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Communication in multilateral bargaining with joint production

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Abstract

We experimentally investigate the effect of pre-bargaining communication on productive incentives in a multilateral bargaining game with joint production under two conditions: observable and unobservable investments. In both conditions, communication fosters fair sharing and is rarely used to pit individuals against each other. Proportional sharing arises with observable investments with or without communication, leading to high efficiency gains. Without investment observability, communication is widely used to truthfully report investments and call for equitable sharing, allowing substantial efficiency gains. Since communication occurs after production, our results highlight a novel indirect channel through which communication can enhance efficiency in social dilemmas. Our results contrast with previous findings on bargaining over an exogenous fund, where communication leads to highly unequal outcomes, competitive messages, and virtually no appeals to fairness.

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Notes

  1. The agreement in place prior to renegotiation was an equal split.

  2. An exception is Van Dolder et al. (2015) who report on a TV show where contestants negotiate how to split their joint profits accumulated through answering trivia questions as a team.

  3. Absent a joint production process, outcomes tend to be positively correlated with bargaining power: i.e. who holds proposal rights. For example, in dictator, ultimatum, and multilateral bargaining games, the evidence shows that proposers typically enjoy a larger share of the endowment. In Settings with symmetric bargaining power, equal splits prevail. For details, see Roth (1987).

  4. Several experiments have examined the unilateral allocation of a jointly-produced surplus, either by a team leader (Van der Heijden et al., 2009; Drouvelis et al., 2017) or a third party (Stoddard et al., 2014, 2020). These studies generally find that allocators reward high contributors, increasing efficiency relative to equal sharing.

  5. See Eraslan and Evdokimov (2019) for a comprehensive review of the theoretical literature.

  6. For two experiments on dynamic bargaining with communication see Baron et al. (2017) and Agranov et al. (2020).

  7. In our experiment communication only takes place during the proposal stage (via chat screens), not at the investment stage. We discuss this issue in light of existing literature in our final discussion.

  8. This feature of our experiment is not common as all BF experiments we are aware of maintain the discount factor constant within a game. A recent meta-analysis Baranski and Morton (in press) showed that regardless of the discount factor in BF experiments with 3 players, the mean proposer share was equal across treatments. Thus, we do not believe this modelling and design choice has an impact on subject behavior in the laboratory. Our goal was to make sure that bargaining games did not go too far in order for sessions to end within reasonable time.

  9. We follow the standard assumption in the literature that players vote in favor whenever indifferent.

  10. We are grateful to Arkadi Predtetchinski for valuable insights in proving our result.

  11. The proof is presented in Sect. 1 of the Online Appendix.

  12. Importantly, Agranov and Tergiman (2019) show that when approval required unanimous voting, communication does not lead to unequal outcomes.

  13. All agreements took place in round 4 or earlier, with only 2 agreements in round 4.

  14. All the MW tests reported are robust to tests at the individual-decision level using cluster bootstrapping as an alternative way to account for within-session correlation.

  15. These differences are significant. The p-values for MW tests are in parentheses: C-NO vs. NC-NO (0.004). NC-O vs. NC-NO (0.058). C-O vs. NC-NO (0.033). No other treatment difference is significant.

  16. See Online Appendix Table 2 for regression results.

  17. See Table 1 in the Online Appendix for session level mean investments by treatment and Fig. 1 for session level mean investments by period of play.

  18. While one may construct alternative measures of distance between the fair proposal and actual proposal, we believe this one embodies the notion of equity as described by Adams (1965). The same measure has been employed in Baranski (2016).

  19. Pooling over observable and unobservable treatments we find no statistically significant difference between treatments with and without communication (p-value = 0.614 two-sided MW test).

  20. In The Online Appendix, Table 3, we examine the prevalence of MWCs and 3-way splits with stronger inclusion criteria, requiring each coalition member to receive a share strictly greater than 1 or 5 tokens. Even with these stronger criteria, 3-way splits remain far more prevalent than MWCs.

  21. The correlation coefficient between \({\hat{c}}\) and \({\hat{s}}\) is 0.02 for NC-NO, 0.13 for C-NO, 0.37 for NC-O, and 0.5 for C-O

  22. A split is defined as proportional if the share received by each member is within 10% of the perfectly proportional share.

  23. This happens 64% of the time in NC-NO, 59% in C-NO, 65% NC-O, and 51% C-O.

  24. As shown in the Online Appendix, Table 4, allocations and shares often fall in between the equality and proportionality benchmarks in C-O (45.8% of allocations), but this occurs less frequently in other treatments.

  25. In the Online Appendix 5 we examine whether subjects are consistent in the types of proposals that they make throughout the experiment. A small percentage of subjects propose consistently proportional allocations (7.2) and equal splits (11.3).

  26. Two independent native English-speaking students were hired as coders for an hourly rate. Both received the same set of written instructions available in the Online Appendix.

  27. On the suggestion of an anonymous referee, we also hired an additional research assistant to code further chat categories, including discussions of past or future periods of play and a friendly tone of conversation. While these categories were coded relatively infrequently, we do find a positive correlation between friendly conversation and the share allocated to a voter. The analysis for these categories is presented in the Online Appendix.

  28. Cohen’s kappa above 0.4 indicates moderate or better agreement based on the benchmark scale of Landis and Koch (1977).

  29. Due to an error, our research assistants were unable to code beyond round 2, which left out two cases in which subjects reached an agreement in round 3. We asked another assistant to code these conversations and re-estimated the model (Table 8 in Online Appendix). There are no meaningful changes in the estimation results.

  30. The data show that in bargaining rounds that were not coded for proportionality, equality, or MWCs, 30% of allocations are MWCs without observability compared to only 4% with observability.

  31. Estimation results are reported in the Online Appendix, Table 11.

  32. See Karagözoğlu (2012) for a review, as well as the previously cited work.

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Acknowledgements

The authors thank Gianluca Campanile, Thomas Yates, and Laila Al-Eisawi for excellent research assistance. We are grateful for helpful comments and conversations with Andrew Caplin, Alexander Cappelen, Guillaume Frechette, Andreas Leibbrandt, Rebecca Morton, Arkadi Predtetchinski, Ariel Rubinstein, Andy Schotter, Simon Siegenthaler, Erik Sorensen, and Bertil Tungodden. We benefited greatly from participants’ comments at the 2019 Maastricht Behavioral and Experimental Economics Symposium, 2019 New England Experimental Economics Workshop, the 2019 and 2021 ESA North American Meetings, and seminars at VCU School of Business, Norwegian School of Economics, and NYU CESS. Funding for this research was generously provided by NYU Abu Dhabi. Additional funding for research assistants was provided by VCU School of Business. Baranski gratefully recognizes financial support by Tamkeen under the NYU Abu Dhabi Research Institute Award CG005. This study is registered in the AEA RCT Registry and the unique identifying Number is: AEARCTR-0003254.

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  1. Division of Social Science, New York University Abu Dhabi, Bldg A5 Office 1131, Saadiyat NYUAD Campus, Abu Dhabi, United Arab Emirates

    Andrzej Baranski

  2. Department of Economics, Virginia Commonwealth University, Snead Hall, 301 W. Main Street, Box 844000, Richmond, VA, 23284, USA

    Caleb A. Cox

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Baranski, A., Cox, C.A. Communication in multilateral bargaining with joint production. Exp Econ 26, 55–77 (2023). https://doi.org/10.1007/s10683-022-09760-z

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