitation, the previously outlined effects of learning from trusted partners are naturally constrained by the marketbounded validity of the knowledge that they can offer.Although marketspecific knowledge may help a firm when entering and expanding its operations in specific markets, entering multiple, distinct locations tends to require a form of knowledge that is neither market-nor entry-mode specific.Such a knowledge type is called internationalization knowledge and is related to a general understanding of how to design, implement, and manage international operations in a broad sense (Eriksson et al., 1997;Fletcher, Harris, & Richey, 2013).This is a procedural form of knowledge that is usually accumulated through the formalization of experience acquired from diversified international settings (Blomstermo, Eriksson, Lindstrand, & Sharma, 2004;Fletcher et al., 2013).If a firm learns too much about a limited set of markets through its trusted partners, it may not build enough internationalization knowledge to enter more diverse locations, especially in different geographic regions.Its additional commitments will likely target existing markets or be limited to the markets that can be deemed similar to them.
In addition, business relationships marked by too high levels of trust can make the firm vulnerable to exogenous shocks and insulate the firm from information beyond its networks (Uzzi, 1997).Too much trust can make knowledge sources redundant and prevents innovation, hindering the firm's ability to adapt to changing market contexts and requirements (Huggins, 2010; Molina-Morales, Martínez-Fernández, & Torlò, 2011).
As Smith-Doerr and Powell (2004, p. 30) put it, "the ties that bind can also become the ties that blind".This effect is called cognitive lock-in and represents a reduction in the range of experiences from which firms may draw to build their knowledge stock (Gargiulo & Ertug, 2006).In an internationalization context, progressive insidership may lock a firm into a particular set of foreign relationships, causing it to focus its commitments on those relationships only.When commitment decisions are restricted to incremental action paths in relationships where information is redundant, we can also expect progressively reduced commercial returns from internationalization efforts.In light of these effects, we propose: • P2.The accumulation of market-specific knowledge mediates: o a.An upward curvilinear relationship between the level of trust that a firm accumulates toward a foreign business partner and the speed of its resource commitment to the relationship with that partner.o b.An inverted U-shaped relationship between the level of trust that a firm accumulates toward its more trusted foreign business partners and the speed at which it enters new foreign markets over time.o c.An inverted U-shaped relationship between the level of trust that a firm accumulates toward its more trusted foreign business partners and the speed at which it expands its international commercial intensity over time.

Alleviating the liabilities of trust in firm internationalization
Previous research has discussed the possibility of optimizing trust as a way to balance the bright and dark-side effects it has on business relationships (Molina-Morales et al., 2011;Parkhe & Miller, 2000;Stevens, MacDuffie, & Helper, 2015;Wicks et al., 1999).However, there are only limited applications of this approach since optimal levels of trust cannot be quantified exactly (Stevens et al., 2015) and trust levels can only be verified as excessive after they become a problem (Gargiulo & Ertug, 2006).An alternative suggestion by Thorgren and Wincent (2011) focuses on handling situations when rigidities stemming from trust are notably pronounced, such as problem sharing, benchmarking, negotiation, and evaluation.The problem with this idea is the fact that these strategies apply to conflict situations which are easy to spot.Liabilities of trust, however, are often rather subtle and difficult to identify.When it comes to business relationships in an internationalization context, cultural and institutional differences can create even more noise that can further prevent firms from perceiving their biases and blindnesses.Anderson and Jap (2005) outline a more promising approach by listing strategies that could be followed in order to suppress the dark side of close business relationships before it emerges.For instance, they suggest regularly evaluating older relationships, developing backup plans, and maintaining an awareness of profitability and potential losses.They also maintain that symmetric commitment and common goals should make both partners actively interested in the success of their business relationship.Similarly, Dant and Gleiberman (2011) stress the importance of clearly specifying and periodically re-examining mutual expectations, conflict handling mechanisms, and dedicated assets brought by each partner into a business relationship.In practice, such recommendations emphasize the importance of cultivating systematic routines that enable the periodic assessment of the performance and utility of business relationships rather than letting them develop organically with little direction or oversight.
