6.4 A Computational Exchange Values Model
6.4.4 Reciprocation Values
In the reciprocation stage of the interaction, the subjective values of credit and debt acquired in the provision stage can be realised as objective values. Here, a credit is spent by requesting a service that has some satisfaction value, and a debt is paid by providing a service that has a renouncement value.
Suppose that two agents α and β have interacted previously and, as a result of these
interactions, α acquired a credit with β and β acquired a debt with α. Now, in the
reciprocation stage of the interaction, α can spend its credit (vαβ0 ) by asking β for a
service in return. Agent β may or may not admit the corresponding debt (t0βα) but, if
it does, it provides the requested service onα’s behalf. The service provided by β has a
renouncement forβ (rβα0 ) and a satisfaction forα (s0αβ).
Unlike the provision stage of the interaction in which subjective values must be deter- mined, when agents are in the reciprocation stage of the interaction, their subjective values already exist (and were acquired in the provision stage). Thus, the determination of credits and debts as reciprocation values involves only retrieving these values from where they are stored. In the case of single interactions, this task is simple but, when subjective values of credit and debt accumulate over time, we must determine how much of an accumulated credit an individual should spend when requesting a service, and how much of an accumulated debt an individual should pay when reciprocating.
The way accumulated credits are spent and accumulated debts are paid is not clear in Piaget’s model, and there can be different approaches to determining reciprocation values. However, it is desirable that solutions for determining reciprocation values allow the following.
• Agents should be able to compare the services they provide with the services they
receive in reciprocation, so that they can identify interaction partners that provide services with similar quality to their own services.
• Agents should be able to make use of high valorisations received in the provision
• Service reciprocation should cope with environments in which agents exchange services with different levels of effort or computational demand (so that a service with higher effort can be reciprocated with more than one service with lower effort).
As mentioned before, reciprocation values correspond to existing values of credit or debt, acquired in previous interactions, in the provision stage. This correspondence between service provision and reciprocation can be direct, such that one service provision cor- responds to one reciprocation, or multiple, such that one or more service provisions correspond to one or more reciprocations. Based on this, there are two possible ap- proaches to retrieving credits and debts, as follows.
1. Direct correspondence (DC): each credit or debt resulting from an interaction is seen as a unit that can be used for one reciprocation. The problem is then to choose which credit (unit) to spend, or which debt to pay in each reciprocation when they accumulate over time.
2. Creditor’s choice (CC): each credit resulting from an interaction can be spent in parts by receiving more than one service in return (in different interactions), or accumulated credits resulting from many interactions can be spent by receiving one service in return. The problem is then to choose the amount of credit to spend or the amount of debt to pay.
The advantage of the DC approach is that the comparison between services that agents provide with services that they receive in reciprocation is straightforward (since there is a one to one correspondence between them). However, making use of high valorisations is difficult, since agents would need to receive one service that has the worth of such high credit in reciprocation. In addition, it restricts applications in which services have different computation demands, since all interactions in which a highly demanding ser- vice is reciprocated with one trivial service will result in a negative balance of exchange values for the agent providing the highly demanding service.
In the CC approach, one provision may yield one or more reciprocations, and the re-
quester (or creditor)chooses the amount of credit to spend with each reciprocation. To
do so, the requester might analyse the quality of the reciprocated service by comparing its satisfaction with the reciprocated service against the average satisfaction associated
with the same service in previous interactions. The idea is that a requester, say α, can
choose how much of the credit received from a partner agent, sayβ, to spend each time,
depending on the service received. Thus, if there is a remaining credit andαis interested
in receiving another service from the same agent (that is, if the satisfaction with the reciprocated service is greater than or equal to the average satisfaction), it spends only
the credit that is equivalent to the satisfaction value, so that vαβ0 = s0αβ. However, if
Algorithm 3Algorithm for instantiating credit(β,sαβ0 ) according to the CC approach. 1: input: β, s0αβ 2: vaccαβ =Pn 1v 0 αβn
3: if |vaccαβ −s0αβ|>tolerance then
4: average satisf action=CalculateAverage(srv)
5: if s0αβ ≥average satisf actionthen 6: choice=s0αβ 7: else 8: choice=vαβacc 9: end if 10: else 11: choice=vaccαβ 12: end if 13: output: choice
Algorithm 4 Algorithm for instantiating debt(α,reciprocation value) according to the CC approach.
1: input: α, reciprocation value
2: taccβα =Pn
1t
0
βαn
3: t0βα=minimum(taccβα, reciprocation value)
4: output: t0βα
average, α may not be interested in requesting another service from the same agent,
and may spend all accumulated credit, which we now define as vacc
αβ, so thatv0αβ =vαβacc.
This solution requires thatαcommunicatesvαβ0 toβ, in a manner similar to the process
of determining subjective values by the requester communicating its valorisation to the provider (and this is possible because the credit to be spent is determined after the
service was received andα has calculated its satisfaction value).
Although with the CC approach both the reciprocation credit and the reciprocation debt are determined based on the creditor’s choice, the maximum amount of credit that the
requester can spend is all the credit that it has received fromβ in previous interactions.
This guarantees thatβ will not pay more debt than it owed.
The advantages of the CC approach to determining reciprocation values is that it al- lows an agent to identify if a reciprocated service compensates for any service that was provided in previous interactions, since the agent decides how much of an accumulated credit to spend based on the quality of the reciprocated service. It also allows agents to make use of high valorisations and copes with an environment in which agents provide services with different computational demands, since one provided service can yield more than one reciprocated service.
Since the CC approach addresses all issues in determining reciprocation values, we adopt
this approach instead of the DC approach. Therefore, the reciprocation values are
vαβ0 =credit(β, s0αβ)
t0βα=debt(α, reciprocationV alue(α))
where the function credit(β, s0αβ) is shown in Algorithm 3, the function
reciprocationV alue(α) just reads the credit to be spent in this reciprocation (com-
municated byαthrough the service completion acknowledge message), and the function
debt(α, reciprocationV alue(α)) is instantiated as in Algorithm 4 (ensuring that the re-
ciprocation value communicated byαis not greater than the debt thatβhas accumulated
withα in previous interactions).
In Algorithm 3, vαβacc is the credit that α has accumulated with β, and the difference
between this accumulated credit and α’s current satisfaction being higher than the tol-
erance value (expressed in line 2) indicates that there is a remaining credit, which can
be spent in parts. The function CalculateAverage(srv) uses α’s history of exchange
values to calculate α’s average satisfaction with the reciprocated service in previous
interactions. In Algorithm 4,tacc
βα is the debt that β has accumulated with α.
The disadvantage of this approach is that malicious agents may always spend low amounts of credit, even if the reciprocated service was good, just to exploit the part- ner agent. However, every time a low credit is spent, it causes a negative balance of exchange values for the agent in debt when its renouncement to provide the service is
greater than the debt it is paying (r0βα> t0βα). Therefore, the agent in debt can identify
this situation and deny the request, avoiding the action of such malicious agents.