Language of Bargaining (2024)

1 Introduction

Bilateral bargaining, in the sense of a goal-oriented negotiation between two parties, is a fundamental human social behavior that takes shape in many areas of social experience.Driven by a desire to better understand this form of interaction, a rich body of work in economics and psychology has evolved to study bargaining (Rubin and Brown, 1975; Bazerman etal., 2000; Roth, 2020).However, this work has seldom paid careful attention to the use of language and its fine-grained impacts on bargaining conversations; indeed, many studies operationalize bargaining as simply the back-and-forth exchange of numerical values.Meanwhile, there is growing interest in bargaining in NLP oriented towards the goal of building dialogue systems capable of engaging in effective negotiation (Zhan etal., 2022; Fu etal., 2023).In this work, we aim to bridge these two lines of work and develop a computational understanding of how language shapes bilateral bargaining.

To do so, building on a widely used exercise involving the bargaining over the price of a house used in negotiation education, we developa controlled experimental environment to collect a dataset of bargaining conversations.¹¹1Dataset access may be requested at: https://mheddaya.com/research/bargaining The treatment in our experiment is the manner in which subjects communicate:either through alternating, written, numeric offers (the alternating offers or AO condition) or unstructured, verbal communication (the natural language or NL condition).Furthermore, to encourage naturalistic interactions, we recruit participants via behavioral labs and allow participants to negotiate in a conversational setting using audio on Zoom instead of crowdingsourcing text conversations as prior work has done (Asher etal., 2016; Lewis etal., 2017; He etal., 2018).In total, we collect a dataset with 230 alternating-offers negotiations and 178 natural language negotiations. In contrast with He etal. (2018)’s Craigslist negotiation dataset, our natural language negotiations have an average of over 4x more turns exchanged during each conversation, so our dataset represents a richer source to explore linguistic aspects of bargaining behavior than has been presented by existing work in this area.

In addition, we enrich the dataset by annotating all the conversations with a set of negotiation-specific speech acts.Inspired by prior work on rhetorical strategies in negotiations (Chang and Woo, 1994; Weigand etal., 2003; Twitchell etal., 2013),we create a simplified taxonomy of what we term bargaining acts and hire undergraduate research assistants to provide annotations.To the best of our knowledge, our dataset of speech acts in negotiations is an order of magnitude larger than existing datasets.

We first provide descriptive results based on our dataset.Although the AO and NL conditions are conducted via different communication mechanisms, they reach the same average agreed prices. However, when subjects can talk, fewer offers are exchanged, negotiations finish faster, the likelihood of reaching agreement rises, and the variance of prices at which subjects agree drops substantially.These observations suggest that the use of language facilitates collaboration.We also find differences in how buyers and sellers employ bargaining acts.

Recorded and transcribed speech provides more direct access to the intuitive attitudes and behaviors of the buyers and sellers. This enables us to identify subtle types of expressionthat are predictive of negotiation outcomes and reveal underlying dynamics of negotiation. Other findings corroborate conclusions from Lee and Ames (2017), who distinguish the effectiveness of negotiators’ different expressions of the same rationale.

We set up prediction tasks to predict the outcome of a negotiation based on features of the conversation and analyze the important features contributing to class differentiation.Our results show that LIWC features provide consistently strong performance and even outperform Longformer (Beltagy etal., 2020) given the beginning of a negotiation.Important features reveal thatsuccessful sellers drive and frame the conversation early on by using interrogative words to prompt buyers with targeted questions, while successful buyers convey their personal considerations and concerns while using negative expressions to push for lower prices.

2 Related Work

Negotiation is a growing area of study in computer science. Zhan etal. (2022) provide an excellent survey of research on negotiation dialogue systems. Lewis etal. (2017) train recurrent neural networks to generate natural language dialogues in negotiations. He etal. (2018) propose a modular generative model based on dialogue acts.Our focus is on deriving computational understanding of how language shapes negotiation.

Several research disciplines have studied bilateral bargaining from different perspectives and using different tools.Economic theory has investigated the role of incomplete information (Ausubel etal., 2002) and highlighted the role of explicit communication (Crawford, 1990; Roth, 2020).Bazerman etal. (2000) and Pruitt (2013) provide an overview of the psychology literature on negotiation.However, these studies tend to overlook the content of the communication, with some notable exceptions (Swaab etal., 2011; Jeong etal., 2019; Lee and Ames, 2017).

