The Basic Models

We start by introducing the three models of concurrent bilateral negotiation dis-cussed in the multi-agent system literature. They are similar in many respects, but there are also some significant differences. Some are also more explicit on the details we are interested in than others.

In particular, Rahwan et al. (2002) were the first to propose a concurrent bi-lateral negotiation model. They have a number of bibi-lateral negotiating threads (called sub-negotiators) controlled by one coordinating agent. In this model, each

50As we will discuss in more detail in section9.1.2, the countertactics we use do not care what offers the opponent makes during the negotiation but instead they use a distribution for the lowest offer the opponent is going to make and set their target price accordingly. With many negotiations, getting this absolutely right is not essential.

sub-negotiator conducts a one-to-one negotiation with a different opponent. The coordinating agent coordinates the efforts of these different threads. To facilitate this, the sub-negotiators report to the coordinating agent after receiving a response (offer, rejection or acceptance) from their opponent. The coordinating agent then evaluates the situation and issues instructions to sub-negotiators accordingly. The most important of these instructions is either an order to continue or stop negoti-ating, but they can also include a change in the negotiation parameters. However, Rahwan et al. do not develop this idea very far and the strategies their coordinat-ing agents use are very simple and somewhat unrealistic.⁵¹ Also these strategies assume a quite one-sided protocol: the offers made during the negotiation are binding for the sellers, but the buyer is allowed to decommit at any time. This lack of balance is not discussed in the paper.

Building on this work, in a series of papers Nguyen and Jennings (2003, 2004, 2005) propose a similar model for the buyer agent. They use time-dependent heuristic strategies (boulware, linear or conceder) in their bilateral negotiations.

Their model is also developed further. In more detail, the architecture consists of three main components: a coordinator, a number of negotiation threads and a commitment manager (see figure2.1). The roles of the coordinator and negotiation threads are similar to Rahwan et al, although the interplay between them is defined in more detail and the coordinator is also given a right to decide the strategy the negotiation thread uses. The big difference is the commitment manager, which makes all centralised decisions on commitment or decommitment for all the threads (Nguyen and Jennings 2005).⁵² This became necessary when the bias for the buyer was removed and both parties were given an equal right to decommit. The commitment manager, in close cooperation with the coordinator, approves any acceptance of an offer (ensuring that only one offer gets accepted at a time) and it also makes the decisions on decommitting in case more than one of the offers gets accepted by the opponents or when a significantly better contract has been found. We will discuss this in more detail later.

Another relevant set of papers is written by Li et al. (2004, 2005, 2006). Their approach is somewhat different. They do not have an explicit coordinator module at all, but instead coordination occurs by calculating the expected value of an outside option for each thread. An outside option is a game theoretic concept used in bargaining models. It means simply the best available outcome outside

51We will return to these strategies in section2.3.3.4.

52The commitment manager was introduced in Nguyen and Jennings (2005). The earlier versions of the model were one-sided in similar way toRahwan et al.(2002) (i.e. the buyer can decommit, but the seller cannot).

Commitment Manager

Thread 1

Thread 2

Thread N−1

Thread N

Seller 1

Seller 2

Coordinator

...

Seller N Seller N−1

...

Figure 2.1: System Architecture in Nguyen & Jennings (2005).

of the current negotiation (should that fail). In concurrent bilateral negotiation, an outside option is the highest expected utility of all other negotiation threads and the possible later negotiations. Since in negotiation the outcome is always uncertain, Li et al. describe several methods for making this estimate. They are less interested in the details of the coordination and it is, therefore, unclear how this would deal with a situation in which more than one of their latest offers gets accepted by the different opponents. Again, we discuss these issues later in this section.

Now, in general, the model introduced by Rahwan et al. and further developed by Nguyen and Jennings seems to offer the best starting point for our work. A controller needs to manage a group of negotiators, handle accepting offers and making decommitments and the negotiators should report about their progress every turn. This is very good and it can be easily extended to cover other problems.

The work by Li et al. is also interesting, however, and, as we see later, some of it does find its way to our model. It should also be noted that one-to-many negotiation can easily be changed into many-to-many negotiation by allowing both parties to use one-to-many negotiations (see figure2.2). However, we will stay in the one-to-many model, since there are many inadequately explored issues in the one-to-many situation and we wish to concentrate on those.

Having introduced the basic models in concurrent negotiation, we will now turn to three broad problem areas that, on one hand, are essential to concurrent ne-gotiation and, on the other hand, are unsatisfactorily dealt with in the current literature. We start from the opponent selection and concurrency control.

Sub−Buyer

Figure 2.2: A many-to-many market in Rahwan et al.(2002).