consequently unfairer agreements. This argumentation also provides a hint for the reason behind the seemingly ’role-dependent’ performance of automated negotiations that achieves agreements of higher individual utility for the seller than for the buyer, found in this and the previous section, as the system components do not discriminate between the roles the reason must lie in the preferences of the parties and the group of buyers seems to have unfavorable preferences compared to the group of sellers.
6.3
Comparison of software agents
After this analysis of the general influence of the protocol on different outcome measures – for the same software agent combinations and negotiation problems – we shift our attention to the software agents as the second main component in automated negotiation systems. As the software agents do not discriminate between the parties they represent, but base decision making only on the preferences indicated to them, we analyze the performance for a focal party – in our case the seller party – grouping together in one sample all treatments that use the same type of software agent to represent the seller party. Thereby across the samples only the software agent that represents the seller differs and within the samples this seller agent is used in simulation runs with all other agent types representing the buyer party (including a version of itself), in all protocols, and for all negotiation problems.5
% LEXact LEXpas MOCact MOCpas MUMact MUMpas SMCact SMCpas LEXact 66.22 LEXpas 58.12 0.0000 MOCact 64.09 0.0000 0.0000 MOCpas 58.96 0.0000 0.0000 0.0000 MUMact 71.56 0.0000 0.0000 0.0000 0.0000 MUMpas 61.40 0.0000 0.0000 0.0000 0.0000 0.0000 SMCact 65.15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SMCpas 58.60 0.0000 0.0151 0.0000 0.0363 0.0000 0.0000 0.0000 TFT 66.62 0.0264 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Table 6.10: Proportion of agreements for different software agents
The proportion of agreements reached in automated negotiation with the nine different software agents representing the seller party – negotiating in all three protocols, with all nine software agents representing the buyer, for three replications of all 2,065 negotiation problems – and multiple pairwise comparisons of these proportions are presented in Table 6.10. The proportions of agreements reached and their statistical comparison – with Pearson’s χ2 independence test –
5Same as for the comparison of protocols, the proportions of agreements and Pareto-optimal agreements in the
samples are compared using Pearson’s χ2 independence tests and differences in all other outcome measures are
analyzed by means of Wilcoxon ranked sum tests. In the nine samples (one for each type of software agent) the samples sizes for proportion measures are 9 ∗ 3 ∗ 3 ∗ 2065 = 167265. This number of simulation runs results from the combination of a specific software agent with all nine other software agents for three replications of the 2065 negotiation problems in the three protocols. As the outcome measures minimal distance to the Pareto frontier, contract imbalance, and utility of the agreement to the focal party and the opponent can be calculated for those simulation runs that resulted in an agreement only, sample sizes for these outcome measures can be derived by multiplying the total number of simulation runs in the sample (167265) with the proportion of agreements reached in this sample – provided in Table 6.10. In Tables 6.10 to 6.15 we omit test statistics due to space restrictions but gladly provide the interested reader with values on request. All p-values reported are adjusted for multiple comparisons by the Bonferroni-Holm method.
reveal, holding all other factors equal at all possible levels, a clear ranking of the software agents (as all p < 0.05 at least). In systems where for the seller party MUMact is used the proportion of reached agreements is highest (71.56 %), followed by TFT, LEXact, SMCact, MOCact, MUMpas, MOCpas, SMCpas, and LEXpas, which reached with 58.12% agreements over all simulation runs the lowest performance in this outcome measure. This ranking indicates that software agents with active concession strategies and TFT reach a higher proportion of agreements than software agents embodying a passive concession strategy. The higher proportion of agreement with active concession making and TFT can be explained by their mechanisms, as these software agents make offers with first concession steps if the opponent reciprocated previous concessions (act) or fully reciprocate the opponents previous concessions (TFT) – thereby also making concession steps ahead –, which is beneficial to the prospects of reaching an agreement in negotiations that could result in a break off or termination of negotiations – in case the protocols enable this – if such concession steps are not taken. The effect of the offer generation strategy is not clear from this ranking, also the effect of the protocol – as in the compared samples all protocols are covered – and whether this ranking is insensitive of the protocol used in the automated negotiation system or if there exist interactions between the software agent and the protocol – this is analyzed for the proportion of agreements, as well as for the other outcome measures, in the subsequent section.
