Reaching Agreements

The relationship between the various concurrent negotiation threads is a key issue in concurrent bilateral negotiation. To this end, we discuss two points:

• how is the decision to accept the opponent’s offer made and • what happens if one or more of the offers gets accepted?

Now, the solutions to both of these questions vary in the literature. In particular,

Rahwan et al.(2002) use autonomous negotiation threads that each try to reach an acceptable agreement on their own. It is, therefore, the thread itself that decides when to accept the offer and when to continue negotiation. The coordinator can order threads to quit negotiating, but not to accept or reject a particular offer. The coordination between different threads is achieved ex post (after agreement), as the coordinator uses one of four strategies to select the agreement to be bound by. Strategies are:

• desperate: as soon as an acceptable offer exists, it is accepted and all other negotiations are ended. If there is more than one acceptable offer, the one with the highest utility is selected.

• patient: threads that have an acceptable deal are asked to wait while other threads finish their negotiation. Then the result offering the best utility is selected and others are decommitted or ended.56

55_{We will discuss this in more detail in section12.2.2.}

56_{The strategy guarantees the best possible deal, but does not care about time constraints.} One variation is that at the deadline the best offer so far is selected and the others are rejected.

• optimised patient: as patient, but the outcomes so far affect the reservation prices of the remaining negotiations, so that each new agreement is better than earlier ones. Thus the utility constraint is updated to the highest offer so far.

• strategy manipulation: the coordinating agent may modify the negotiation strategies of different sub-negotiators at run time.

All but the last one are very one-sided, since they assume that the providers obediently wait until the consumer makes a decision on which offer to accept and that negotiator can decommit from any other agreements without any problem at any time. It seems that the agent does not need to pay anything to decommit and the possibility that the opponent accepts the agent’s offer is not discussed in the paper. The most interesting approach for our purposes (strategy manipulation) is not explained in any detail.57 _{In the model it has no strategic relevance whether}

the consumer agent’s offer was accepted or whether it was the consumer agent that accepted the provider’s offer, since in either case coordination is done ex post. A different approach is offered byLi et al.(2004), in which all negotiation decisions are made in the negotiation threads, but the coordinator does influence the tactics used in each thread already during the negotiation. The coordinator estimates the outcomes of different threads and uses these estimates to set the reservation utility for each thread.58 _{In order to make the estimates several big assumptions are made:}

the buyer agent is assumed to know the distribution of the providers’ reservation prices, the newcomers’ arrival probability and their items’ value distribution. As Li et al. have done, we assumed that the sellers can exit and more sellers can enter at any time (requirement R5). Any reasonable negotiation model that works in the market environment should usually consider this requirement and consider any good contracts the latecomers might bring with them. It may not be a good idea to take a mediocre deal if there are good providers probably coming later. Li et al. use analytic approach and knowledge of many distributions to calculate their estimate, but we will instead use empirical data collected on previous runs,

57_{Only one example is given and that is also very one-sided: Once an acceptable offer exists,} all the other threads are ordered to send a take-it-or-leave-it offer with higher utility than the one already reached. If none of these offers gets accepted, then the original agreement is selected. However, if one of these new offers gets accepted, it will get selected and if more than one offer is accepted, one is selected at random.

58_{The reservation utility is equal to the expected utility of the outside option (highest expected} utility of all other negotiation threads and negotiation threads starting in the future). They use a simple time-dependent heuristic strategy to find out what offers to make. They also offer different methods to estimate the outside options and compare the results.

because we believe that is more realistic. Moreover, it allows us to consider settings in which such distributions for future expected utilities might be difficult to derive. A problem with the model by Li et al. is that they do not discuss the coordination issue any further, so either they assume that once one thread accepts an offer, others are automatically ordered to quit (and there is enough time to do this) or that the consumer agent is able to decommit from all extraneous contracts for free. Since cases where the consumer agent’s offer is accepted and the consumer agent accepts the offer are not separated, the latter seems more probable. This is inappropriate for our settings because decommitment policies and how they should affect the parties behaviour is a central theme to our work and this particular problem (extra contracts) is an important part of what we investigate. Therefore, for us, it is obvious that simultaneous contracts are possible and the buyer should have to pay a decommitment fee for any extra contracts it does not need.

Finally, Nguyen and Jennings (2005) use very explicit coordination mechanisms and, unlike the other models, all decisions on acceptance are made by the coordi- nator. This coordinator gets all the opponent offers from the negotiation threads and then decides whether to accept the best of them or to continue negotiating. The negotiation thread’s task is then to implement this decision. However, more difficult situations occur when more than one offer gets accepted by the provider agents. In such cases, the consumer agent just decommits from these extra con- tracts and it seems that it can do so by paying a decommitment fee.

We require that our model must have an unbiased protocol. Therefore, a situation where one party can and the other cannot decommit is not acceptable to us. On the other hand, we think that, if and when a contract has been made, the decommitment should usually cost something. Consequently, we think that the last approach by Nguyen and Jennings is the most appropriate starting point for our work. Their model is also the most explicit when it comes to the mechanics of committing and decommitting. The other models seem to have suprisingly little to say about these topics, although they seem essential to any concurrent bilateral negotiation model.