Abstract
Using a series of laboratory experiments in the context of bilateral bargaining over whether and how to engage in a joint venture, this paper shows that fairness concerns result in failures to undertake profitable joint production opportunities. We find that framing an opportunity as an employment relationship rather than as a partnership significantly reduces these inefficiencies and increases subjects’ welfare. Consistent with the theoretical model developed in the paper, text analysis and a followup experiment demonstrate that the lower likelihood of an efficient outcome in the partnership frame is driven primarily by a concern for fairness generated by the perceived social relationship associated with partnerships, and not by differences in the economic structure, cognition, subject motivation, or changes in relative bargaining power.
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Notes
Each agent knows the outside wage of their potential partner.
Message boards and blog posts hosted by major startup communities, including YCombinator, Medium, Inc.Com, and CoFoundersLab, demonstrate little consensus over whether to bring on a founding partner or to hire a first employee.
A related paper is Charness and Rabin (2002), who investigate how social preference affects subjects’ willingness to sacrifice own payoffs.
Another recent example of freeform chat between players is provided by Huang and Low (2018), who analyze gender effect on negotiation strategies where subjects communicate using freeform chats prior to a battle of sexes game with a limited number of possible outcomes.
A notable exception is Binmore et al. (1989) who present experimental results from alternatingoffer bargaining with outside options and time discounting.
The online appendix is available at http://www2.rotman.utoronto.ca/tanjim.hossain/HLSOnlineAppendix.pdf.
We allowed three minutes of chatting in the five practice periods. The time limit for chat was typically not binding.
The first assumption simplifies the proofs and makes the results slightly more general. Nonetheless, similar results can be shown if we assume that players have fairness concerns when they receive outside options.
Assuming that participants choose the optimal production specification if they produce jointly (which is supported by our empirical findings in the next section) we restrict attention to a fixedsized pie and focus on whether players can reach an agreement on how to share it and how they divide the pie in case of agreement.
We assume that the effect of inequality for a given player is independent of which player receives higher payoff or surplus, unlike in Fehr and Schmidt (1999). Nonetheless, this assumption is made only for expositional simplicity and does not affect the results qualitatively.
The proofs are provided in “Appendix”.
The number of distinct individuals per session is between 6 and 14. This structure allows us to use subject fixed effects to determine whether efficiency differences across cases are driven by individualspecific differences. However, one may argue that each session might be considered as an independent observation. To address this concern, we performed Wilcoxon Rank tests on the mean optimal production and mean equal division per session by cases. We find that even with 7 observations in the partnership frame and 6 in the employment frame, there are significant differences across frames. For instance, the p values for Wilcoxon tests of the differences in mean optimal production and in mean equal profit sharing for case 3 are 0.022 and 0.087 respectively.
Summary statistics are available in the online appendix.
This table reports linear probability regressions for simplicity. However, all our results stay qualitatively unchanged if we use probit or logit regressions with individual fixed effects.
Participants in the partnership frame who receive a lower payoff than their outside option by agreeing to an equal profit split in case 3 do not subsequently reduce their willingness to split profits equally in a future case 3 periods suggesting that that learning to incorporate outside options in the partnership frame is limited.
In analyses not reported here, we find that more time spent in negotiation is associated with slightly worse outcomes (e.g., 1 more second spent negotiating is associated with a 0.2 percentage point decreased likelihood of optimal production), but also a slightly lower likelihood of equal profit sharing (which is somewhat mitigated in the employment frame). Moreover, we do not find evidence that the relationship between chat length and optimal production differs by frame type.
However, we find that if the subsequent proposal involves a new profit division, this relationship disappears.
In case 1, it is quite rare that offers are made at all, as partners generally agree quite quickly not to produce jointly. However, even in those instances in which profit division offers are made, they are more likely to make the subject receiving the offer at least as well off as she would be in wage work under the employment frame.
For instance, among these pairs, those under the employment frame are 10 and 11 percentage points more likely to form a firm in cases 2 and 3, respectively (p value = 0.04 for both differences).