When it comes to firm internationalization, a growing body of research has employed the terms causation and effectuation to indicate that firms can follow approaches that are more or less structured when making decisions related to foreign expansion (Karami, Wooliscroft, & McNeill, 2020 & Parente, 2019).These terms were originally coined by Sarasvathy (2001), with causation representing an attitude that prioritizes scenario analysis and clear goals while effectuation focuses on making the most of available resources and leveraging emerging opportunities.In this paper, we use the term effectuation to refer to this less structured way of making decisions, whose focus is on controlling resources and contingencies; we do not attempt to establish a formal connection with the theory of the same name that Sarasvathy developed to describe what can be called effectual decisions.Inspired by Anderson and Jap (2005) and Dant and Gleiberman (2011), we expect that firms adopting causation and effectuation experience to different degrees the liabilities caused by the trust accumulated toward foreign partners, with consequences for their internationalization speed.

Effects of the decision approach on the liabilities of trust
Compared to effectuation, the adoption of causation may be a more useful way to manage the direct negative consequences of trust for internationalization speed.First, there is the fact that success for firms adopting effectuation is understood as "a mutually negotiated consensus among stakeholders" (Sarasvathy, Dew, Velamuri, & Venkataraman, 2010, p. 82), while those following causation define success in exact terms and search for a means to achieve it (Sarasvathy, 2001).They do not incorporate other firms in their decision-making.
This means that a firm using causation will focus on finding ways to reach well-defined goals, predicted in advance, such as minimum levels of foreign market share or increasing foreign sales in specific markets (which can be expressed in quantitative terms that do not involve trust dimensions).If it follows effectuation, a firm is likely to be bounded by its alignment with foreign partners and by criteria that may be abstract and difficult to implement, such as a shared vision of the future driving their collaboration (Chandler, DeTienne, McKelvie, & Mumford, 2011;Sarasvathy et al., 2014).This suggests that causation may be better than effectuation in minimizing the resource misallocations that might happen due to trust, considering that the use of explicit assumptions and metrics may avoid commitments driven by reciprocity only.
Causation may also contribute to preventing a situation in which internationalization speed is limited by an escalation of the commitment to trusted partners.Accordingly, researchers have verified that commitment escalation is more likely when goals are vague than when they are explicit (Kernan & Lord, 1989;Sleesman, Conlon, McNamara, & Miles, 2012).They have also shown that the salience of neglected opportunities and information acquisition can reduce its likelihood, while social pressures and organizational interdependencies can foster it (Sleesman et al., 2012).As the goals and targets in causal decisionmaking are easy to codify, it follows that trust, which is difficult to codify, is less important for causation.
Given that causation provides the definition of explicit goals and extensive systematic searches for alternative means to reach them as safeguards (Fisher, 2012;Sarasvathy, 2001), firms employing it should be able to avoid the trap imposed by high trust and see the benefits reflected in their internationalization speed.Conversely, for firms adopting effectuation, the focus on the resources under their control may make them more exposed to an escalation of commitment, given that such a behavior can be associated with a perception of control (Drummond, 1995;Keil, Depledge, & Rai, 2007).
In line with Kerr and Coviello (2020), who argue that when a firm pursues an effectual strategy it is likely that its counterpart does the same, since effectuation is based on networks, we contend that there is a positive link between trust and effectuation.To Sarasvathy (2001) three classic questions, therefore, we could add a fourth: 'Whom do I trust?' Trust gives the firm a sense of security (Goel & Karri, 2006) but at the same time leads to the exclusion of other alternatives, thus reliance and vulnerability increase.When a firm trusts its business partner more than is necessary, and more than the situation requires (Karri & Goel, 2008), over-trust emerges.
With comparable levels of trust accumulated toward foreign business partners, the lower escalation of commitment that seems possible with causation may make certain resources available that firms may employ in new market entries and opportunities.With that, they can produce more foreign sales than firms using effectuation.In line with this, Ciravegna, Majano, and Zhan (2014) have shown that firms with a more proactive attitude toward searching out foreign business opportunities tend to export more and to enter a higher number of markets, compared to others that base their expansion plans on serendipitous events.We thus expect: • P3a.The direct (upward curvilinear) relationship between the trust accumulated toward a foreign business partner and the speed at which the firm commits resources to the relationship with that partner is weaker when it adopts causation than with effectuation.• P3b.The direct (inverted U-shaped) relationship between the trust that a firm accumulates toward its more trusted foreign business partners and the speed at which it enters new foreign markets over time is weaker when it adopts causation than with effectuation.• P3c.The direct (inverted U-shaped) relationship between the trust that a firm accumulates toward its more trusted foreign business partners and the speed at which it expands its international commercial intensity over time is weaker when it adopts causation than with effectuation.
