Abstract
We report results from a laboratory experiment on strategic bargaining with indivisibilities studying the role of asymmetries, both in preferences and institutions. We find that subjects do not fully grasp the equilibrium effects asymmetries have on bargaining power and identify how subjects’ observed behavior systematically deviates from theoretical predictions. The deviations are especially pronounced in case of asymmetric institutions which are modelled as probabilities of being the proposer. Additionally, in contrast to previous experimental work, we observe larger than predicted proposer power since subjects frequently propose and accept their second-preferred option. Quantal response equilibrium and risk aversion explain behavior whenever probabilities are symmetric, but less so when asymmetric. We propose the ‘recognition is power’ heuristic which equates bargaining power with recognition probabilities to explain these findings.
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Notes
With three alternatives called A, B and C, Condorcet cycles under majority voting feature either A beats B, B beats C and C beats A, or the opposite sequence. Condorcet cycles rule out Condorcet winners and preserve the essence of no Condorcet winner in perfectly divisible divide-the-dollar bargaining.
This setup is strategically equivalent to selecting one player as the random proposer and also has several advantages. It keeps subjects engaged, all subjects have the same incentives in submitting their proposals as compared to a randomly selected proposer and more data on proposals are obtained.
This implements the voting procedure in Herings and Houba (2016), who show that sequential voting eliminates the equilibrium in weakly-dominated strategies where both voters vote in favor of the proposal believing that the other will vote ‘yes’. This reduction in equilibrium multiplicity has to be traded-off against a loss of data since we do not observe how the second voter would have voted when being non-pivotal. However, it is not clear how informative a non-pivotal vote is since such a vote has no impact on the outcome. Furthermore, the fact that subjects almost never accepted their least preferred option suggests that subjects understood the incentives they faced.
The mechanism underlying the mixed strategies in SymPayAsymRec and AsymPayAsymRec is very similar and omitted.
For screenshots of the interface as well as the text of the instructions and the summary handout, see Appendix F.
148 of the 225 participants were students in business or economics.
They are informed that there will be three parts in the experiment but not what these parts will entail.
This does not have any effect on the equilibrium predictions, provided the risk-neutrality also holds at this payoff level.
Subjects were simply told that they would be rematched with other participants.
The larger number of subjects in treatment SymPaySymRec is due to an oversight where one session that was supposed to be AsymPaySymRec was run as SymPaySymRec instead. This error was noticed immediately and was made up for by running a session of AsymPaySymRec the next day.
Indeed, in line with theory players almost never proposed their worst option (14 out of 2697 decisions) and rarely accepted it (6 out of 173 decisions) and these frequencies do not vary much by treatment. Furthermore, a player almost never rejected her best option (1 out of 57 decisions).
Unless mentioned otherwise all p values are taken from a logit regression with proposing (accepting) the middle option as dependent variable and standard errors clustered at the matching group level. All regression results are reported in Appendix C.
The difference between players 1 and 2 is significant at the 1%-level while the difference 1–3 gives a p value of 0.08.
In Appendix D, we investigate to what degree subjects’ behavior can be explained by them best-responding to the other players’ observed behavior in each independent matching group. The conclusions from this analysis are similar to the discussion in this section.
An analysis of decision-making at the individual level shows no systematic or substantial influence of risk-aversion and gender on behavior. Detailed results of this analysis are presented in Appendix C.
In Appendix B we present the underlying model specification.
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Acknowledgments
The authors are very grateful to the Associate Editor and two anonymous reviewers for valuable comments. We also thank Rebecca Morton, Matthew Embrey, Arthur Schram, Simon Siegenthaler, as well as (seminar) participants at the 2015 UECE Lisbon Meetings in Game Theory and Applications, the 2016 NYU Global Network Experimental Social Sciences Workshop, the University of Amsterdam and the Vrije Universiteit Amsterdam. Financial support from the University of Amsterdam Research Priority Area in Behavioral Economics and the Department of Econometrics and OR of the Vrije Universiteit Amsterdam is gratefully acknowledged.
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Kamm, A., Houba, H. A bargaining experiment with asymmetric institutions and preferences. Soc Choice Welf 52, 329–351 (2019). https://doi.org/10.1007/s00355-018-1150-4
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DOI: https://doi.org/10.1007/s00355-018-1150-4