A simple Google search of this question yields hundreds of expert opinion pieces and question and answer discussions on the pros and cons of cofounders versus employees. See, for instance, https://medium.com/villageglobal/whoshouldgetthetitlecofounderatyourstartupd3af016c924, and https://firstround.com/review/LookingforLoveinAllTheWrongPlacesHowtoFindaCoFounder/.
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The authors are grateful to Quinn Lewis for excellent research assistance, and to Mitch Hoffman and Charles Sprenger, and participants in seminars at the Harvard Business School, University of Toronto, Ryerson University, and the National University of Singapore for valuable feedback. We gratefully acknowledge funding support from UC San Diego Academic Senate and SSHRC Insight Grant No. 502502.
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Appendix: Proofs
Appendix: Proofs
Below we present the proofs for the propositions presented in Sect. 3 and two related lemmas. Without loss of any generality, we assume that \(w_{1} \ge w_{2}\).
Lemma 1
We can characterize the outcomes under three different cases as following:

(1)
When the size of pie is smaller than the sum of outside options then the players will always choose the outside options.

(2)
When \(\pi >w_{1}+w_{2}\) and \(\frac{\pi }{2}>w_{i}\) for both \(i\in \left\{ 1,2\right\} \), then there is a Pareto improving division of \(\pi \) for any \(\alpha \), if either both players or neither player incorporate outside options in fairness consideration. However, if one player incorporates outside options in fairness consideration and the other player does not, then there is a Pareto improving division of \(\pi \) only if \( \alpha \) is low enough.

(3)
When \(\pi >w_{1}+w_{2}\) and \(\frac{\pi }{2}<w_{i}\) for some \(i\in \left\{ 1,2\right\} \), then there is a Pareto improving division of \(\pi \) for any \(\alpha \), if both players incorporate outside options in fairness consideration. However, if at least one player does not incorporate outside options in fairness consideration, then there may not be a Pareto improving division of \(\pi \) if \(\alpha \) is high enough.
Proof
First we consider case 1, where \(\pi <w_{1}+w_{2}\). Note that, for joint production, \(u_{i}\left( x_{1},x_{2},w_{1},w_{2}\right) \le x_{i}\) independent of whether player i incorporates outside options to define fairness. As \(x_{1}+x_{2}<w_{1}+w_{2}\) for any allocation of the pie, both cannot be (weakly) betteroff by sharing the pie. Hence, the players should choose the outside options in the bargaining game.
For case 2, where \(\pi >w_{1}+w_{2}\) and \(\frac{\pi }{2}>w_{i}\) for both \( i\in \left\{ 1,2\right\} \), \(u_{i}\left( \frac{\pi }{2},\frac{\pi }{2} ,w_{1},w_{2}\right) =\frac{\pi }{2}>w_{i}\) if neither player incorporates outside options in fairness and \( u_{i}\left( w_{1}+\frac{\pi w_{1}w_{2}}{2},w_{2}+\frac{\pi w_{1}w_{2}}{2} ,w_{1},w_{2}\right) =w_{i}+\frac{\pi w_{1}w_{2}}{2}>w_{i}\) if both players do. Thus, there is some allocation of the pie that makes both players better off when they both define fair allocation the same way. However, if the two players differ in how they define fair allocation, then it is possible that there is no division of \(\pi \) that makes both better off if \( \alpha \) is large enough and \(w_{1}\ne w_{2}\).
