Offer generation strategy

Depending on the combinations of the options in the issues – i.e. the offer configuration – and the user’s preferences over these options, the difference in the demanded utility between the last and penultimate offer of a negotiator can either be positive – indicating a higher demand –, the same – indicating an insistence– , or negative – indicating a concession – from the point of view of the focal negotiator. When negotiators follow a concession-based approach in negotiations, i.e. start with extreme demands and lower these in the course of the negotiation – as the agents proposed in this conceptual model do and as found to be the dominant approach in human negotiations (e.g. Pruitt, 1981) – then making concessions in continuously lowering the demand is the only viable way to reach an agreement. The software agents in our conceptual model follow this concession making approach in generating their offers. Different forms of concession making to generate offers – depending only on the negotiation object and the user’s preferences over this negotiation object – are discussed in detail in the subsequent paragraphs.14

Current research identified concessions as a common phenomenon in negotiations, as almost all negotiation processes consist of at least some concessions. Frequent concessions increase the probability to reach an agreement and reduce the duration of negotiation. Obviously the reduction of demand implied by concessions leads to agreements that provide lower utility to the conceding negotiator, however, the joint performance – i.e. Pareto optimality – of reached agreements is not negatively influenced by concession making, which underlines the importance of concessions for successful negotiations (Filzmoser and Vetschera, 2008).

When an agent has no information about the preferences of its opponent, which is the case in our study, an offer intended by one party as a concession to the other party could be perceived by the opponent as a reverse concession (higher demand) or no change in the demanded utility level (insistence) (Kersten et al., 2000). To avoid problems of wrong perceptions, in our setting of unavailable information about the opponent’s preferences, the software agents act purely myopic in making their decisions. Offers are evaluated according to the only available precise information the agents have access to, namely the preferences of the software agent’s user over the negotiation object. Therefore the opponent is perceived to make a concession if the utility difference – from the point of view of focal software agent – between the last and the penultimate offer of the opponent is positive i.e. the last offer affords a higher utility to the focal software agent. Similarly a bargaining step is said to be a concession by the focal software agent if the

for future negotiations but this remains an aspect to be investigated in subsequent studies.

14_{Note that some of the agents do not follow strict concession making, but if possible propose offers of same}

utility level, like the subsequently discussed monotonic concession strategy, however if there are no such offers of same utility level these agents also reverse to concession making, so their general strategy allows to classify them as concession strategies.

4.2. Automated negotiation system 91

utility difference between its last and penultimate offer is negative i.e. the last offer affords lower utility to the software agent.

4.2.2.4.1 Strictly monotonic concession SMC Contini and Zionts (1968) propose a model in which the players in a bilateral negotiation start with an extreme offer and afterwards follow a strictly monotonic concession strategy. Unlike the monotonic concession strategy discussed next, in the strictly monotonic concession strategy the demanded utility is continuously lowered with every offer proposed, so that never two offers of the same utility are submitted. In this game as in our conceptual model (due to the acceptance criterion discussed below) agreement is reached when the demanded utility levels of the negotiators intersect. To avoid exploitation a software agent following this offer generation strategy has to reduce the demanded utility with each subsequent offer it makes by the minimal amount possible. This offer generation strategy can be implemented easily by ordering all offers not sent yet and that afford strictly lower utility than the last offer sent by decreasing utility – offers of same utility between which the agent is indifferent are ordered randomly so that they are chosen with equal probability – and the first offer on this ordered list is selected to be the next offer to propose.

