Trust Networks. Rino Falcone and Cristiano Castelfranchi

Transcription

1 Trust Networks Rino Facone and Cristiano Castefranchi Nationa Research Counci Institute of Cognitive Sciences and Technoogies Via San Martino dea Battagia, Roma, Itay {rino.facone, cristiano.castefranchi}@istc.cnr.it Abstract. Dependence networks among agents (describing how each agent can be inked with each other abe to satisfy any need/goa/desire) are reay important for evauating future coaborations among them. In fact, the Dependence Networks aone are not sufficient for a rea aocation of tasks among the agents. For this aocation, it is aso necessary that each agent coud satisfy his own expectations about the trustworthiness of the other agents with respect to the specific tasks. We present in this paper a cognitive theory of trust as a capita, which is, in our view, a good starting point to incude this concept in the issue of negotiation power. That is to say that if somebody is (potentiay) strongy usefu to other agents (in the sense that are decared a set of its skis), but it is not trusted, its negotiation power does not improve. Our caim is to underine how (for a set of agents inked to each other) the competitive advantage is not simpy of being part of a network, but more precisey of being trusted in that network. Keywords: Trust, Dependence Networks, Reationa Capita. 1 Introduction In amost the present approaches to the trust study the focus of the anaysis is on the trustier and on the ways for evauating the trustworthiness of other possibe trustees. But trust can be viewed at the same time as an instrument both for an agent seecting the right partners in order to achieve its own goas (the trustier s point of view), and for an agent of being seected from other potentia partners (the point of view of the trustee) in order to estabish with them a cooperation/coaboration and to take advantage from the credit of the accumuated trust. In this paper we wi anayze trust as the agents reationa capita. Starting from the cassica dependence network (in which needs, goas, abiities and resources are distributed among the agents) with potentia partners, we introduce the anaysis of what it means for an agent to be trusted and how this condition coud be strategicay used from him for achieving his own goas, that is, why it represents a form of power. We address this point, anayzing what it means that trust represents a strategic resource for agents that are trusted, proposing a mode of trust as a capita for individuas and suggesting the impication for strategic action that can be performed. Our thesis is that to be trusted:

2 i) increases the chance to be requested or accepted as a partner for exchange or cooperation; ii) improves the price, the contract that the trustee can obtain. The need of this new point of view derives directy from the fact that in human societies as we as in muti-agent systems it is strategicay important not ony to know who is trusted by who and how much, but aso to understand how being trusted can be used by severa potentia trustiers. It has been aready shown that using different eves of trust represents an advantage in performing some task such as aocating task or choosing between partners. Therefore, having trust as a cognitive parameter in agents decision making can ead to better (more efficient, faster etc.) soutions than proceeding driven by other kind of cacuation such as probabiistic or statistica one. In order to improve this approach and to better understand dynamics of socia networks, now we propose a study of what happens on the other side of the two-way trust reationship, focusing on the trustee, in particuar on a cognitive trustee. Our aim is an anaytica study of what it means to be trusted. The idea of taking the other point of view is particuary important if we consider the judge amount of studies in socia science that connect trust with socia capita reated issues. Our caims are: - to be trusted usuay is an advantage for the trustee (agent Y); more precisey received trust is a capita that can be invested, and that requires decision and costs to be cumuated; - it is possibe to measure this capita, which is reationa, that is depends on a position in a network of reationships; - trust has different sources: from persona experience that the other agents have had with Y; from circuating reputation of Y; from Y s beongingness to certain groups or categories; from the signs and the impressions that Y is abe to produce; - the vaue of this capita is context dependent (and market dependent) and dynamic; - received trust strongy affects the negotiation power of Y that cannot simpy be derived from the dependence biatera reationships. Athough there is a big interest in iterature about socia capita and its powerfu effects on the webeing of both societies and individuas, often it is not cear enough what is it the object under anaysis. Individua trust capita (reationa capita) and coective trust capita not ony shoud be disentanged, but their reations are quite compicated and even conficting. To overcome this gap, we propose a study that first attempts to understand what trust is as capita of individuas. How is it possibe to say that trust is a capita? How is this capita buit, managed and saved? Then we aim to anayticay study the cognitive dynamics of this object, with a particuar focus on how they depend on beiefs and goas.

