Making concessions during a negotiation is vital for getting an agreement. Successful negotiations are only possible when both parties employ an effective conceding strategy. Designing a good strategy of when and how much to concede is challenging, and that is why there are many current negotiation implementations that concede in very different ways.
In this chapter, we characterized negotiation strategies by how they concede through- out the negotiation, and we did so by using a quantitative measure called the concession rate of an agent. We first formally defined the notion of concession rate as a normalized measure of the largest concession that was made during the negotiation. This formalizes the concept of an agent’s willingness to concede against different opponents.
We then presented an empirical method to effectively compute the concession rate of agents, and then applied our approach to a selection of well-known agents (including all participants of ANAC 2010 and 2011) in an experimental setting. For the first time, this gives insight into the strategy space of negotiation tactics employed in ANAC. We subsequently used our method to classify the agents into four categories of concession behavior.
In addition to classifying agent strategies, various conclusions can be drawn based on charting the experimental results. Indeed, there is a wide spread in concession rates of current agents, and our classification chart is a useful method to cluster strategy types. The concession rate diagram shows that similar strategies have similar concession characteristics, and makes it easy to understand the agent’s main negotiation characteristics at a glance.
Some extreme agents are located in the extreme regions of the chart, while the stronger agents form a cluster in the competitive corner. The results indicate that in order to be successful in an automated negotiation competition, an agent should not concede much, especially not to very cooperative strategies.
In general, the correlation is very high between the concession rate and utility obtained against such a conceding strategy. This means that a low concession rate is a good predictor for high performance against a conceding agent. The same behavior
would be inappropriate against a very competitive agent that does not concede at all during the negotiation. We have also demonstrated that, in general, the nicer an agent plays against this type of opponent, the more utility it obtains. This is because, against such a hard-headed opponent, there is a high chance the negotiation would break down if no concessions are made.
This then leads to a dilemma for the agents to be either a teacher (who tries to entice their opponent to adapt by employing a tough strategy) or a learner (who tries to adapt to maximize its own utility, given the behavior of the opponent), which lies at the heart of many bilateral negotiation problems. If the opponent is flexible and adapting to one’s demands, there is little point in conceding. However, if the opponent is being strictly hard-headed (even appearing irrationally so), reaching some agreement is typically preferable to no agreement. The importance of learning strategies that try first to detect the adaptivity of the opponent (such as Gahboninho, which proved very robust in ANAC 2011) is an important insight which could be taken up in further research in bilateral negotiations beyond the competition.
9
Optimal Non-adaptive
Concession Strategies
In the previous chapter we presented an empirical method to classify agents into four broad categories of concession behavior, and we formulated guidelines on how agents should bid against each category. This chapter follows an alternative approach by devising optimal concession strategies against specific classes of acceptance strategies.
Many time-based concession strategies have already been proposed, but they are typically heuristic in nature, and therefore, it is still unclear what is the right way to concede toward the opponent. We provide a theoretical model in which a bidder makes a series of offers to an acceptor with unknown preferences. We apply sequential decision techniques as we did in Chapter 5, but this time to find analytical solutions that optimize the expected utility of the bidder, given certain strategy sets of the opponent. We then compare our solution to state of the art concession techniques in a negotiation simulation. Our solutions turn out to significantly outperform current approaches in terms of obtained utility. Our results open the way for a new and general concession strategy that can be combined with various existing learning and accepting techniques to yield a fully-fledged negotiation strategy for the alternating offers setting.
This chapter is based on the following publications:
Tim Baarslag, Rafik Hadfi, Koen Hindriks, Takayuki Ito, and Catholijn Jonker. Optimal non-adaptive concession strategies with incomplete information. In Proceedings of The Seventh International Workshop on Agent-based Complex Automated Negotiations (ACAN 2014), 2014
9.1
Introduction
A key insight of negotiation research is that making concessions is crucial to con- ducting a successful negotiation. There are important reasons to make concessions during the negotiation [216]: it is often used to elicit cooperation from the other, in the hope that the other will reciprocate in kind. Second, it conveys information to the opponent, both about the negotiator’s preferences and about the perceptions of the opponent. But most importantly, it is the time pressure of the negotiation itself (typically in the form a deadline or a perceived maximum number of bidding rounds) that operates as a force on the parties to concede [51]. An approaching deadline puts important pressure on the parties to reduce their aspirations, especially when the time pressure heightens, which is referred to as the “eleventh hour effect”.
Given the paramount importance of time in bargaining, it is not surprising that many negotiating agents adjust their level of aspiration based on the time that is left in the negotiation. There is a clear rationale behind the design of such agents, given their aim to maximize the chance of reaching an agreement in a limited amount of time. For example, well-known time dependent tactics (see Section 2.3.3), such as Boulware and Conceder, are characterized by the fact that they consistently concede throughout the negotiation process as a function of time. The same kind of time-based concession curves can also be observed in practice in ANAC (see Appendix B). However, in the TDT’s, as well as in some very effective agents, such Agent K (winner of ANAC 2010) and HardHeaded (winner of ANAC 2011), the specific concession curve is selected rather arbitrarily, and is not informed by any other insights; therefore, they make largely unfounded choices on how much to concede at each time interval.
Alternatively, behavior dependent tactics such as Tit for Tat (cf. Section 2.3.3) base their decision to make concessions on the actions of the other negotiating party. However, such adaptive approaches do not give us any information on how to concede based on time alone.
Work that presents optimal choices of how much to concede includes game theoretic work (e.g. [217]) and single-shot bargaining, also known as the ultimatum game [202]. However, these approaches usually assume a complete information setting, or a game where the deal is struck immediately, which we cannot apply to a typical concession-based negotiation. Furthermore, this type of work typically revolves around equilibrium strategies, which assumes full rationality on the part of both agents. We are more interested in optimal solutions for one negotiating party, playing against various classes of acceptance strategies.
This chapter aims to find out how time pressure alone, in the form of a deadline, should influence the concession behavior of a negotiator against specific opponent classes. To do so, we employ methods from sequential decision theory to devise negotiation strategies that make optimal concessions at each negotiation round. Finally, we show that an agent making these optimal concessions performs better
than any other in our experimental setup.
We begin with an example in Section 9.2 that sets the stage for our time-based concession model in Section 9.3. We apply our methods to find optimal concessions against opponents that accept according to acceptance thresholds in Section 9.4 and 9.5. We subsequently compare the optimal bidding strategy with state of the art bidding strategies in a series of tests (Section 9.6). We conclude our chapter with a discussion of the contributions of this chapter, as well as its implications (Section 9.7).