The most related work to ours is Lee and Ames (2017), who study how bargaining outcomes are affected by the way a rationale is expressed. They find that expressions that hint at a constraint (e.g., “I can’t pay more”) are more effective at shaping a seller’s views of the buyer’s willingness to pay than critique rationales (e.g., “it’s not worth more”).

3 Dataset

While contributing greatly to our understanding of negotiation, existing bargaining datasets are somewhat limited in being based on written exchanges (He etal., 2018), often in the context of a highly structured game (Asher etal., 2016; Lewis etal., 2017).

Descriptive statistics.

Table 1 provides descriptive statistics of the AO and NL treatments.Since a failed negotiation results in no bonus for both sides, most negotiations end with a successful sale.Nevertheless, the probability of agreement is roughly 7 percentage points higher under NL than AO (97.2% versus 90.0%). A two-tailed t-test with heteroskedasticity-robust standard errors shows that thedifference in agreement probability is significant.Moreover, in contrast with the AO treatment, the NL treatment produces negotiations that, on average, have $\sim$1.5x more turns, but NL turns are over 50% shorter in duration, and NL negotiations are roughly 30% shorter in total duration and feature about 74% fewer offers.

Surprisingly, without the ability to communicate using language, buyers and sellers are less efficient in reconciling their differences. In the AO treatment, the combination of fewer turns that are each, individually, longer in duration is telling. Interlocutors are spending more time silently strategizing and considering their next act. However, this time invested is not fruitful individually nor at the level of coordination, as exemplified by a lower probability of agreement and equivalent agreed prices among successful negotiations,likely due to an impoverished channel of communication.

Bargaining Act	Definition	Example
New offer	Any numerical price, not previously mentioned, that is offered by either the buyer or seller throughout the course of the negotiation.	That’s still $30,000 out of my budget but I would be willing to pay 210,000
Repeat Offer	Any numerical price presented that is an exact repeat of a previously presented offer; in a literal sense, these are redundant offers that were already on the table.	Yeah I understand um you still think that to 240,000 is too high right
Push	Any overt linguistic effort made by either party to bring the other party’s offer closer to theirs.	Might just be a little too low for what I have to offer here
Comparison	Evokes a difference or similarity between an aspect of the seller’s house and other external houses or considerations.	Like there’s one for 213k Which is like smaller and it’s nearby so that’s closer to our budget, we’ve seen that apartment it’s not as like it’s not as furnished and it’s kind of old and so
Allowance	Any time either party adjusts their offer price closer to the other party’s most recent offer. An allowance may be interpreted as the accompanying interaction to a successful push act.	I mean really like it probably should be higher than 233 but we’re willing to drop it to 233
End	End of negotiation via offer acceptance entering mutual common ground - explicitly only happens once.	Alright 228 it is

Figure1shows that the distributions of agreed prices largely overlap between the two treatments, but the distribution in prices under NL is substantially narrower than under AO.Between the two treatments, the mean agreed price conditional on reaching agreement is identical ($229.8 thousand). However, the standard deviation of agreed prices under NL is about one-third of that under AO (3.1 versus 10.4). A Fligner-Killeen (FK) (Fligner and Killeen, 1976) two-sample scale test shows that the standard deviation of the AO price distribution is statistically larger than the NL counterpart.

4 Bargaining Act Annotation

Previous researchers have recognized the inherently speech-act-like character of negotiations (Chang and Woo, 1994; Weigand etal., 2003; Twitchell etal., 2013).Many or most utterances in a bargaining context can be thought of as taking some action with reference to the negotiation. Here we propose and present a simplified ontology of negotiation-oriented speech acts (hereafter, bargaining acts) relevant to the present context of negotiation.Two trained undergraduate research assistants annotated all transcripts according to five bargaining acts: 1) new offer, 2) repeat offer, 3) push, 4) comparison, 5) allowance, and 6) end. Table 2 provides definitions and examples.Note that each turn can include multiple bargaining acts.In addition, each speech act is also annotated with a numerical offer, if applicable.

Twenty-four transcripts were annotated by both annotators to allow agreement to be calculated. Using MASI distance weighting (Passonneau, 2006), we found a Krippendorff’s alpha (Hayes and Krippendorff, 2007) of 0.72, representing a high degree of agreement for a pragmatic annotation task.

Figure2 shows thatnew offers, pushes, and comparisons are relatively more frequent and appear more consistently in all the negotiations than allowances and repeat offers. We note in Table1 that repeat offers are dramatically more common in the AO condition than the NL condition (11.3 vs. 1.56 per negotiation). With linguistic context, negotiators are less likely to engage in fundamentally uncooperative behavior by simply repeating past offers over again.