Because causation and effectuation, understood as distinct approaches to decision-making, lead firms to employ their means and learn about alternatives differently, they may also modify the indirect negative effects that trust can cause on firms' internationalization speed through knowledge accumulation.Effectual decisions build essentially on firms' identities, their knowledge stocks, and their networks to ultimately answer the question of what is possible to do (Sarasvathy, 2001;Sarasvathy et al., 2014).To overcome limitations derived from existing resources, firms employing effectuation rely on networking strategies to expand their available means with those of their stakeholders.Firms adopting causation, on the other hand, assume their future is somewhat predictable and use such predictions to guide their search for resources (including knowledge) that can secure them favorable outcomes (Wiltbank, Dew, Read, & Sarasvathy, 2006).
Given that causation and effectuation inspire distinct attitudes toward knowledge, firms employing effectuation are more likely than those adopting causation to be over-embedded in the foreign market network and trapped by the knowledge that they access through foreign business relationships.In fact, because experience is accumulated by interacting in the business network, the focus of effectuation on the resources and relationships at hand will likely result in the incremental accumulation of market-specific knowledge until unexpected events disrupt such a pattern.In the absence of unexpected opportunities to break this cycle (Kalinic, Sarasvathy, & Forza, 2014), the knowledge accessed by firms through foreign business partners may contain elements of limited market validity and feature considerable redundancy.
Causation, on the other hand, may help to drive firms outside their knowledge domains, if this is required for achieving their goals.In other words, firms adopting causation will probably exhibit a more proactive attitude toward the acquisition of more diverse, but still market-specific, knowledge than those using effectuation.This idea falls into line with results reported by Chetty, Ojala, and Leppäaho (2015), which suggest that firms adopting causation tend to be more adventurous in exploring psychically and culturally distant countries than those using effectuation.Firms who pursue causation select a target market first and only then start looking for ways to overcome the eventual liabilities of outsidership.Firms pursuing effectuation, on the other hand, are more likely to accumulate knowledge limited to the activities that they perform in their business networks.
In this sense, we contend that the relationship between trust in existing business relationships and the accumulation of knowledge about specific foreign markets is strengthened by the emphasis that effectuation puts on knowledge acquired through experience in the network.By adopting causation, firms can be exposed to more diverse environments and hence to more diverse learning.Such learning can induce the accumulation of internationalization knowledge, which contains general procedures, rules and guidelines on how to enter foreign markets.Thus, we expect: • P4a.The adoption of causation instead of effectuation weakens the direct relationship between the trust that a firm accumulates toward a foreign business partner and the knowledge it gains about specific foreign markets.• P4b.The adoption of causation instead of effectuation weakens the direct relationship between the trust that a firm accumulates toward its more trusted foreign business partners and the knowledge it gains about specific foreign markets.• P4c.The adoption of causation instead of effectuation weakens the direct relationship between the trust that a firm accumulates toward its more trusted foreign business partners and the knowledge it gains about specific foreign markets.
Propositions P3a-c suggest that, for comparable levels of trust toward foreign business partners, firms adopting causation may grow relationship commitment at a slower speed than firms adopting effectuation, although the former firms may enter more markets and sell more abroad than the latter.A similar picture may derive from P4a-c, although less explicitly, as an effect of the reduced constraints that causation, compared with effectuation, puts on the diversity of market-specific knowledge that the firm accumulates during internationalization.Such expectations, however, seem to contradict those that Prashantham et al. (2019) outline in their discussion of the effects of causation and effectuation on the speed that international new ventures (INVs) can develop after entering foreign markets.These authors argue that the adoption of effectuation dampens the speed of foreign commitment but fosters the speed of new market entries, whereas causation triggers increasing commitment but decreasing new market entries over time.Their analysis of commitment speed is based on a contrast between effectuation's open but careful approach to decisions, on the one hand, and the deliberate way in which causation guides firms to commit to their goals, on the other.They also assume that effectuation, by privileging nonsystematic interactions instead of goal-constrained search efforts, should produce more opportunities for the fortunate accidents (or serendipity) that can help firms to enter new markets rapidly.