4.2.2.4.2 Monotonic concession MOC Kelley (1966) proposes an algorithm for offer se- quencing to navigate the progression of offers towards the Pareto frontier of the negotiation problem. He calls this algorithm ’systematic concession making model’. Negotiators start with an extreme opening offer, if their offer is not accepted by the opponent, they propose alterna- tive offers of same utility. The sequence in which these offers of same utility are proposed is arbitrary as the negotiator is indifferent between offers of equal utility. Only if all offers for a given level of utility are proposed the negotiator lowers the demanded utility level to the next lower one and again proposes all offers of this utility level. In the systematic concession making model proposed by Kelley (1966) offers are accepted if the utility levels demanded by the two negotiators intersect – as in our acceptance criterion discussed below. Such an intersection of demands then is likely to present a Pareto-optimal solution as found in experimental studies, where subjects following this systematic concession making strategy succeeded in settling for Pareto-optimal solutions (Kelley, 1966). This offer generation strategy can simply be followed by software agents in ordering all offers not proposed so far decreasingly according to the utility the offers afford to the software agent – as the agent is indifferent between offers of same utility they can be ordered randomly so that there is always the same probability of choosing one out of a set of offer with same utility. The next offer to be proposed then is always the first on this ordered list. Unlike the strict monotonic concession strategy discussed above the software agent not necessarily makes a concession with each offer it proposes, but the utility of the proposed offer could be the same as the utility of the last offer if there exist offers of same utility, so that in this step no concession is made, though the whole process in general constitutes a concession making process.

4.2.2.4.3 Least-cost-issue concession MUM The least-cost-issue concession strategy was proposed by Mumpower (1991) and Mumpower and Rohrbaugh (1996) as a simple heuristic negotiators could follow in negotiations. The authors argue that negotiators due to uncertainties and complexities associated with negotiations and their limited cognitive capacities will apply

simple ’rules of thumb’ when making their decisions about offers and counter-offers. An example for such a heuristic, they propose for multi-issue negotiations, is what we call the least-cost-issue concession strategy (Mumpower and Rohrbaugh, 1996, p. 395): ’One common heuristic, for

instance, is simply to offer concessions successively on that issue for which such concessions cost least in terms of the negotiator’s utility.’

Basing on the last offer proposed the negotiator compares the last offer with those where only the option in one of the issues is changed and choses the offer where this change in one issue causes the lowest costs i.e. constitutes the lowest concession. Minimal concessions are chosen to avoid exploitation as the negotiator has limited or no information about the preferences of the opponent, which are private information of the negotiator, and also not knows when the threshold of acceptability of an offer is reached by his concessions. Unlike the two previously mentioned strategies the least-cost-issue strategy no purely bases on utilities of offers but also on the content of the offer. The next offer to propose must not differ from the last one by more than one issue in terms of options. From all these offers that differ in just one issue the one where this change costs least is chosen as next offer, i.e. the one where the difference between the last offer and the next offer is zero or the smallest positive value of all the candidate offers – again in case of ties an offer is chosen randomly with equal probability for all tied offers to be chosen as next offer to be sent. The implementation of this offer generation strategy in a first step needs to determine the similarity of the not yet sent offers and the last offer in comparing in how many issues the options of the last offer and the not yet sent offers are the same and selecting those offers that differ only in one issue as candidates for the next offer to be submitted. In a second step the software agent has to chose that offer out of these candidates for which the utility difference between last and candidate is zero or the minimal positive one.

4.2.2.4.4 Lexicographic concession LEX This software agent starts with the highest utility offer and then bases offer generation on a lexicographical ordering of offers. Lexicographical ordering of alternatives in multi-attribute decision making problems as an alternative to additive multi-attribute utility functions was proposed and investigated by Beroggi (2003). The software agent changes the option in the issue of the lowest weight to the next lower level and evaluates whether or not this offer constitutes a concession (or at least no increase of the level of demanded utility) which is the case when the offer has lower utility than (or equal utility as) the last offer of the focal software agent. If no concession is found in changing the options of the issue of lowest importance the software agent continues to change the option in the second lowest weighted issue to find such an offer etc. To implement the lexicographic concession strategy the software agent first has to establish a lexicographic ordering of all offers in ordering the issues and within the issues the options by decreasing utility, i.e. by the issues weights and the options partial utility to the user (and randomly in case of ties). Next the software agent has to chose the subset of offers from this ordered list that afford same or lower utility compared to the last offer made and propose the first package of this resulting subset as the next offer.