3 2 Being Trusted The theory of trust and the theory of dependence are not independent from each other. Not ony because as we modeed (1, 2, 22), before deciding to activey trust somebody, to rey on him (Y), one (X) has to be dependent on Y: X needs an action or a resource of Y (at east X has to beieve so). But aso because objective dependence reationships (10) that are the basis of adaptive socia interactions, are not enough for predicting them. Subjective dependence is needed (that is, the dependence reationships that the agents know or at east beieve), but is not sufficient; it is aso necessary to add two reevant beiefs: (i) the beief of being dependent, of needing the other; (ii) the beief of the trustworthiness of the other, of the possibiity of counting upon him. If X woud not fee dependent on Y, she coud not rey on him. 2.1 Objective and Subjective Dependence The theory of dependence incudes in fact two types of dependences: (1) the objective dependence, which says who needs whom for what in a given society (athough perhaps ignoring this). This dependence has aready the power of estabishing certain asymmetric reationships in a potentia market, and it determines the actua success or faiure of the reiance and transaction (see Figure 1). Figure 1: objective dependence network (2) the subjective (beieved) dependence, which says who is beieved to be needed by who. This dependence is what determines reationships in a rea market and settes on

4 the negotiation power; but it might be iusory and wrong, and one might rey upon unabe agents, whie even being autonomousy abe to do as needed. In Figures 2 is shown the dependence reationships as beieved by X: it is different from the objective dependence showed in Figure 1. Figure 2: subjective dependence network (beieved by X) More Formay, et Agt={Ag 1,..,Ag n } a set of agents; we can associate to each agent Ag i Agt: - a set of goas G i ={g i1,..,g iq }; - a set of actions Az i ={α i1,.., α iz }; these are the eementary actions that Ag i is abe to perform; - a set of pans Π ={p i1,..,p is }; the Ag i s pan ibrary: the set of rues/prescriptions for aggregating the actions; and - a set of resources R i ={r i1,..,r im }. The achievement/maintenance of each goa needs of actions/pans/resources. Then, we can define the dependence reationship between two agents (Ag j and Ag i ) with respect a goa g jk, as Obj-Dependence (Ag j, Ag i, g jk ) and say that: An agent Ag j has an Objective Dependence Reationship with agent Ag i with respect to a goa g jk if for achieving g jk are necessary actions, pans and/or resources that are owned by Ag i and not owned by Ag j. More in genera, Ag j has an Objective Dependence Reationship with Ag i if for achieving at east one of its goas g jk G j, are necessary actions, pans and/or

5 resources that are owned by Ag i and not owned by Ag j (or, that is the same, they are owned by Ag j but not usabe by it for severa reasons). As in (12) we can introduce the uniatera, reciproca, mutua and indirect dependence (see Figure 3). In very short and simpified terms, we can say that the difference between reciproca and mutua is that the first is on different goas whie the second is on the same goa. Figure 3 We introduce the formuas Be k G z that represents Ag z s Goa set as beieved by Ag k. The same for Be k Az z, Be k Π z, and Be k R z, respectivey for actions, pans and resources. In practice, the dependence reationships shoud be re-moduated on the basis of the agents subjective interpretation. The thing reay operative in the resuting interactions among the agents is due to their beiefs about the reciproca dependences rather than the objective dependences. We ca Subj-Dependence(Ag j, Ag i, g jk ) for representing the Ag j s point of view with respect its dependence reationships with Ag i about its k-th goa g jk. Anaogousy, we ca Obj-Dependence(Ag j, Ag i, g jk ) for representing the objective dependence reationship of Ag j with Ag i about its k-th goa g jk. We define Dependence-Network(Agt,t) the set of dependence reationships (both subjective and objective) among the agents incuded in Agt set at the time t: Dependence-Network(Agt,t) = Obj-Dependence(Ag j, Ag i, g jk ) Subj-Dependence(Ag j, Ag i, g jk ) with Ag j,ag j Agt. 2.2 Power of Negotiation in the Dependence Networks Given a Dependence-Network(Agt,t), we define