Comparing buyers to sellers, we observe that buyers make on average 1 more new offers per negotiation than sellers (independent sample, heteroskedasticity robust t-test, $p=0.02$). We find no statistically significant differences between roles for the other five bargaining acts.

The bargaining act annotations allow us to describe a negotiation as a sequence of offers proposed by the buyer and seller. We compare how the frequency and pattern of numerical offers differ across 1) experimental treatments (NL vs. AO) and 2) negotiation outcomes.We characterize different properties of the negotiations as well as their trajectories over the course the interaction.

Figure3 reveals three general patterns on offer trajectories. First, both AO and NL bargaining feature a similar range of new offers exchanged in the early stages of the negotiation. Early on, buyers in both treatments present new offers as low as 170; and sellers, as high as 270. But extreme offers are more prevalent in AO than NL bargaining. Second, both the AO and NL trajectories exhibit a rhythmic pattern of low and high offers, which is familiar to real-world negotiations. The buyer’s low offer is countered by the seller’s high offer, which is then countered by the buyer’s slightly increased low offer, and so on. Third, NL bargaining takes far fewer new offers to reach agreement than AO bargaining. Figure2(b) clearly demonstrates that NL negotiations converge quicker, with consecutive offers converging to within $5K after 6 new offers. AO negotiations take over 40 new offer exchanges to reach a similar convergence.

5 Predicting Negotiation Outcomes

Finally, we set up prediction tasks to understand the relationship between the use of natural language and negotiation success.Overall, our models demonstrate performance gains over majority class in most settings. Surprisingly, Logistic Regression using bag-of-words and LIWC category features outperform the neural model. We observe differentiation between classification accuracy on seller only and buyer only speech, and highlight features that explain this difference.

5.1 Experimental Setup

Task.

We consider a binary classification task with two classes: 1) “seller win” and 2) “buyer win”, where a negotiation is classified by whether it concluded with an agreed price greater than $230K or less than $230K, respectively.We focus on negotiations that end with an advantage for either the buyer or seller to better understand the dynamics that produce an asymmetric outcome.Hence, we omit the negotiations that ended with $230K or that did not reach an agreed price.This leaves us 119 negotiations.

As the predictive task may become trivial if we see the entire exchange, we build 10 versions of each negotiation by incrementally adding proportions of the negotiation to the input with a step size of 10%.Thus, we obtain input/output pairs $(X_{k},y)$ for a given negotiation, where $k=\{10\%,\dots,100\%\}$, and each $k$ corresponds to a different prediction task; namely, whether the negotiation outcome can be predicted by the first $k$ percentage of the interaction.

Methods.

We test two setups for our task. The first is a standard linear model with logistic regression. The second is an end-to-end approach using Longformer, a transformer-based model for encoding and classifying long sequences. In particular, we use the encoder and output modules of LongformerEncoderDecoder (LED) (Beltagy etal., 2020), a variant of the original Longformer model, which can encode sequences up to 16,384 tokens in length. This exceeds the maximum input length in our dataset.

In the logistic regression experiments, we treat the numerical offers as an oracle and consider three other feature sets:1) Transcription texts;2) Bargaining acts;3) LIWC categories Tausczik and Pennebaker (2010).⁴⁴4We also tried the union of these features, but it did not materially affect the performance.We represent each negotiation as a binary bag-of-words encoding of the features listed above. For bargaining acts, we construct the vocabulary based on unigrams and bigrams;for the other feature sets, we only include unigrams. We include bigrams for bargaining acts to capture local combinations of bargaining acts. To maintain a reasonable vocabulary size, we only consider unigrams from the transcribed text that occur in at least 5 negotiations (see Appendix C for total feature counts). We replace numbers mentioned in the text with a generic [NUM] token to eliminate the strongly predictive signal of new offers and focus on language instead.In experiments with LED, we add two special tokens [SELLER] and [BUYER] that we concatenate to the start of each turn depending on who is speaking. We make no other changes to the transcribed text. The input to LED is the concatenation of all the turns.

Evaluation.