4.2.2.4.5 Tit-for-tat concession TFT Recently Shakun (2005) proposed a slightly modified version of tit-for-tat – a strategy known for being very successful in the iterated prisoner’s dilemma (Axelrod, 1980a,b), which is closely related to negotiation – for software agents in automated negotiation, which fully reciprocates concession – in terms of their own utilities –

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received by the opponent’s last offer. As mentioned in the review, imitating strategies can simply define the level of utility the next offer should provide, but have no means to determine the actual configuration of the next offer. Therefore Shakun’s software agent not only reciprocates concessions but also informs the opponent on which of the issues it would like the opponent to make the next concession. As this is not possible with the messages allowed by the protocols in our conceptual model we decided to combine tit-for-tat concession making with a trade-off mechanism for offer generation. Trade-off mechanisms try to propose offers as similar as possible to the opponents last offer, thereby trading issues to potentially achieve mutually beneficial outcomes. Similarity of offers could be defined in many ways like Hamming distance, for a discrete set of possible solutions, or Euclidean distance, otherwise. The software agent resulting from the combination of tit-for-tat concession and trade-off offer generation operates as follows: In a first step the offers constituting the same (or higher) concession as that provided to the software agent by the opponent with his last offer are selected from the not yet sent offers. In case of ties the offer with the lowest Hamming distance to the last offer of the opponent is chosen i.e. that offer which is most similar to the opponents last offer in terms of the options for the issues. Note that in contrast to the other software agents the TFT concession strategy also considers the configuration of the opponents offers in making its decisions about the configuration of the next offer and the magnitude of the concession to be made. Concessions of the opponent are fully reciprocated therefore considerations about following either an active or passive concession strategy – discussed in the next section – are not applicable for the tit-for-tat agent. It always has a basis to further negotiate and reciprocates a concession made by the opponent, however it also reciprocates reject messages in protocol 3, thereby triggering termination of the negotiation by the interaction protocol.

Note that different weights can be given to the similarity of the concession to the last concession of the opponent, on the one hand, and the similarity in offer configuration to the last offer of the opponent on the other hand, in designing such tit-for-tat trade-off strategies. As can be seen from the above discussion our design first considers reciprocation of concessions – i.e. assigns highest weight on this aspect – and only in a second step considers the similarity of offers. This is justified with the concerns about avoiding exploitation or unfavorable agreements in relation with continuous concession strategies. The offer of highest similarity to the last offer of the opponent would be an offer that coincides with it – i.e. proposing the same package – which would lead to the acceptance of the first offer of the opponent according to the acceptance criterion employed in our study. Accordingly all offers more similar to those of the opponent increase the probability that these offers are accepted, which however could result in inferior outcomes for the software agent that focuses too much on similarity of offers and concedes too much. However, following the logic of trade-off offer generation proposing more similar offers could result in offer configurations acceptable for the opponent without having to give in too much in terms of utility and thereby leading to favorable agreements. So there exist many possible parameterizations for such tit- for-tat trade-off strategies (with different weights assigned to concession reciprocation and offer similarity), however, to evaluate them would exceed the scope of this study and we therefore focus on the design proposed above for the mentioned reasons and postpone a detailed analysis of the possible configurations to later studies.

If a software agents runs out of offers according to the above determined offer generation strategies it checks whether the opponent made an offer of higher or same utility compared to the last own

offer sent (see Figure 4.9). If this is the case values are manipulated so that this last offer of the opponent is accepted. Thereby the software agent does not risk to break off negotiations by sending reject or quit messages but rather accepts the opponent’s offer. Otherwise, if the software agents has no offers left to propose according to its offer generation strategy and the last offer is not acceptable it rejects the last offer of the opponent, breaks-off the negotiations, or finally accepts the last offer of the opponent (in this order), whatever is possible according to the restrictions of the interaction protocol.