We consider that Prashantham's et al. (2019) arguments should be correct as long as the focus is on the resource-constrained reality of INVs, which are usually small companies with an early insertion in foreign markets (Oviatt & McDougall, 1994).As firms grow in age and size, however, they may have different perspectives on the levels of resources they can afford to commit using effectuation-based decisions, due to their higher resource availability.As they grow, bad investments are not as much of a threat to their survival as is the case for smaller firms.Given that older or larger companies are likely able to afford larger investments, though, they may be more exposed than smaller firms to the escalation of commitment that we associated earlier with high trust and effectuation adoption.It is thus especially important for these firms to have clear goals and specific criteria in place to be able to evaluate the utility of their relationships.Therefore, we maintain that causation is more likely to control the level of commitment speed, for comparable levels of trust, when firms have greater available resources.
In addition, firms with more available resources may also be able to build a portfolio of foreign investments that offers them more or better opportunities than those stemming from random, fortunate accidents.Resource-constrained companies do not have such alternatives; hence, they are likely to be better off by leveraging emerging opportunities.This point suggests that causation may be a better tool for larger/older firms than for smaller/younger ones in increasing their rate of new market entries at comparable levels of trust.The speed at which foreign commercial intensity levels grow should be related to foreign investments and the scope of foreign activities; hence, it may be similarly subject to the effects of resource availability.Altogether, we reconcile our propositions with Prashantham et al. (2019) by arguing that the level of resource endowment of the firm under analysis (possibly proxied by its size or age) may moderate the effects of the decision logic that it adopts during internationalization.This should be particularly true for the effects outlined in P3a-c, which resulted from arguments that are more directly comparable with those listed by Prashantham et al. (2019).When the firm suffers from resource constraints, therefore, the effects anticipated in those propositions may be reversed.Hence: • P5a.Resource constraints negatively moderate the effects of causation on the direct relationship between trust and the various dimensions of internationalization speed (namely: commitment of foreign resources, dispersion of international markets, and international commercial intensity).• P5b.Resource constraints negatively moderate the effects of effectuation on the direct relationship between trust and the various dimensions of internationalization speed (namely: commitment of foreign resources, dispersion of international markets, and international commercial intensity).
Fig. 3 updates the model that we illustrated in Fig. 2 with the relationships suggested in our propositions.

Final remarks
In this paper, we have discussed how internationalization speed is affected by trust, a core element of the research tradition inspired by the Uppsala Model but one that is rarely acknowledged for its dark-side effects.Using the Uppsala Model as our base, we have outlined a model for internationalization speed and discussed how its dimensions could be affected when firms strengthen their insidership in foreign business networks by accumulating trust toward foreign business partners.We have also discussed the greater utility of causation, compared to effectuation, as a strategy to alleviate the liabilities caused by trust.From this base, our paper offers a number of important contributions and points to promising future research opportunities.

Theoretical implications
Our paper offers two major theoretical contributions to internationalization research in International Business.Firstly, while previous studies have largely neglected trust in the study of internationalization speed, we make the role of this less visible variable explicit.For instance, although Chetty et al. (2014) also use the Uppsala Model as the theoretical lens through which they approach internationalization speed, they do not look at the role of the change variables listed by Johanson and Vahlne nor do they consider the role of trust in the internationalization process specifically.It was our explicit focus on trust and the acceptance that its bright side cannot be taken for granted that gave us our new insights into how a firm's internationalization speed can be affected by its foreign business relationships.Oviatt and McDougall (2005) model of internationalization speed also falls short from fully acknowledging the role of trust.Rather than focusing on strong ties, which seem more likely to engender trust, they argue that weak ties are more important for internationalization and concentrate on them instead.Although some firms may indeed expand abroad by leveraging opportunities and taking advantage of the absence of strong relationships, particularly in technology-intensive industries, we argue that the Internationalization Speed -Commitment of foreign resources -Dispersion of international markets -International commercial intensity

Causation vs Effectuation
Resource availability P1a, P1b, P1c P2a, P2b, P2c P3a, P3b, P3c P4a, P4b, P4c P5a, P5b relational aspect of foreign business relationships is a more general phenomenon.This aspect is driven by the dynamics of trust that firms experience as they strengthen their relationships with foreign partners, with the potential for manifesting both bright and dark-side effects.
