2.1 Defining the Method and Making the Concessions
The method describes an iterative process which works towards a consensus among the negotiators. The negotiation protocol we suggest is based on a multi-criteria ap- proach. There are still some requirements:
The decision that has to be made is the choice of one of the predefined alternatives. This is the fact that will lead us to a guided solution on an ill-structured problem. However, this case imposes the following requirement: The final choice has to be one of the predefined alternatives. Negotiators do not have the ability to combine each alternative’s best characteristics in order to shape a new one. So, the final so- lution is certainly the best among the already formulated alternatives, but we can not be sure if this solution is also globally optimal.
As the method is based in a multi-criteria approach, the decision criteria have to fulfill the three fundamental principles as declared by Roy [4]: Monotony, exhaus- tively and non-pleonasm. In addition, the protocol we propose demands these crite- ria to be the same for all the negotiators. All the negotiators have to utilize the same scale to evaluate each criterion. Namely, the margin utility functions for each criterion are explicitly defined before the beginning of the process. Of course, each negotiator can construe the importance and the purpose of each criterion according to his beliefs.
We consider that negotiators act in a reasonable and rational way. This attitude should dominate in their decisions about the ranking of the alternatives, in their definitions of the criteria thresholds and generally, in the entire negotiation proc- ess. The final objective must be to reach consensus.
1.
2.
3.
Holding in mind the constraints – requirements of the method, let us define the vari- ables that the method employs: Let
M to be the number of the negotiators A the set of the alternatives
k number of the alternatives G the evaluation criteria set n the total of the criteria
A Multi-criteria Protocol for Multi-agent Negotiations 105 alternative’s i performance in criterion j
weight of the criterion j as declares by negotiator m mean weight of the criterion j
standard deviation of the criterion j alternative’s i score
2.2 The Proposed Methodology
The negotiation protocol’s flow chart is illustrated in Figure 1. This paragraph ex- plains step by step the negotiation process:
Step 1: Input Data. Data needed as input consist of the criteria data, the alterna- tives’ data and the negotiators’ preferences data. Analyzing these requirements, we end up with the final data categories: As far as it is concern the criteria, the process demands their scales (one scale can be either quantitative or qualitative) and their marginal utility functions. While the criteria scales are the same for every negotia- tor, their marginal utility functions can vary according to the decision makers’ atti- tude. As regards the alternatives’ data, each alternative must have a certain per- formance (grade) in every criterion. Moreover, the negotiators should declare an indicative ranking of the alternatives. This ranking is used by the protocol to evalu- ate negotiators’ preferences and should indicate preference or indifference between the alternatives. Finally, the negotiators should also declare the criteria thresholds. These thresholds reveal the minimum (if the criterion monotony is ascending) or the maximum (if the criterion monotony is descending) accepted value for every criterion.
Step 2: Implementing UTA II method to estimate criteria weights. The method implements UTA II [13], [19] once for each negotiator. This way, the method es- timates each negotiator’s criteria weights. Hence, by the end of this step, a table dimensioned [M+2,n] (where M is the total of the negotiators and n the number of the evaluation criteria) is available to the protocol. The rows of this table represent the negotiators and each column denotes a criterion. Thereby, cell includes the weight for the criterion j, as it was estimated by UTA, for the negotiator m. Obvi- ously, the sum for each row is 1. The last two rows contain the mean weight for each criterion and its standard deviation.
Step 3: Formulation of the global aggregative function to evaluate the alterna- tives. In this step we use the results of the Step 2. We are able therefore to express the global function as follows :
Step 4: Ranking the alternatives. The method ranks the alternatives according to the score that they achieved during the previous step. The final ranking is a de- scending order of the alternatives, so that the alternative with the biggest score is first in this rank.
106 Nikolaos F. Matsatsinis and Pavlos Delias
A Multi-criteria Protocol for Multi-agent Negotiations 107 Step 5: Check the alternatives. The model checks one by one every alternative in their ranking order. If there is no other alternative then go to step 8
Does the alternative breaks any of the negotiators’ thresholds as declared in step 1? If not, then go to step 9, else the method keeps on with step 6.
The protocol check the negotiators one by one, therefore, if there is a threshold breaking, that means that this breaking is the first met. If there are many threshold breakings about the same criterion, these will be met during the next step of the it- erative process.
Step 6: Negotiators’ information. The protocol informs the negotiators that the alternative currently checked breaks one of the thresholds. This communication process is implemented through a message that contains the following fields: Which alternative is currently checked, what was the rank of this alternative, the negotiator that broke the threshold and his history (history means here how many times has this particular negotiator brake criteria threshold before), the negotiator’s criterion threshold that was violated and finally the distance between negotiator’s threshold and the alternative’s performance in this criterion.
Step 7: Negotiate with the decision maker (negotiator). The negotiator who blocked the process (being informed that his threshold was the block) is being asked if he is attainable to reconsider that threshold’s value. The answer could be either “yes” or “no”. In the “no” case the method returns to step 5 while in case of “yes” the negotiator’s threshold is set equal to the alternative’s performance in the criterion that the breaking took place. The process reveals its iterative style by re- turning to step 5.
Step 8: Negotiation Failure. The model is not capable to solve the negotiation problem. Actually, there is no alternative that satisfies all the negotiators’ require- ments. Inform the negotiators and go to step 10.
Step 9: Select the alternative. Select the current alternative. The method worked out the negotiation problem. The protocol has chosen the optimal solution. Inform the negotiators about the negotiation success and step forward.
Step 10: Negotiators’ evaluation. The process implements the evaluation model. The results are sent to the negotiators with a message and are posted to a database. End of the process.
Negotiators’ Evaluation Model 2.3
In a negotiation process, its outcome is fully dependent on the negotiators, no matter what the protocol is. Moreover, in this study, the negotiation takes place among hu- mans, so it is not a great sin to suppose that a negotiator would behave the same way every time he is involved in a negotiation process.
Consider the above, and we realize how important is to evaluate the humans that participate in the negotiation. Such an evaluation method should reveal how co- operative or how reactive a negotiator is. The method should reward the negotiators who let the process flow towards a consensus but the method should also “punish” the negotiators who obstruct the process and keep the negotiation away from a final (op- timal) solution. This model could be used in future negotiations processes as it pro- vides an actual “preference” of the negotiators. So, humans that stand against consen- sus should have fewer possibilities to join a future negotiation process.
108 Nikolaos F. Matsatsinis and Pavlos Delias
Fig. 2. Negotiators’ Evaluation Model.
The model we propose is illustrated in figure 2. Three main aspects configure the final score for each negotiator, these are: the distance between the negotiator’s prefer- ences from the final solution, the will for co-operation that the negotiator demon- strated through this process and finally, his negotiating behavior during past proc- esses. These aspects participate to the final score’s definition by certain weights. In order to estimate these weights, it is possible to implement once again UTA II method, or just any other analytical regression’s method.