In order for us to apply mathematical techniques to the analysis of negotiation, we must be able to express the domain of interest to us in appropriate mathematical terms. Such a formal representation can then be used as the basis upon which to construct computer programs that can negotiate in this domain. For example, suppose you are aiming to build a computer program that can negotiate on your behalf in the purchase of a used car. Then your formalisation should capture at least the following two things:

1. All attributes of the car and the associated purchase that might play a part in determining how desirable (or otherwise) the car is, both for you and for your negotiation counterparts. Relating to the car itself, these attributes might include make, model, colour, age, mileage, condition of bodywork and so on, and relating to the purchase would include price (of course!), length of insurance, and potentially others such as the vendor of the car.

2. A utility function, which defines, for every possible combination of values of the attributes characterising the negotiation domain, the utility that you would obtain from a deal on the purchase of a car.

Our aim in this chapter is twofold. First, we present a three-point classification scheme for negotiation domains, which was introduced by Rosenschein and Zlotkin (1994). This scheme provides a useful point of reference for understanding negotiation domains.

In the previous chapter, we took the agenda as given and studied the strategic behaviour of agents for the different multi-issue negotiation procedures. This study showed that, for a given agenda, the procedure is a key determinant of the outcome of a negotiation. In this chapter, we will learn the importance of the agenda: we will treat the procedure as given and see how the outcome of a negotiation can be changed by changing the agenda.

Given this influence, an economic agent will clearly prefer an agenda that maximises her individual utility. Such an agenda is called the agent's optimal agenda. But it may not always be computationally easy to find such an agenda. Thus, we will focus on some specific negotiation settings and study polynomial-time methods for finding an optimal agenda. These methods have both economic and computational significance: by using them, a player will be able to maximise her utility, and the methods have computational feasibility. In other words, they facilitate the design of software agents that can not only negotiate optimally over a given set of issues, but also choose the right agenda before actual negotiation begins.

Let us begin by looking at some example scenarios where the parties must choose an agenda for negotiation.

We hope that by now you will have a good understanding of the scope and applicability of negotiation techniques, as well as a feel for the kinds of techniques used to analyse negotiation settings and build negotiating systems. Our aim in this chapter is to describe briefly some other research areas that are related closely to negotiation. Specifically, we discuss the domain of social choice theory (which is concerned with the general problem of group decision making using techniques such as voting), the area known as argumentation (which is about trying to make sense of domains when there are conflicting arguments about the domain), and fair division (which is concerned specifically with the problem of how to divide goods/resources among a group of agents).

13.1 Social choice

We begin by looking at the domain of social choice theory. Social choice theory addresses itself to the problem of how a group of agents can make a group decision when they have conflicting preferences. The mechanisms that social choice theory studies for this problem are typically voting procedures, in the sense that we are familiar with voting procedures in everyday life, where they are used for political decision making in democratic societies.

The basic setting considered in social choice theory is as follows. As usual, we have a set P = {1,…,|P|} of agents, who in this chapter we will often refer to as voters.

As we saw in Chapter 1, the purpose of negotiation is to resolve a conflict between individuals and reach a mutually acceptable agreement with respect to some domain. A classic example of such conflict occurs when there are some scarce resources, and the individuals in question must reach a mutually acceptable agreement over how to divide/allocate the resources between themselves. The resources could be anything the individuals want: commodities, services, money, food, and so on. Typically, the negotiating individuals will have conflicting preferences over the possible divisions. Negotiation can be used to find a mutually acceptable way of dividing the resources. In this chapter, we will show how game theory can be used to analyse situations in which participants have conflicting preferences. We will later apply these techniques to the analysis of negotiation settings.

Before we start our analysis of such situations, we must identify and extract the information that is required to understand a situation of conflicting preferences. This information is represented in a game-theoretic model. In general, the models used in game theory represent abstractions of the underlying domain, which aim to capture all and only those aspects of the domain that are relevant for the decisions that must be made by those participating in it. The mathematical models of such conflicts of interests are called games.

In the previous chapters, we saw that finding optimal offers can be computationally expensive, especially in the context of solving the trade-off problem for the PDP and for finding optimal agendas. Because software agents have limited computational resources at their disposal, heuristic approaches can be useful for the design of negotiating agents in such situations. In such approaches, a heuristic is used to generate counter offers that are “good enough” (i.e., close to optimum) but not necessarily optimal.

Dealing with the bounded rationality of agents is just one of the reasons for using a heuristic approach. Another reason is that an opponent might not always play equilibrium strategies. In such cases, a strategy that is a best reply to the opponent's strategy must be played rather than an equilibrium one.

Irrespective of the reason for using this approach, heuristics can be designed for a number of purposes. For example, they can be designed to generate optimal counter offers, to predict information about an opponent, or to find optimal agendas. Research into the design of heuristics has been growing continuously and several different approaches – including local search methods, approximation methods, and machine learning methods – have been adopted. Below, we introduce a number of representative works in terms of their key underlying ideas, goals, and main results.