By outlining the role of trust and its dark side effect on the speed of the internationalization process, our paper illustrates a theoretical path that could benefit studies relating to other aspects of network internationalization.For instance, as Gargiulo and Ertug (2006) point out, excessive trust can induce blind faith and make a firm the victim of opportunistic behavior from its counterpart.As trust develops, a firm's decision-makers may be more inclined to be transparent and more willing to engage in risky business interactions, actions their partners may see as an occasion to be opportunistic (Villena et al., 2011).This kind of effect is little explored in the Uppsala Model, which sees opportunism and trust as mutually exclusive concepts (Johanson & Vahlne, 2009).Another aspect of network internationalization that could benefit from the insights gained from a dark-side perspective on trust is the liability of insidership.Although such liability can stem from excessive embeddedness and can be a potential antecedent to the dark side of trust (Forsgren, 2016), it is not sufficiently acknowledged in a body of literature that generally portrays relationship development only as a positive path to further internationalization.Besides overembeddedness, the extant literature (e.g., Noordhoff, Kyriakopoulos, Moorman, Pauwels, & Dellaert, 2011) points out that there are other aspects of the dark side of trust that can make insidership a considerable liability, such as the loss of objectivity (Grayson & Ambler, 1999) and the tendency to continue to rely on a business partner even when it is clear that the relationship should be terminated (Sorenson & Waguespack, 2006).
Our second contribution comes from the examination of the role of decision logic in the internationalization process.This has not been thoroughly investigated despite more than four decades of research surrounding the Uppsala Model (Vahlne & Johanson, 2017), its early association with firm decision systems (Johanson & Vahlne, 1977, p. 26), and a (brief) acknowledgment by Johanson andVahlne (2009, p. 1423) of the connection between their model and Sarasvathy (2001) Effectuation theory.Various calls for research on the decision logic shaping the internationalization process have since been put forward (Coviello et al., 2017), with some recent research starting to close this gap (Karami et al., 2020;Prashantham et al., 2019).By addressing the effects of effectual and causal decisions on the speed of firm internationalization, our paper seeks to add to this debate.
The idea that causation might be useful as a way to alleviate the darkside effects of trust influencing the speed of firm internationalization, as we suggest in our paper, offers a more practical strategy than approaches seeking to control the level of trust in business relationships, such as those suggested by Wicks et al. (1999) and Stevens et al. (2015).Urging firms to adopt causation might also be considered more effective than encouraging them to focus on managing specific episodes where trust is critical, as Thorgren and Wincent (2011) have proposed.The contrast between our proposal and the arguments advanced by Prashantham et al. (2019) has allowed us to identify resource endowment as a contingency factor and thus to draw a line between the experience of small/ young and large/old firms during internationalization.Still, if we acknowledge that causation and effectuation are not exclusive choices but can actually be balanced and combined (Smolka, Verheul, Burmeister-Lamp, & Heugens, 2018), firms aiming to strategically control the liabilities of trust may face the challenge of equalizing both decision approaches according to the concrete feedback they get from their internationalization speed.When the balance between the speed of foreign commitment, dispersion of foreign markets, and commercial intensity is unsatisfactory, the firm may perceive a need for changing the way it makes internationalization-related decisions.

Practical implications
Following our propositions, if firms want to avoid experiencing the dark side effects of trust in internationalization speed it may be necessary for them to adopt causation, either alone or in combination with effectuation.This means cultivating routines that provide business relationship development with some direction or oversight.Managers may find examples of such routines in suggestions similar to those advanced by Anderson and Jap (2005), who suggest regularly evaluating older relationships and keeping backup plans, and Dant and Gleiberman (2011), who suggest specifying and periodically reexamining the mutual expectations and contributions that each partner brings to the business relationship.Conventional literature on planning-based decision-making also illustrates the practical applications of causation, which may include the extensive collection of information about alternatives, a disciplined evaluation of scenarios, and the pursuit of clearly specified goals (Miller & Cardinal, 1994;Wiltbank et al., 2006).Routines like these are particularly important to the extent that internationalization speed has been shown to have important performance implications for both small and large firms (Hilmersson & Johanson, 2016;Mohr & Batsakis, 2017;Musteen et al., 2010).It is important to stress that our concern to alleviate the effects of the dark side of trust on internationalization speed should not be confused with a normative defense of high internationalization speed as an ideal to be pursued.We are particularly aware that an internationalization speed that is too high may backfire due to the associated challenges of learning and developing capabilities over a very short period (Dierickx & Cool, 1989;Jiang, Beamish, & Makino, 2014).The discussion that we develop in this paper should help managers to better understand how their actions may affect the benefits they gain from their foreign business relationships and what mechanisms are available to them to change their situation.

