Trust models such as CREDIT can help reduce the uncertainty underlying the honesty and reliability of the interacting agents. However, most trust models are only put to use in selecting interaction partners (see section 3.3). In addition, however, we use CREDIT to influence the bargain that takes place before an agreement is signed (the next chapter is devoted to its application in MD). This is achieved by coupling CREDIT to the decision making model of a agent (see figure 1.3). In this way, CREDIT can directly
function: F T(β, x, v,Ω, Uα
x,L,M, R, κ)
with
x∈X; issue under consideration.
v ∈ Dx; the value for issuex.
Ω = [(O1, O10), ...,(On, On0)]; the list of past contracts.
L= [L1, ..., Lk], k≥2; fuzzy sets characterising performance.
M= [µL1, ..., µLk]; membership functions for fuzzy sets. R ={Rep(x, L)}L∈L; reputation levels of agent β in all labels. begin
1. ∆U ={Uα
x(Oi(x))−Uxα(O0i(x))}i=1..n,(Oi,O0i)∈Ω ; obtaining utility variations in past contract executions.
2. P ∼N(∆Ux, σ∆Ux) ; obtain a Normal probability distribution of utility variations.
3. δ1= ∆Ux−σˆ∆Ux√|·Ωlconf| andδ2= ∆Ux+ˆσ∆Ux√|·Ωlconf| determine the 95% confidence interval of Φ. with lconf = 1.96;
4. for each L∈ Ldo
a. C(β, x, L) = min(µL(δ1), µL(δ2)) ; obtain confidence levels for each label
given the confidence interval.
b. CR(x, L) =κ·C(x, L) + (1−κ)·Rep(x, L) ; compute combined measure based on confidence and reputation.
5. Laux=L; copying labels.
6. repeat
a. E∆Ucr(x) =
T
L∈Laux{u|µ
x=v
L (u)≥CR(x, L)} obtaining range of expected values given reputation and confidence.
b. if(E∆Ucr(x) =∅)
andL= arg minL∈Laux{Rep(x, L)}) correct inconsistency by removing then Laux=Laux−L; low importance sets using linear search
(could be logarithmic as well).
7. until E∆Ucr(x)6=∅; inconsistency removed
8. ∆cr
loss= sup(E∆Ucr(x)) ; calculating maximum possible utility loss .
9. returnmin(1,1−∆crloss) ; returning the trust value.
end
Table 5.2: Algorithm used to calculate trust values.
influence the quality of agreements reached and the efficiency of the negotiation. Thus, in the remainder of this section we examine these two scenarios.
5.3.1 Influencing an Agent’s Choice of Interaction Partners
When an agent, sayα, has a particular task to contract for, it will decide on the issues to be negotiated and identify possible interaction partners, say {β1, β2, ..., βn} ⊆ Ag. For each agent in this set, we can calculate the trust value for each issue (as per equation 5.8) and aggregate these to give a general trust value for each agent (using equation 5.9). That is, T(α, β1, X0), T(α, β
2, X0), ..., T(α, βn, X0), where X0 ⊆ X is the set of issues under consideration. Trust can thus provide an ordering of the agents in terms of their overall reliability for a proposed contract. Agentα can then easily choose the preferred
Step Complexity Incremental Complexity 1 O(n) O(k) 2 O(n) O(k) 3 O(k) O(k) 4a O(b) O(b) 4b O(b) O(b) 5 O(k) O(k) 6a O(b) O(b) 6b O(b) O(b) 7 O(k) O(k) 8 O(k) O(k) 9 O(k) O(k) Overall O(kn) O(kb2)
Table 5.3: Computational complexity of individual steps of the algorithm. Here, n
is the number of cases recorded in the case base,b is the number of labels and k is a constant.
agent or the set of agents it would want to negotiate with (i.e. by choosing the most trustworthy one(s)).
5.3.2 Influencing an Agent’s Negotiation Stance
In the next two subsections we detail ways in which CREDIT can be used to change the negotiation stance. First, we show how CREDIT can be directly used to adapt negotiation intervals on different issues depending on the confidence level for each issue. Second, we show how issues to be negotiated can be varied according to the level of trust in the opponent.
5.3.2.1 Redefining Negotiation Intervals
At contracting time, issue-value assignments,xn =vn, are agreed upon. Agents accept values that lie within a range [vmin, vmax], such that Ux(vmin) >0 and Ux(vmax) >0. This interval is the acceptable range which an agent uses to offer and counter offer (according to a strategy) during negotiation (Jennings et al., 2001). Moreover, given a potential issue-value assignmentx=v in an offer, an agent can compute an interval of expected values. Thus, using equation 5.7 we have EVcr(x, v) = [ev−, ev+] over which the value v0 actually obtained after execution is likely to vary. This range defines the
uncertainty in the value of the issue and if the acceptable range [ev−, ev+] does not
fit within [vmin, vmax], there exists the possibility that the final value may lie outside the acceptable region. This, in turn, means that Ux(v0) may be zero which is clearly undesirable and irrational.