% LEXact LEXpas MOCact MOCpas MUMact MUMpas SMCact SMCpas LEXact 28.16 LEXpas 24.15 0.0000 MOCact 42.32 0.0000 0.0000 MOCpas 38.35 0.0000 0.0000 0.0000 MUMact 34.41 0.0000 0.0000 0.0000 0.0000 MUMpas 28.98 0.0000 0.0000 0.0000 0.0000 0.0000 SMCact 32.29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SMCpas 28.66 0.0046 0.0000 0.0000 0.0000 0.0000 0.0442 0.0000 TFT 37.93 0.0000 0.0000 0.0000 0.0223 0.0000 0.0000 0.0000 0.0000
Table 6.11: Proportions of Pareto-optimal agreements for different software agents
Also for the proportion of Pareto-optimal agreements a clear ranking of software agents emerges from the multiple pairwise comparisons summarized in Table 6.11 (all p < 0.05). While we found no differences between the ordering of interaction protocols concerning the proportion of agreements and the proportion of Pareto-optimal agreements that are achieved with automated negotiation systems using different interaction protocols in the previous section of this chapter, for the software agents these rankings differ. Automated negotiations in which – for all opponent software agents, negotiation protocols, and negotiation problems – MOCact represents the seller party reach a significantly higher proportion of Pareto-optimal agreements than all other agents with 42.32 % of the simulation runs ending with a Pareto-optimal agreement. MOCact – which makes offers with monotonically decreasing utility and first concession steps if the opponent reciprocated previous concession – is followed by MOCpas, TFT, MUMact, SMCact, MUMpas, SMCpas, LEXact, and finally LEXpas, which reaches Pareto-optimal agreements only in 24.15% of the simulation runs where this software agent is used for the seller party.
This ranking is not only different from the previous one concerning the proportion of agreements, but also reveals a different pattern. While for the proportion of agreements reached the concession strategy was of highest importance, for the upper and lower end of the ranking of software agents for the proportion of Pareto-optimal agreements the offer generation strategy matters – as the two
6.3. Comparison of software agents 129
MOC-agents achieved the two highest while the two LEX-agents achieved the two lowest proportions of Pareto-optimal agreements. The concession strategy then determines in a second step the ordering of these agents, as for both MOC and LEX the active version is ranked higher. Higher influence of the concession strategy can be found for the middle of the software agent ranking for the proportion of Pareto-optimal agreements, as for both MUM and SMC, the active versions achieve better values in this outcome measure than the passive concession making versions do. That the offer generation strategy is of higher importance for the proportion of Pareto-optimal agreements than for the proportion of agreements is plausible as Pareto-optimality depends more on the actual configuration of the offers, while for the acceptance of an offer of the opponent it ’only’ has to provide higher utility than the next offer the focal software agent would send – according to the acceptance criterion used with the software agents (see Chapter 4). However, one must not forget, that the proportions of Pareto-optimal agreements are absolute proportions over all simulation runs, so that the proportion of agreements reached influences this outcome measure. This can be an explanation for the higher proportions of Pareto-optimal agreements reached by active concession making strategies and TFT compared to passive concession making for the same offer generation strategy – which reach more agreements – as we would assume the opposite here. Passive concession making strategies resist making first concession steps and thereby should increase the utility of an agreement – however, simultaneously lowering the prospect of reaching an agreement as can be derived from Table 6.10 – to the party using a software agent that follows this strategy and thereby should push agreements towards the Pareto frontier. Given this we will see the actual effect of software agents concerning the efficiency of reached agreements in the discussion of the next outcome measure – minimal distance to the Pareto frontier, which only can be calculated for simulation runs that reached an agreement – which was found to closely resemble the results concerning the relative proportion of Pareto- optimal agreements in Section 6.2.