6 Objective Potentia for Negotiation of Ag j Agt about an its own goa g jk -and ca it OPN(Ag j, g jk )- the foowing function: 1 OPN(Ag j,g jk ) = f (" ) = 1+ p ki i=1 " i= p ki Where: - f is in genera a function that preserves monotonicity (we wi omit this kind of functions in the next formuas); - represents the number of agents in the set Agt that have a objective dependence reation with Ag j with respect to g jk ; - p ki is the number of agents in Agt that are objectivey requiring the same actions/pans/resources (as usefu for g jk ) to Ag i on which is based the dependence reation between Ag j and Ag i and that in consequence are competitors with Ag j on that actions/pans/resources in a not compatibe way (Ag i is not abe to satisfy at the same time a the agents: there is a saturation effect). See Figure 4 for an exampe. Figure 4 So, if there are no competitors with Ag j (p ki =0 for each i {1,, }) we have: 1 OPN(Ag j,g jk ) = f (" ) = 1+ p ki In genera, we can represent the objective dependence of Ag j as shown in Figure 5: set1 represents the set of agents who depend from Ag j for something (actions, pans, resources), set2 represents the set of agents from which Ag j depends for achieving an own specific goa g jk. The intersection between set1 and set2 (part set3) is the set of agents with whom Ag j coud potentiay negotiate for achieving g jk. The greater the overap the greater the negotiation power of Ag j in that context. i=1

7 Figure 5 However, the negotiation power of Ag j aso depends on the possibe aternatives that its potentia partners have: the few aternatives to Ag j they have, the greater its negotiation power (see Figure 4). We can define the Subjective Potentia for Negotiation of Ag j Agt about an its own goa g jk -and ca it SPN(Ag j, g jk )- the foowing function: 1 SPN(Ag j,g jk ) = Be j (" ) 1+ p ki where we have the same meanings as for the previous formua but now we make reference to the beieved (by Ag j ) dependence reations. More in genera, we can say that: the Average Subjective Potentia for Negotiation of Ag j Agt about the whoe set of its own goas (G j ) in the Dependence-Network(Agt,t) is: i=1 k " k=1 i=1 SPN(Ag j,g j ) = Be j ( 1 s 1 " ) s 1+ p ki Where s is the number of goas of Ag j, and k is the number of other agents in the set Agt, that have a dependence reation with Ag j with respect to the specific goa g jk. 2.3 Trust Roe in Dependence Networks We are interested now to introduce into the dependence network aso the trust reationships. In fact, the dependence network aone is not sufficient for a rea aocation of tasks among the agents. It is true that Ag i shoud be abe and wiing to reaize the action α k : But how? And, it wi be sufficient given Ag i s expectations? Woud be it more or ess trustworthy than Ag z? For answering to these questions the

8 agents in the dependence network have to estabish among them aso the reciproca trust about the different tasks they can aocate to each other. Indeed, athough it is important to consider dependence reationship between agents in a society, there wi be not exchange in the market if there is not trust to enforce these connections. Considering the anaogy with the Figure 4, we wi have now a representation as given in Figure 6 (where Set 4 incudes the set of agents that Ag j considers trustworthy for achieving g jk ). Figure 6 We have now a new subset (darked agents in Figure 7) containing the potentia agents for negotiation. Introducing in the Subjective Potentia for Negotiation (of Ag j Agt about an its own goa g jk ) aso the basic beiefs about trust (we introduce the superscript index T for differentiate from the SPN without trust), we have: DoA SPN T (Ag j,g jk ) = Be j ( ik * DoW " ik ) 1 DoA ik, DoW ik 0 1+ p ki i=1 DoA ik and DoW ik are, respectivey, the degree of abiity and wiingness (with respect the goa g jk ) of the agent Ag i as beieved by Ag j (Be j (DoA ik ) and Be j (DoW ik )). Anaogousy, but ess reevant in this case, we can introduce the Objective Potentia for Negotiation (of Ag j Agt about an its own goa g jk ), we have: OPN T (Ag j,g jk ) = " i=1 DoA ik * DoW ik 1+ p ki