In our everyday lives, negotiation is ubiquitous. At work, we bargain with clients about the terms of a contract; we bargain with our boss about a pay rise when the contract is signed. At home, we bargain with our partners about who will tidy the house; we bargain with our children about how many stories they can read before bed. And politicians, of course, routinely bargain in situations that have life or death consequences. The purpose of negotiation is to reach an agreement, and in particular, agreement in the presence of conflicting goals and preferences. If your preferences, goals, and aspirations were completely aligned with mine, then there would be no conflict, and hence there would be no need for negotiation. In this case, the best outcome for me would also be the best outcome for you, and so we could simply determine such an outcome, and then implement it. Neither of us would have any incentive other than to find such a mutually optimal best outcome – our joint problem is nothing more than an optimisation problem. Unfortunately, of course, the real world is not like that. More often than not, people have very different goals and preferences, and when this occurs, some method is required to find an outcome that will be acceptable to all concerned. Negotiation provides such a mechanism.

So far in the book, we have been focusing on situations in which all the negotiating participants are software agents. However, there are many applications where automated negotiators should be able to interact proficiently and collaborate with people. Automated negotiators can be used with humans in the loop or without them. When used with humans, they can alleviate some of the effort required of people during negotiations and can assist people less qualified in the negotiation process (Kersten and Lai, 2007). Also, there may be situations in which automated negotiators can even replace human negotiators (Durenard, 2013). Another possibility is for people embarking on important negotiation tasks to use these agents as a training tool, prior to actually performing the task (Lin et al., 2014). For example, automated negotiators in e-commerce applications can bargain over a price with their site's buyers (Kauppi et al., 2013). Personalised agents that support their users can negotiate with humans with conflicting preferences towards deciding on a meeting time (Tambe, 2008). They can also negotiate the formation of a “care plan” for patients requiring a course of medical treatment (Amir et al., 2013). A person who is preparing for a job interview can train herself with an agent that plays the role of the employer (Lin et al., 2009).

In this chapter we discuss a number of applications where agents can be used to negotiate on behalf of their human counterparts. In general, agents can be used for any kind of negotiation over the allocation of limited resources. For our discussion, however, we focus on the following representative cases. While some of the applications will involve direct negotiations between the parties, others will go through a trusted mediator. Also, while some will only involve software agents, others will deal with both software agents and human negotiators. Then, some applications will be for bilateral negotiations and others for multilateral ones. Finally, some will be industrial applications and others commercial ones.

12.1 Business process management

A business process is composed of a number of interdependent tasks that must be executed in a controlled and ordered way. This execution involves the consumption of resources. In most organisations, these resources are grouped into business units that control the way in which they are deployed. This is also the case with the British Telecom (BT) business process of providing a quote to a customer for installing a network to deliver a specific type of telecommunications service. For the management of this process, Jennings et al. (2000) and Norman et al. (1997) developed an agent-based negotiation framework called Adept (Advanced Decision Environment for Process Tasks).

In this chapter, we turn our attention to negotiation mechanisms – the protocols that will be used by agents when negotiating over domains of the type discussed in the preceding chapter. The first protocol we look at is concerned with negotiation over a single issue. Many real-world situations involve negotiation over a single issue. Typical examples include a buyer and a seller negotiating over the sale price of a commodity, a landlord and a tenant negotiating over the rental price of some accommodation, and an employer and an employee negotiating over the employee's salary. We will refer to the issue over which negotiation takes place as a “pie”, with the terminology arising from the analogy of a group of people negotiating about how to share a pie amongst themselves.

We know that, in order to negotiate, the parties must follow a protocol. There are many different protocols in the literature on negotiation, but arguably the most influential of these is the alternating offers protocol. This protocol was first analysed by Ingolf Stahl (1972) in the context of the division of a discretely divisible pie (i.e., a pie that can only be divided in a finite number of ways), and later by Ariel Rubinstein (1982) in the context of the division of a continuously divisible pie (i.e., any division of the pie is possible).

We all of us have to negotiate – whether formally, as part of our jobs, or informally, as part of our everyday lives – and the outcomes of our negotiations have direct and often dramatic consequences, for us and others. However, it is surely a safe bet that most of us wish we were better negotiators. There are many reasons why we might not be as good at negotiating as we would wish. For one thing, it is often hard for us to really understand the issues at stake and the consequences of various potential settlements, and for this reason we can end up with outcomes that are not as good as those that we might in fact have been able to obtain. Moreover, in many cultures, negotiation is regarded as greedy or impolite, and as a consequence, some people may find it socially awkward or stressful to negotiate. Cultural inhibitions like these can prevent us from obtaining the best outcome even when the topic of negotiation is of great importance to us. Wouldn't it be wonderful, then, if we had computers that could effectively negotiate on our behalf…? In short, the main aim of this book is to investigate this idea.

In many practical negotiations, the parties involved negotiate over not one but multiple issues. For example, when trading goods or services, buyers and sellers negotiate on the price, the quality, the method of payment, and other related issues. Political parties bargain over tax structures, foreign policy programmes, domestic spending programmes, etc. Nations negotiate trade terms in multiple markets.

One of the key differences between single and multi-issue negotiations is that, for the latter, the players may have different evaluations regarding the importance of the issues. We will study how these evaluations can be represented in the form of utility functions. Another difference is that multiple issues can be negotiated in different ways. For instance, the issues can all be discussed together or, alternatively, they can be discussed one-by-one in a sequence. A negotiation procedure specifies the way in which the issues will be negotiated. The procedure is crucial because the strategic behaviour of the players depends on it (Schelling, 1956, 1960; Sutton, 1986). Consequently, the outcome of such negotiations also depends on the procedure.

In this chapter, we begin by describing the main multi-issue procedures. Then, we analyse the players' strategic behaviour for different procedures and compare the procedures in terms of their equilibrium solutions.