⊘ LEXact LEXpas MOCact MOCpas MUMact MUMpas SMCact SMCpas LEXact 5.56 LEXpas 5.78 0.0014 MOCact 2.52 0.0000 0.0000 MOCpas 2.61 0.0000 0.0000 0.0127 MUMact 4.85 0.0000 0.0000 0.0000 0.0000 MUMpas 5.13 0.0000 0.0000 0.0000 0.0000 0.0092 SMCact 3.96 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SMCpas 4.07 0.0000 0.0000 0.0000 0.0000 0.0008 0.0000 0.0274 TFT 4.06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Table 6.12: Minimal distance to the Pareto frontier for different software agents
The results and comparative analyses concerning the minimal distance to the Pareto frontier again form a clear ranking of software agents (all p < 0.05), similar to that found for the proportion of Pareto-optimal agreements – see Table 6.12. MOCact agents achieve results closest to the Pareto frontier – with an average minimal distance of 2.52 points in the utility space – followed by MOCpas, SMCact, TFT, SMCpas, MUMact, MUMpas, LEXact, and with an average minimal distance of 5.78 points agreements reached in automated negotiation systems with LEXpas representing the seller were farthest from the Pareto frontier.
Compared to the software agent ranking found for the proportion of Pareto-optimal agreements, this ranking shows the importance of the offer generation strategy more clearly, however the
assumed better outcomes of passive concession making are not present as for the same offer generation strategy actively conceding software agents always achieve agreements closer to the Pareto frontier than passively conceding versions.
Tables 6.13 and 6.14 show the average individual utilities of a reached agreement to the focal party (seller – Table 6.13) and the opponent party (buyer – Table 6.14) for specific software agents used to represent the seller side in the automated negotiation systems, as well as the outcomes of multiple pairwise comparisons for these outcome measures.
⊘ LEXact LEXpas MOCact MOCpas MUMact MUMpas SMCact SMCpas LEXact 68.24 LEXpas 68.82 0.0000 MOCact 82.31 0.0000 0.0000 MOCpas 82.98 0.0000 0.0000 0.0000 MUMact 63.91 0.0000 0.0000 0.0000 0.0000 MUMpas 64.94 0.0000 0.0000 0.0000 0.0000 0.0000 SMCact 72.42 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SMCpas 73.11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 TFT 58.64 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Table 6.13: Focal agent’s (seller) utility for different software agents
⊘ LEXact LEXpas MOCact MOCpas MUMact MUMpas SMCact SMCpas LEXact 68.13 LEXpas 68.33 0.0326 MOCact 56.83 0.0000 0.0000 MOCpas 56.66 0.0000 0.0000 1.0000 MUMact 72.22 0.0000 0.0000 0.0000 0.0000 MUMpas 72.19 0.0000 0.0000 0.0000 0.0000 1.0000 SMCact 65.99 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SMCpas 65.99 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6008 TFT 78.83 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Table 6.14: Opponent’s (buyer) utility for different software agents
Utilities of agreements achieved for the party they represent significantly differ between the software agents (all p < 0.001) as can be seen from Table 6.13. Here, MOCpas achieves, with 82.98 points the highest utility score for its party, followed by MOCact, SMCpas, SMCact, LEXpas, LEXact, MUMpas, MUMact, and finally TFT, which achieved a relatively low utility score of 58.64 points only. So, as for the proportion of Pareto-optimal agreements and the minimal distance to the Pareto frontier outcome measures, also for the individual utility of an agreement to the focal software agent the offer generation strategy has major impact. Moreover, for individual utility of the agreements – and therefore the individual performance of software agents – we find the positive effects assumed for passive concession making strategies – which, however were not found for joint performance measures as discussed above. We argue that this ordering results from the more systematic offer generation followed by the higher ranked agents. As can be derived from the description of the different offer generation mechanisms in Chapter 4, MOC is the most systematic offer generation mechanism, proposing first all offers of a given utility level before this level is decreased to the next lower level, where again all offers are proposed etc. SMConly is different from MOC in that it never proposes offers of the same utility level but strict monotonically decreases the level of demanded utility. MUM proposes offers with least concession in one issue only, and LEX proposes offers that constitute concession following a lexicographic
6.3. Comparison of software agents 131
ordering of possible solutions. TFT, which is ranked lowest in the average utility of agreements achieved for the party it represents, on the other hand, can be considered as following the least systematic offer generation as it generates offers that reciprocate the opponents’ concessions but does not follow any rules in this offer generation that prescribe a specific path through the set of possible solutions.
