Subjective Values

Subjective values of credit and debt result from the valorisation that the agent receiving a service gives to the provider, as defined previously in Section 6.3.2, so that the origin of subjective values is clear. However, this raises one limitation of Piaget’s model, which is how the provider is aware of the receiver’s valorisation. As discussed in Section 6.2.4, this issue must be addressed either by explicit communication of the valorisation from the receiver to the provider, or by enabling the provider to model what it believes the receiver’s valorisation is based on its own information.

Moreover, subjective values are affected by influences that may distort (by increasing or decreasing) the original value on which they are based, as described in Section 6.3.3. To consider such subjective influences on determining debts and credits, we need to represent influences computationally.

In this context, before determining the subjective values of debt and credit, we ad- dress the communication of the debt value from the requester to the provider and the computational representation of influences, as described below.

6.4.3.1 Communication

To allow agents to reason about their interactions in terms of the compensation of provided and received services, it is important that they are aware of the valorisation that others give to their services, so that providers can identify possible disequilibrium situations caused by under-valorisation or over-valorisation of their services. Through explicit communication, the provider can gain accurate knowledge of the valorisation it is receiving, and even if the receiver lies about its valorisation, a resulting disequilibrium situation can then be identified by the provider.

To communicate its valorisation, the receiver needs only to reply to the message con- taining the service result with an acknowledgement message including its debt value in the content. Thus, if this acknowledgement message is already part of the interaction protocol between agents, this communication does not increase the number of messages exchanged between them. If the acknowledgement to the service result message is not part of the protocol, the number of messages in the total interaction increases only by 1, which does not impose a message overload on the system.

Therefore, based on the above analysis, we assume that the service receiver first deter-

mines its debt value, and thencommunicates this debt to the provider as a valorisation.

6.4.3.2 Influences

Influences over subjective values may increase or decrease the values on which they are

based. We define influences as tuples ι = (condition, δ), where condition specifies the

situation in which the influence is valid (if the influence is always valid, the condition

is true), and δ ∈ [−1,1] is the influence intensity, with δ < 0 representing a negative

influence that decreases the subjective value andδ >0 representing apositive influence

that increases the subjective value. Note that the intensity of each influence must be defined according to the desired impact of that influence on the subjective evaluation,

such that influences with high impact have intensity close to −1 or 1, those with low

impact have intensity close to 0, and those with null impact have intensity equal to 0. The set of all possible influences on an agent’s subjective evaluation is denoted as

I ={ι1, .., ιn}.

We have already discussed in Section 6.3.3 examples of subjective influences that

may be present in the kind of cooperative applications we are modeling. Here,

a number of conditions can be identified for these influences to be valid, such as HighlySkilled(prt), HigherPosition(prt), UnilateralDependence(prt), Abundant(srv),

ReachedExpectation(srv), and Saturated(prt), where prt is the interaction partner and

srv is the service being provided or received. Although we consider just this group of

Algorithm 2 Algorithm for the influence functioninfluence(prt,srv).

1: input: prt,srv

2: totalι= 0

3: for all(ιj = (conditionj(prt, srv), δj))∈I do

4: if conditionj(prt, srv) =truethen

5: totalι=totalι+δj

6: end if 7: end for

8: output: totalι

conditions can be identified (but for ease of presentation, we discuss only the influences above, instead of presenting an extensive list).

For example, if agent β exhibits unfair behaviour that always has a negative effect

on its subjective evaluation (that is, it always decreases its debt), such an influence

is represented by ι1 = (true, x), where 0 > x > −1. Similarly, if β’s unilateral de-

pendence with the interacting partner (identified as agent α) has a positive influence

on its subjective evaluation (that is, it may increase the debt), this influence is rep-

resented by ι2 = (UnilateralDependence(α), x), where 1 > x > 0, and the condition

UnilateralDependence(α) is true ifβ depends onα butα does not depend onβ. Thus,

if there is a mutual dependence between the two agents, influence ι2 does not affect β’s

subjective judgement (it is not valid).

The set of influences that an agent considers in its subjective evaluation depends on the agent’s design objectives (for example, agents can be designed to have fair or unfair behaviour), and on what is important to capture from the environment (for example, in a system with no social hierarchy, agents do not need to consider the influence of social position).

6.4.3.3 Determining Influenced Debt and Credit

Until now, we have seen that an agent receiving a service first determines its debt value and then communicates this debt to the agent providing the service, which takes it as a credit. The process of determining debt and credit can be affected by subjective influences on those values.

To determine the debt that is acquired when a requester receives a service, we must consider the satisfaction of the requester with this service, and the subjective influences that may apply over this satisfaction. Given the representation and use of influences

described previously, β determines its debt value as follows:

where the functioninfluence(α,srv) specifies the influence thatβapplies to its objective

evaluationsβαwhen interacting with partner agentαand receiving servicesrv, and the

functionk(x) constrains the resulting value to a [0,1] scale.

The function influence(α,srv) is described in Algorithm 2 and calculates the total in-

fluence totalι over a value (which for the requester is sβα). To combine influences, we

assume that positive and negative influences can cancel each other out, and that two or more positive (or negative) influences have greater impact on the original value than one influence alone. Thus, the total influence over the original value is determined in

Algorithm 2 by adding the intensities (δj) of all individual influencesιj in the set I that

have conditionj(prt, srv) =true.

Suppose that agentβhas an influence setI ={ι1, ι2}, whereι1 = (Abundant(srv),−0.4)

and ι2 = (U nilateralDependence(prt),0.2). This means that when β is requesting a

service (srv) it undervalues the provider if this service is abundant in the system, and

β overvalues the provider if it depends on that provider (prt) but the provider does

not depend on β. If both conditions are true, the total influence calculated according

to Algorithm 2 is totalι =−0.2 (as a result of −0.4 + 0.2). If β’s satisfaction value is

sβα= 0.6, this results in a debt of tβα = 0.4 (from k(0.6−0.2)). Here, the influence of

service demand decreases β’s debt in relation to its satisfaction. If only the condition

U nilateralDependence(prt) is true, the total influence on sβα is totalι = 0.2, which

results in a debt of tβα = 0.8 (from k(0.6 + 0.2)). Here, in contrast, the influence on

the agent’s subjective evaluation increases its debt in relation to its satisfaction. In this

case, if β’s satisfaction is sβα = 0.9, the function k(0.9 + 0.2) limits the value to 1,

resulting in a debt oftβα= 1.

After the requester has determined its debt, it communicates this debt to the provider agent to express its valorisation of the provider’s service. The provider then accepts this valorisation as a credit for the future. However, as for the debt value, subjective influences may alter the original valorisation, increasing or decreasing the provider’s credit. Given the same representation and use of influences described previously, a

provider α determines itscredit value as follows:

vαβ =k(valorisation(β) +influence(β,srv))

where the function valorisation(β) just reads the valorisation (tβα) communicated by

the requester (β) through the service completion acknowledgement message, and the

functioninfluence(α,srv), described in Algorithm 2, calculates the total influence over

the valorisation thatαreceived fromβ. One possible influence over the provider’s credit

issaturation, as described in Section 6.3.3.

If there is no influence on the accepted credit, there is a direct correspondence between

tion that agents do not lie about their debts when communicating them, but if they do

lie (such thatvαβ < tβα), causing a provider’s balance of exchange values to be negative

(that is, the renouncement is greater than the credit), such behaviour may reduce the

chances of future interactions with that provider. Moreover, the direct correspondence between the provider’s credit and the requester’s debt allows the provider to identify any under-valorisation or over-valorisation given by the requester.