Abstract
We investigate the haggling process in bargaining. Using an experimental bargaining game, we find that a first offer has a significant impact on the bargaining outcome even if it is costless to reject. First offers convey information on the player’s reservation value induced by his social preferences. They are most often accepted when they are not above the equal split. However, offers which request much more than the equal split induce punishing counter-offers. The bargaining outcome is therefore critically influenced by the balance of toughness and kindness signalled through the offers made in the haggling phase.
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Notes
An interesting related study by Goldreich and Pomorski (2011) looked at the effect of the decision to initiate the bargaining process by making a first offer. In our case, the initiating role is pre-assigned and we study the effect of the level of the first offer.
This is the case because communication has no direct payoff implications. Players with competing interests, as in a bargaining process, have no incentive to communicate truthfully.
Early experimental studies with unstructured bargaining designs already indicated that free communication between bargainers plays a role. In particular, face-to-face bargaining has been found to improve the likelihood of a bargaining agreement, possibly because it provides a richer array of channels of communication “including tone of voice, body language and facial expression” (Roth, 1995, p. 296).
In the remaining, all monetary amounts are in Australian dollars.
In the experiment, the wording was neutral for both players to characterise a proposed split between them and the other player.
Note that while the first offer is costless to reject, it can also be accepted. For that reason, it is not a cheap-talk message but bears a cost for the Proposer: for any offer assigning him less than the full amount, he accepts the possibility to forego higher amounts. An ultimatum game with a pure cheap talk request in a pre-play cheap-talk communication phase was investigated by Rankin (2003). The study unexpectedly found a negative effect of the option to make a request. In light of our results, this finding can be the consequence of the high level of the requests observed in the study (and possibly from the emotional effect of the words “I request” used by the receiver). Our study does not include an ultimatum game as a benchmark. We investigate the causal effect of different first offers rather than the existence of a first offer as such. An ultimatum game would differ from our game in that it does not offer to the player having to consider the (last) offer the opportunity to make a first offer first. That may change the players’ feeling of entitlement and their claims and decisions as a result.
There are potential factors such as a reduction in incentives or a “hot” vs. “cold” effect that might affect the participants’ choices using the strategy method (Zizzo 2010). However, the experimental evidence does not report any case in which a treatment effect is observed with the strategy method and not with the direct-response method (Brandts and Charness 2011). The strategy method may also be more complex to understand for participants. We ensured that participants understood the decision they were making using questions, at the start of the experiment, testing their understanding of the meaning of different decisions.
When participants made their action decisions, they did not know about the belief-estimation task yet. Following Dufwenberg et al. (2011), we decided on this timing to avoid any influence on decisions through strategic choice making to subjectively simplify subsequent guesswork.
This prediction would be modified in real-world situation by discounting. If bargaining takes place sequentially over time, there is a cost to reach an agreement later. For a discounting factor \(\delta\), the Responder would only receive \(\delta \times 10\) in the second stage and he/she would, therefore, be willing to accept to get only that amount in the first stage, leaving \((1-\delta )\times 10\) to the Proposer. In our experiment discounting is unlikely to play a role since all payments are made at the same moment in time, at the end of the experiment.
It is not simply explained by the effect of first offer on the perceived minimum acceptable offer from the Proposer. Suppose we observe that high requests are associated with low counter-offers. An alternative explanation to Hypothesis 4 would be that high offers signal a low credibility of the bargainer and possibly a lower MAO than a smaller request. Our elicitation of players’ beliefs allows us to disentangle these two possible reasons which would lead higher initial requests to be associated with lower counter-offers.
Participants who answered wrongly to some of these questions received additional explanation until the experimenter was satisfied that they understood the game.
The authors observed that “Making an offer to someone whose demand you have just rejected, in the second stage of the two-stage game, is not viewed as equivalent to opening the seemingly identical continuation game, with no history of interaction” Binmore et al. (2002).
This is the belief of observers. As observers put themselves in the shoes of the Responder, we keep the same notation as the belief elicited from Responders.
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We thank James Cox, Nick Feltovich, Martin Kocher, Ariel Rubinstein, Tom Wilkening, Erte Xiao and Daniel Zizzo as well as participants from the ANZWEE and the Econometrics Society Summer School for their comments.
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Engler, Y., Page, L. Driving a hard bargain is a balancing act: how social preferences constrain the negotiation process. Theory Decis 93, 7–36 (2022). https://doi.org/10.1007/s11238-021-09835-y
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DOI: https://doi.org/10.1007/s11238-021-09835-y