First, the agent can restrict the negotiation interval [vmin, vmax] with respect to the set of expected values [ev−, ev+] as shown below. To do this, we first define the set of possible
contracts,Ox, that are consistent with the expected values ofxand its acceptance range, and then define the corrected values forvmin and vmax:
Ox={O|(x=v)∈O, EVcr(x, v)⊆[vmin, vmax]} v0 min = inf{v∈Dx |(x=v)∈O, O∈ Ox} v0 max = sup{v∈Dx|(x=v)∈O, O∈ Ox} (5.11)
This will shrink the range of negotiable values for an issue (i.e. from [vmin, vmax] to [vmin0 , v0max], where either v0min ≥ vmin or vmax0 ≤vmax depending on which of the two limits v0
min and v0max gives higher utility respectively) to ensure that the final outcome will fit within the range [vmin, vmax]. As well as reducing the possibility that the executed value will lie outside the acceptable range, reducing the negotiation range can also bring some other added benefits. It can help the agent reduce the time to negotiate over the value of each issue (e.g. if the range is smaller, the number of possible offers is also smaller) and it can help the agent to make better decisions that depend on the negotiation outcome (e.g. if a seller is expected to deliver goods 1 day later than the agreed 3 days, the buyer can adjust its other tasks to fit with delivery in 4 days). Second, given information about a possible defection on the part of its opponent from an agreed value x = v0, an agent can also decide to defect from its own issues (by a given degree) in order to recover the expected utility loss. This means that the agent will calculate min{Ux(ev−), Ux(ev+)} and then achievey=u0 instead of y=u0 (which
has been agreed in the contract for issuey which it handles) such that:
Uy(u0)−Uy(u0) = min(0, Ux(v0)−min{Ux(ev−), Ux(ev+)}) (5.12) However, if the opponent is also fitted with a trust model, it will distrust the defecting agent and this may lead to an arms race (Axelrod, 1984; Fisher and Ury, 1983) until the agents will distrust each other so much that they avoid each other (or cannot find a coinciding negotiation range if they both use the procedure described in equation 5.11) .
5.3.2.2 Extending the Set of Negotiable Issues
Initially we argued that higher trust could reduce the negotiation dialogue and lower trust could increase the number of issues negotiated over. In this section we deal with this particular use of trust in defining the issues that need to be negotiated. To this end, issues not explicitly included in a contract Oα may receive an expected value through one of the rules inRules(α) for an agent α:
Thus, if the premise of such a rule is true in a contract, the issue x is expected to have the value v. If, however, the trust in the agent fulfilling the values of the issues present in the premises is not very high, it means that the agent believes that the values v1, v2, ..., vn may not be eventually satisfied. In such a case, to ensure that the issue x actually receives valuevit should be added to the negotiated terms of the contract. This means that, when the trust is low in the premises, the unspecified issues (as discussed in section 5.2.1) are added to the contracted issues in order to try and ensure that they will be met (whereas if trust is high the issue is not negotiated). For example, if a buyer believes that the quality of a product to be delivered (the premise of a rule) will not be the quality of the product actually delivered, the buyer might request that the product satisfies very specific standards (e.g. kitemark or CE), which it privately expected and would not normally specify in a contract if trust were high.
Formally, this means that ifT(α, β, Xr) ≤threshold, (where (T(α, β, Xr) is defined as
per equation 5.9 and Xr is the set of issues in the premise of rule r), then the issue
x in the conclusion of the rule should be added to the set of contract terms. On the other hand, as an agent becomes more confident that its interaction partner is actually performing well on the issues in the contract, it might eventually be pointless negotiating on the issue if the premises of the issue pre-suppose that the value expected will actually be obtained. Thus, ifT(α, β, Xr)> threshold, then the issuex in the conclusion of the
rule can be removed from the set of contract terms. An example of this would be: If T(α, β,price)>0.8 and T(α, β,qos)>0.7 Then avoid negotiating anti-DoS which means that the if the trust in provider β giving the quoted price a telecommu- nication line (bought from some Internet Service Provider (ISP)) is above 0.8, and the trust in its quality of service guarantee (qos) is above 0.7, then the ISP can be trusted to give an anti denial-of-service (DoS) on the line and this issue can be avoided in the negotiation process.
The two processes described above serve to expand and shrink the space of negotiation issues. For a new entrant to the system, for example, the trust value others have in it are likely to be low and hence the number of issues negotiated over will be large. But, as it acquires the trust of others, the number of issues it would need to negotiate will go down. Ultimately, with more trust, the set of negotiable issues can thus be reduced to a minimal set, affording shorter negotiation dialogues. Conversely, with less trust, the negotiable issues expand, trading off the length of dialogues with higher expected utility.