Limitations and opportunities for future research
The conceptual model that we outlined in this paper should be tested empirically by future researchers.In particular, the effect of variables such as industry, technology, ownership, firm size, and firm age, should be evaluated together with our propositions.We did not account for them when building our theoretical framework because of the difficulty in profiling the kind of firm that may be more likely to trust a counterpart excessively.However, these are variables that could play a role in creating trust asymmetry in interorganizational relationships.In addition to that, empirical research will also help explain the validity limits of the relationships implied in some of our propositions, whose inverted U-shaped behaviors suggest that some dimensions of internationalization speed may become negative when trust is high enough.We believe either that those relationships are likely to exhibit different shapes for extremely high levels of trust, or the firm is likely to take action before such scenarios materialize.Hence, it is of theoretical and practical relevance to understand how the internationalization process unfolds in such extreme conditions.
In the same way that we discussed constraints imposed by resource availability on the interaction between a firm's decision logic and the direct relationships between trust and internationalization speed (P5ab), future studies could investigate similar constraints on the interaction between decision logic and the indirect path involving trust, marketspecific knowledge, and internationalization speed.Since these represent longer and more complex causal chains, they are likely to require attention to variables that fall outside the scope of this paper.Future studies should also look into scenarios in which relationships already start with some level of trust, like when firms build on information from their social context to evaluate the reliability of a potential new partner (Gulati, 1995;McEvily & Zaheer, 1999).In such contexts, the trust that is already present may allow for the manifestation of dark-side effects at a very early stage.The bright side of trust may manifest only later, if that situation is resolved, which would imply a dynamic opposed to what we anticipated in our propositions.Our arguments are mostly valid for relationships that start with low relational trust, reflecting the ideas suggested by the Uppsala Model and other research that has addressed the evolution of trust in interfirm relationships (e.g., Laaksonen, Pajunen, & Kulmala, 2008;Rousseau et al., 1998).
It may be useful to note that our model outlines expectations for the different dimensions of internationalization speed but is not sufficient to determine speed itself.Other factors must still be accounted for to understand the materialization of changes in firms' internationalization state.For example, decision-makers' traits such as their international orientation and global mindsets are of particular relevance.Having an international orientation implies an attitude of "active exploration of new business opportunities abroad" (Knight & Kim, 2009, p. 260).A global mindset is manifested in proactive attitudes characterized by an openness to and awareness of cultural diversity, and has a strong causal relationship with internationalization behavior (Felício, Meidut ė, & Kyvik, 2016;Kyvik, Saris, Bonet, & Felício, 2013).International orientation, then, can be associated with changes in firms' international commercial intensity, while global mindset can be linked with changes in the dispersion of their international markets.
It is also important to remember that we have chosen to focus on the roles of relational trust in our model of internationalization speed.Although this type of trust is probably the major cause of relational benefits and challenges, as we discussed, it is important to acknowledge that calculative trust is often considered a potential substitute or complement for relational trust (Poppo, Zhou, & Li, 2016;Robson, Katsikeas, & Bello, 2008), whereas institutional trust is taken as a foundational component on which other types of trust are built (Johanson, 2008).The importance of these other types of trust may be particularly salient at an early stage of business relationship development, when relational trust tends to be low compared to other trust bases.They may also be relevant when firms enter a host market that is largely different from their home country and which may slow down the accumulation of relational trust.Under certain circumstances, it is also possible that old relationships show a low relational orientation and turn into transaction exchanges (Pillai & Sharma, 2003).Hence, future research should expand our discussion by considering the roles that other bases of trust may play in affecting internationalization speed alongside that of relational trust.
Finally, to prioritize the relationship between trust and internationalization speed, our discussion did not account for other theoretical elements of interfirm relationships.One such element is power, which research has shown can affect firms' decision to use either trust or control to govern their interfirm relationships (Brito & Miguel, 2017) and to interact with trust to underpin their strategic choices (Patnaik, Pereira, Temouri, Malik, & Roohanifar, 2020).Our lack of attention to power reflects our use of the Uppsala Model as a frame of analysis, given that this model has historically given power only a minor role (Forsgren, Holm, & Johanson, 2015).However, we acknowledge the importance of this concept and agree it should be addressed in future studies.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.