Abstract
Communication has been shown to increase proposer power in multilateral bargaining settings that use majority voting rule via competition between non-proposers for a place in the coalition. In this paper we investigate whether communication affects bargaining outcomes and the bargaining process in settings in which the competition effect is not present. We study committees that use unanimity rule to pass allocations. We find that in these settings, communication has the complete opposite effect compared with the majority settings: under unanimity, communication eliminates the inefficiencies that are present in settings without communication and it shifts bargaining outcomes towards egalitarian allocations with no proposer power. Communication logs provide insights regarding the topics subjects discuss and communication content correlates with bargaining outcomes.
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Notes
Our communication tool allows committee members to send any kind of text message to any subset of members in their group, including private messages to individual members and public messages that are delivered to all members of the group.
Our results are in line with those documented in bilateral bargaining settings: Roth (1995) shows that in a two-player game, allowing face-to-face communication, leads to more equal shares of the bargainers. Unfortunately, there is no record of face-to-face communication between bargainers, which precludes a more thorough investigation of the content of communication and comparison with our current setup.
The Council of the European Union for example has to vote unanimously on any “sensitive” issues, such as the joining of new members or common security policies. In the United States, many private clubs admit new members only if they are accepted by unanimity. Also in the United States, the certificate of incorporation of a majority of companies requires action by written consent to be unanimous.
Specifically, stationarity here means that strategies used by proposer and non-proposers are independent of the history of play. Moreover, symmetry means that proposers treats all non-proposers the ‘same’ way (i.e., offer all non-proposers who are included in the coalition the same share) and non-proposers act the ‘same’ way irrespectively of which committee member is selected to be the proposer (i.e., use the same cutoff rule to decide whether to accept or reject the proposal).
This software was developed from the open source Multistage package and is available for download at http://software.ssel.caltech.edu/.
The sessions were also conducted around the same time, removing the possibility that a change in behavior across the Unanimity and Majority settings would be due to changes in the economic or social environments.
The only difference between the current set of experimental sessions and those reported in Agranov and Tergiman (2014) is the voting rule used to pass the proposals. In the previous paper we analyzed bargaining with majority voting rule, in which at least three yes votes were required for the proposal to pass, i.e., \(q=3\).
The communication protocol is identical to that of Agranov and Tergiman (2014).
Statistical analyses based on GLS regressions, in which observations are clustered at the session level, confirm that in the Unanimity Baseline treatment in the last 5 games the likelihood of delays is greater than the theoretically predicted level of 0% (\(p=0.008\)) and that bargainers appropriate less than 100% of available resources (\(p=0.003\)). In fact, the 95% confidence interval for probability of delays in the last 5 games of Baseline treatment is (0.27, 0.60), while the 95% confidence interval for the the proportion of appropriated pie is (0.82, 0.89). Neither confidence intervals do not include the point prediction identified by the theoretical analysis.
We cannot reject the null hypothesis that probability of delays is equal to 0% as predicted by the theory and that bargainers appropriate 100% of available resources in Unanimity Chat treatment in the last 5 games (\(p>0.10\) in both tests).
The reason we chose to present this regression analysis for the first 5 games rather than for the very first game is that there are very few negative votes in the first game in both treatments: only 3 out of 64 observations in the Baseline treatment and only 4 out of 60 observations in the Chat treatment. This is not enough variation to be able to identify the determinants of voting behavior in the first game.
While the coefficient is negative in the first 5 games, the magnitude of those effect is rather small.
Similarly, in the first game, without communication, fewer then half of the final allocations are equal splits, versus over 90% when communication is allowed.
The full transcripts of the chats and their classification are available from the authors upon request.
The level of inter-rater agreement is extremely high at 94.67%. While Cohen’s kappa is particularly relevant in situations when there is no “objective” truth (for example, different individuals rating movies), we report it as well even though we believe that in these conversations there is an objective way to interpret them and that when there is disagreement, often it is clear which coder is mistaken. The value of Kappa is also very high at 0.825. There is also a very high degree of agreement at the individual subject level: 91.78% with a Kappa of 0.836.
Similar patterns are observed in the very first game: all but two groups discuss relevant to the game things, one group talks about irrelevant things, and one group proceeds to the bargaining stage without any discussions.
There is also a very high degree of agreement at the individual subject level. We observe high agreement between coders regarding classification of messages into those related to fairness and those related to self-interest: 92.27 and 90.93%, respectively. The corresponding Kappa statistics are very high at 0.831 and fair at 0.438. A large fraction of the disagreements come from how each coder interpreted a message of just a single thing (“50”) that was sent to everyone. One coder classified this message as fairness message, while another classified it as self-interest message.
Statistical tests show that in a conversation, the likelihood of proposers to engage in relevant conversation is significantly smaller than that of non-proposers during deliberation stage (\(p<0.001\)).
Regression analysis confirms that the fraction of subjects who exclusively used public messages in the last 5 games is significantly higher than the fraction of subjects who exclusively used private messages with \(p<0.001\) for both non-proposers and proposers.
In the last 5 bargaining games of the Unanimity Chat treatment, 93% of all first-stage submitted proposals are passed right away. Therefore, there is not enough data to analyze voting patterns of non-proposers.
Given that the vast majority of all messages sent by both proposers and non-proposers are public messages talking about fairness, one may ask whether there is a relationship between who (proposer or a non-proposer) sent the first message about fairness to the public chat and the proposal type or the share of the proposer. Our data indicate that such a correlation is not significant at any standard significance levels, which suggests that who spoke about fairness first (proposer or non-proposer) is irrelevant and that what may matter instead is that there was a group discussion about fairness at all: there is a positive correlation between having a fairness discussion and the probability of proposing an equal split allocation and, also, a lower share for the proposer.
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This research was made possible thanks to the generous support from the Social Science Humanities and Research Council (Canada). We thank the editor and the two anonymous referees for many valuable suggestions, which improved the current paper. The authors would also like to thank Gary Bolton, Alessandra Casella, Timothy Cason, Pedro Dal Bo, Eric Dickson, Sanford Gordon, Yoram Halevy, Alessandro Lizzeri, Rebecca Morton, Muriel Niederle, as well as the seminar participants at Florida State University, London School of Economics, Penn State University, Purdue University, Stanford University, the University of British Columbia, and finally the conference participants of the Economic Science Association (2013), the Public Choice Meetings (2014), the Royal Economic Society (2014) and the Design and Bargaining Workshop in Dallas (2014).
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Agranov, M., Tergiman, C. Communication in bargaining games with unanimity. Exp Econ 22, 350–368 (2019). https://doi.org/10.1007/s10683-018-9571-6
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DOI: https://doi.org/10.1007/s10683-018-9571-6