9 When a cognitive agent trusts another cognitive agent, we tak about socia trust. We consider that the set of actions, pans and resources owned/avaiabe by an agent that can be usefu for achieving a set of tasks (τ 1,, τ r). We take now the point of view of the trustee in the dependence network: so we present a cognitive theory of trust as a capita. That is to say that if somebody is (potentiay) strongy usefu to other agents, but it is not trusted, its negotiation power is not good. As showed in (2) we ca Degree of Trust of the Agent Ag j on the agent Ag i about the task τ k (DoT(Ag j Ag i τ k )): DoT(Ag j,ag i ) = Be j (DoA ik ) * Be j (DoW ik ) At the same way we can aso define the sef-trust of the agent Ag i about the task τ k : ST(Ag i ) = Be i (DoA ik ) * Be i (DoW ik ) We ca the Objective Trust Capita of Ag i Agt about a potentia deegabe task τ k : OTC(Ag i ) = # Be j (DoA ik ) * Be j (DoW ik ) = # DoT(Ag j,ag i ) j=1 Where is the number of agents (incuded in the dependence network) needed for the task τ k. We ca the Subjective Trust Capita of Ag i Agt about a potentia deegabe task τ k the function: STC(Ag i ) = Be i (# Be j (DoA ik ) * Be j (DoW ik )) = Be i (# DoT(Ag j,ag i )) j=1 Subjectivity means that both the network dependence and the beieved abiities and wiingness are beieved by (the point of view of) the agent Ag i. Starting from the Trust Capita we woud ike evauate its usabe part. In this sense, we introduce the Subjective Usabe Trust Capita of Ag i Agt about a potentia deegabe task τ k as: DoT(Ag SUTC(Ag i ) = Be i ( j, Ag i ) # ) 1+ p kj where p kj is (foowing the Ag i s beief about the beiefs of Ag j ) the number of other agents in the dependence network that can achieve the same task to whom Ag j can deegate the task τ k (see Figure 8). We have two comparabe trust vaues when the difference between them is in a range under a given threshod that coud be considered meaningess with respect to the achievement of the task. In Figure 8, Ag 1 and Ag 2 strengthen the trust capita of Ag i (they are concurrent with Ag j about the task τ); whie Ag 3, Ag 4 and Ag 5 weaken the trust capita of Ag i because they are concurrent with Ag i in offering (at the same trustworthy vaue) the task τ. j=1 j=1 j=1

10 Figure 8 Of course, we can anaogousy introduce the Objective Usabe Trust Capita of Ag i Agt about a potentia deegabe task τ k as: OUTC(Ag i ) = # j=1 DoT(Ag j,ag i ) 1+ p kj In this paragraph we have introduced in the dependence network (that estabishes, objectivey or subjectivey, how each agent can potentiay depend from other agents for soving its own tasks) the trust reationships (that introduce an additiona dimension, again assessabe both objectivey and subjectivey, in a potentia partner seection for achieving tasks). In genera, we can say that the introduction of trust reationships reduces the set of potentia partners for each agent and for each task, with respect to the situation with the dependence reationships aone: OPN>OPN T, and SPN>SPN T. 3 Dynamics of Reationa Capita What has not been considered enough in organization theory is the fact that the reationa capita is pecuiar in its being cruciay based on beiefs: again, what makes reationships become a capita is not simpy the structure of the networks (who sees whom and how ceary) but the eves of trust which characterize the inks in the networks (who trusts whom and how much). Since trust is based on beiefs incuding, as we said, aso the beieved dependence (who needs whom) it shoud be cear that reationa capita is a form of capita, which can be manipuated by manipuating beiefs.