Concerning the utility of a reached agreement – with different software agents representing the seller side and all types of software agents representing the buyer side in systems using all pro- tocols and negotiating all negotiation problems – to the opponent the highest average utility is achieved when TFT is used by the focal party (78.83). Second best results for this outcome measure are achieved for the opponent if the focal party’s software agent is of type MUM, fol- lowed by LEX, SMC, and MOC, which results in the worst agreements from the point of view of the opponent’s utility. While differences are highly significant between offer strategies, they are insignificant between active and passive concession making strategies for software agents follow- ing the same offer generation strategy – with exception of LEX, which follows a lexicographical ordering of offers in its offer generation strategy, where passive concession making is slightly better than active concession making and this difference is significant at p < 0.05. That it is better for the opponent if the focal party uses a LEXpas rather than a LEXact software agent is surprising, as passive concession making means fewer and smaller concessions compared to active concession making, but can result from canceling out of ’bad’ negotiation problems, which could lead only to mediocre agreements when LEXpas is used, as LEXpas is the software agent that achieved the lowest proportion of agreement. So negotiation problems that would lead to unfavorable agreements, reach no agreement at all in simulation runs that use LEXpas and the remaining negotiation problems cause not only higher utility to the focal party but also to the opponent – compared to the usage of LEXact.
⊘ LEXact LEXpas MOCact MOCpas MUMact MUMpas SMCact SMCpas LEXact 19.65 LEXpas 20.36 0.0002 MOCact 27.31 0.0000 0.0000 MOCpas 28.12 0.0000 0.0000 0.0000 MUMact 23.87 0.0000 0.0000 0.0000 0.0000 MUMpas 24.63 0.0000 0.0000 0.0000 0.0000 0.5405 SMCact 21.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SMCpas 22.60 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 TFT 24.58 0.0000 0.0000 0.2350 0.0000 0.0000 0.0000 0.0000 0.0000
Table 6.15: Contract imbalance for different software agents
These results, for the opponent’s utility of an agreement if different software agents are used by the focal party, not only underline the higher influence of the offer generation strategy for both, the focal as well as the opponent’s individual utility of an agreement, but also show that the ordering of offer generation strategies is opposite for the parties. Moreover, from the above considerations concerning the effects on the utility of the focal and the opponent party when a certain agent is used by the focal party, one already can derive some expectation about the effects of the usage of agents on the contract imbalance – unfairness – of reached agreements. As the agents that perform good for a focal party make the opponent party worse of and vice versa, those agents which lie in the middle of both rankings should be the best in terms of contract imbalance – i.e. achieve more balanced and therefore fairer agreements. Recall that the ranking
of offer generation strategies in decreasing order of their average utility score for the focal agent was MOC – SMC – LEX – MUM – TFT, and for the opponent party’s average utility score exactly inverse, i.e. TFT – MUM – LEX – SMC – MOC. So we assume LEX agents to lead to fairer agreements followed by SMC and MUM agents and finally TFT and MOC agents.
Table 6.15 supports this assumption, as LEX agents achieve smaller contract imbalance than SMC agents, which again achieve fairer contracts than MUM agents. Furthermore, TFT and MOC software agents used to represent the focal party (seller) in the automated negotiations achieve agreements where the difference between the two parties utilities is highest (all p < 0.001, with exception of MOCact versus TFT). The significant differences between active and passive versions of the agents – for same offer generation strategies – indicates a minor but significant effect of the concession strategy on the contract imbalance, namely that active conceding leads to fairer outcomes than passive conceding (all p < 0.001, except for MUM offer generation – which makes offers in order to provide concessions in the issue where they cost least – where differences in contract imbalance between MUMact and MUMpas are not significant). So besides the major effects of the offer generation strategy, the positive effect of passive concession making strategies on the utility of the agreement to the party that uses them and the lack of effects on the opponent party’s utility shown in Tables 6.13 and 6.14 respectively, leads to imbalance and therefore smaller fairness of the agreements.