We use accuracy as our main evaluation metric.In all experiments, due to the relatively small size of our dataset, we use nested five-fold cross validation for both inner and outer cross validations. For logistic regression, we grid search the best $\ell_{2}$ coefficient within $\{2^{x}\}$, where $x$ ranges over 11 values evenly spaced between –10 and 1.We further concatenate the speaker (‘buyer’ or ‘seller’) and the turn position within the negotiation. We treat these as hyper-parameters.We represent the position as $k$, where $k$ corresponds to a fraction of the conversation, as defined earlier. For example, the word “house” spoken by the seller in the first 10% of turns in a negotiation would be tokenized as “s1-house”.In the LED experiments, we omit the inner cross validation and use a batch size of 4, the largest possible batch size given our memory constraints.⁵⁵5We use a single Nvidia A40 GPU in our LED experiments. We select the best performing learning rate out of $\{5e-5,3e-4,3e-3\}$ and early stop based on training loss convergence.

6 Conclusion

In this work we design and conduct a controlled experiment for studying the language of bargaining. We collect and annotate a dataset of alternating offers and natural language negotiations. Our dataset contains more turns per negotiation than existing datasets and, since participants communicate orally, our setting facilitates a more natural communication environment.Our dataset is further enhanced with annotated bargaining acts.Our statistical analyses and prediction experiments confirm existing findings and reveal new insights.Most notably, the ability to communicate using languageresults in higher agreement rates and faster convergence.Both sellers and buyers benefit from maintaining an active role inthe negotiation and not being reactive to the other party.

Limitations

We note several important limitations of this work. Perhaps most importantly, our dataset is "naturalistic," but not actually "natural" in the sense of independently occurring in the world. Though the interactions between our participants are real, the task itself is ultimately artificially constructed. In a real-world negotiation over something as valuable and significant as a house, the negotiating parties will be much more invested in the outcome than our experimental participants, whose actions change their outcome to the order of a few dollars. This difference in turn could lead real-world negotiating parties to speak differently and possibly employ substantially different strategies than we observe.

Methodologically, our study has a few limitations. Firstly our analyses are based entirely on language that has been automatically transcribed (with some manual checks), and while this helps with expense and scale, these transcripts could be missing important subtleties that influence the outcome. Koenecke etal. (2020) uncover an important limitation of these systems, finding significant racial disparities in the quality of ASR transcriptions. The linguistic feature analysis we perform should be treated as largely exploratory, and provides suggestive and correlational rather than causal evidence for the relationship between language in the interactions and negotiation outcomes.

Lastly, there are further linguistic and interactional phenomena at play that we have not yet integrated into the analysis. For one, we have access to the audio channel of participants’ actual speech, but we have not analyzed it in this work. There could very well be acoustic cues in participants’ speech that are as significant to the interactions as the textual features analyzed here, particularly speech prosody which has been shown to communicate social meanings that could be highly relevant to negotiation like friendliness Jurafsky etal. (2009). This particularly extends to more interactional questions of not simply who said what, but what was said in response to what and in what way. For instance, existing research has shown that acoustic entrainment in dialog (e.g., interlocutor adaptation to one another in terms of prosody) has important social associations with dialogue success Levitan etal. (2012). We leave a deeper investigation of these phenomena for future work.

Broader Impacts

This research, collectively with prior and future related work, has the potential to advance our understanding of negotiation, a ubiquitous human activity.Our dataset can enable future research into the dynamics of human bargaining as well as interpersonal interactions more broadly.By employing the findings and insights gained from such research, individuals mayenhance their ability to negotiate effectively in various settings, such as salary negotiations, personal relationships, and community initiatives.Meanwhile, we must acknowledge that while a better understanding of language as an instrument in social interaction can be empowering, it may also be used as a tool for manipulation.

Acknowledgements

We are grateful to Jessica Halten for helping us run the experiment through the Yale SOM Behavioral Lab. The experiment also would not have been possible without the excellent study session coordination by Sedzornam Bosson, Alexandra Jones, Emma Blue Kirby, Vivian Wang, Sherry Wu, and Wen Long Yang. We thank Rajat Bhatnagar for developing the web application used in the study. The human subjects experiment in this research was deemed exempt by the Yale University Institutional Review Board (IRB #2000029151). We thank Allison Macdonald and Sammy Mustafa for their effort in the data annotation process. Their work was an invaluable contribution to the success of this research project.We thank all members of the Chicago Human+AI Lab and LEAP Workshop for feedback on early versions of this work. Finally, we thank all anonymous reviewers for their insightful suggestions and comments.

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Appendix

Appendix A Negotiation Excerpts

Appendix B Controlled Experiment

Appendix C Logistic Regression Features

Appendix D Hyperparameters