11 Thanks to a structura theory of what kind of beiefs are invoved it is possibe not ony to answer some very important questions about agents power in network but aso to understand the dynamica aspects of reationa capita. In addition, it is possibe to study what a difference between trustee s beiefs and others expectations on him impies in terms of both reactive and strategic actions performed by the trustee itsef. 3.1 Changing Trust Capita For what concerns the dynamic aspects of this kind of capita, it is possibe to make hypotheses on how it can increase or how it can be wasted, depending on how each of basic beiefs invoved in trust coud be manipuated. In genera, starting from the anaysis of the previous paragraph, we can see how matching the different terms we have different interesting situations. First of a, even if OTC(Ag i,τ k ) is a reevant factor for the agent Ag i (it shows in absoute terms how is recognized the trustworthiness of Ag i ), in fact the reay important thing for an agent cumuating trust capita is OUTC(Ag i,τ k ) that indicates not ony the trustworthiness cumuated on the dependent agents, but aso the number of possibe other concurrent agents on that offered task. Again more interesting is to consider the SUTC(Ag i,τ k ) factor (in which a reevant roe is payed by the beiefs of the invoved trustee) and its reationships with OUTC(Ag i,τ k ), SPN T (Ag j,g jk ), and OPN T (Ag j,g jk ) factors. As we have seen in the previous paragraph, these factors are constituted by the beiefs of the trustee or the trustier, so can be interesting to anayze the different situations matching them and evauating the consequences of their coherence or incoherence. Let us consider what kind of strategies can be performed to enforce the other s dependence beiefs and his beiefs about agent s competence. If Ag i is the potentia trustee (the coector of the trust capita) and Ag j is the potentia trustier we can say: i) Ag i can make Ag j dependent on him by making Ag j acking some resource or ski (or at east inducing Ag j to beieve so). He has to work on SPN T (Ag j,g jk ). ii) Ag i can make the Ag j dependent on him by activating or inducing in her a given goa (need, desire) on which Ag j is not autonomous (14) but is dependent from Ag i (or in any case she beieves so). In this case he has to find the way for incuding in G j an additiona g jk such that Ag j is dependent from Ag i for that goa (and she beieves that). iii) Since dependence beiefs are stricty reated with the possibiity of the others (for exampe Ag j ) to see the agent (for exampe Ag i ) in the network and to know her abiity in performing usefu tasks, the goa of the agent who wants to improve his own reationa capita wi be to signaing his presence and his skis (15,16,17). Whie for showing his presence he might have to shift his position (either physicay or figurativey ike, for instance, changing his fied), to communicate his skis he might have to hod and show something that can be used as a signa (such as certificate, socia status, proved experience, and so on). It is important to underine that using these signas often impies the participation of a third subject in the process of buiding trust as a capita: a third part which must be trusted (2). Obviousy aso Ag i s previous performances are signas of trustworthiness. And this information is aso provided by the circuating reputation of Ag i (18, 19).

12 iv) Aternativey, Ag i coud work for reducing the beieved (by Ag j ) vaue of abiity of each of the possibe competitors of Ag i (in number of p kj ) on that specific task τ k : he has again to work SPN T (Ag j,g jk ). Let us now consider how wiingness beiefs can be manipuated. In order to do so, consider the particuar strategy performed to gain the other s good attitude through gifts (20). It is true that the expected reaction wi be of reciprocation, but this is not enough. Whie giving a gift Ag i knows that the Ag j wi be more incined to reciprocate, but Ag i aso knows that his action can be interpreted as a sign of the good wiingness he has: since he has given something without being asked, Ag j is driven to beieve that Ag i wi not cheat on her. Then, the rea strategy can be payed on trust, sometimes totay and sometimes ony partiay this wi basicay depend on specific roes of agents invoved. Again in forma terms, we can say that Ag i has to work for increasing his DoW i as beieved by Ag j (Be j (DoA i )). Aternativey, it coud work for reducing the beieved (by Ag j ) vaue of wiingness of each of the possibe competitors of Ag i (in number of p kj ) on that specific task τ k. An important consideration we have to do is that a dependence network is mainy based on the set of actions, pans and resources owned by the agents and necessary for achieving the agents goas (we considered a set of tasks each agent is abe to achieve). The interesting thing is that the dependence network is modified by the dynamics of the agents goas: from their variations (as they evove in time), from the emergency of new ones, from the disappearance of od ones, from the increasing request of a subset of them, and so on (21). On this basis, changing the roe of each agent in the dependence network, changes in fact the trust capita of the invoved agents. 4 Concusions Individua trust capita (reationa capita) and coective trust capita not ony shoud be disentanged, but their reations are quite compicated and even conficting. In fact, since the individua is in competition with the other individuas, he has a better position when trust is not uniformy distributed (everybody trusts everybody), but when he enjoys some form of concentration of trust (an oigopoy position in the trust network); whie the coective socia capita coud do better with a generaized trust among the members of the coectivity. References [1] Castefranchi C., Facone R., Principes of trust for MAS: cognitive anatomy, socia importance, and quantification, Proceedings of the Internationa Conference of Muti-Agent Systems (ICMAS'98), pp , Paris, Juy, 1998.

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