Now consider case 3, where \(\pi >w_{1}+w_{2}\) and \(w_{1}>\frac{\pi }{2} >w_{2} \). If both players incorporate outside options in fairness, \( u_{i}\left( \frac{\pi +w_{1}w_{2}}{2},\frac{\pi w_{1}+w_{2}}{2},w_{1},w_{2}\right) = \frac{\pi +w_{i}w_{j}}{2}>w_{i}.\) Thus, there will be a Pareto improving division of the pie in that case. When at least one player does not incorporate the outside options in fairness, then if \(\alpha \) or \(w_{1} w_{2}\) is large enough, there might not be any division of \(\pi \) that is Pareto improving, leading to bargaining failure. Note that even when both players believe that equal division is the fair allocation, when the outside options are very different, giving player 1 just \(w_{1}\) would already make player 2 worse off than her outside options. \(\square \)
Lemma 2
Suppose the two players differ in how they define fair allocation. If \(\alpha \) is such that successful bargaining outcome is feasible for some outside option combination \(\left( w_{1},w_{2}\right) \) where \(w_{1}> \frac{\pi }{2}>w_{2}\), for a given \(\pi \), then successful bargaining outcome will be feasible for any outside option combination \(\left( w_{1}\epsilon ,w_{2}+\epsilon \right) \) such that \(\frac{w_{1}w_{2}}{2}\ge \epsilon >0\).
Proof
The restriction on \(\epsilon \) implies that \(w_{1}\epsilon \ge w_{2}+\epsilon \). First, we consider the case where \({\mathbf {1}}_{O_{1}}=0\) and \({\mathbf {1}}_{O_{2}}=1\) and joint production is feasible. Hence, there are \(x_{1},x_{2}\) such that \(x_{1}+x_{2}=\pi \) and
If we offer the two players \(x_{1}\epsilon \) and \(x_{2}+\epsilon \) when the outside options are \(\left( w_{1}\epsilon ,w_{2}+\epsilon \right) \), then player 1’s utility from agreeing to accept \(x_{1}\epsilon \) is
Moreover, player 2’s utility from bargaining agreement is
Hence, bargaining agreement will be feasible.
Similarly, when \({\mathbf {1}}_{O_{1}}=1\) and \({\mathbf {1}}_{O_{2}}=0\), bargaining success under case 3 implies,
Using arguments similar to the ones above, we can show that for a different set of outside options \(\left( w_{1}\epsilon ,w_{2}+\epsilon \right) \) such that \(\frac{w_{1}w_{2}}{2}\ge \epsilon >0\), there will be a share of pie which makes both players better off. Note that the restriction on \(\epsilon \) covers all possible case 2 situations as well as case 3 situations with less lopsided outside options. Thus, the existence of feasible bargaining solution in a case 3 scenario involving two players whose fairness definitions differ, would suggest that there will be feasible bargaining solution in any case 2 scenario involving those two players. \(\square \)
Proposition 1
Bargaining failure is more likely in case 3 than in case 2.
Proof
Lemma 1 characterizes scenarios where bargaining failure may occur under cases 2 and 3. It suggests that it will suffice to focus on the case where the players differ in their definition of a fair outcome. Lemma 2 shows that, in that scenario, fixing \(\pi \) and the sum of outside options, if the parameters (\(\alpha ,w_{1},w_{2}\)) are such that there is a Paretoimproving allocation of \(\pi \) when \(w_{1}>\frac{\pi }{2}>w_{2}\), then there must be a Paretoimproving allocation of \(\pi \) when \(w_{1}\) is decreased and \(w_{2}\) is increased by the same amount in a way that \(\frac{ \pi }{2}\ge w_{i}\) for \(i\in \left\{ 1,2\right\} \). Hence, while bargaining failure can happen in both cases 2 and 3, it would happen more frequently under case 3. \(\square \)
Proposition 2
Suppose more players believe that fair allocation is equal division of surplus under frame A than under frame B. Then, the probability of bargaining success is higher under frame A for both cases 2 and 3.
Proof
We will prove this result by considering different scenarios. First, consider case 2. When both players define fairness the same way, they will successfully bargain to share the pie. If the two players define fairness differently, if \(\alpha \) is small enough given \(\left( \pi ,w_{1},w_{2}\right) \) then the players will bargain successfully. Therefore, we need to compare bargaining success probability under the two frames when bargaining failure occurs if the two players define fairness differently. In that case, the probability of bargaining success under frame \(j \in {A,B}\) is \(p_{j}^2+\left( 1p_{j} \right) ^2\) for j. The difference in the success rate between frames A and B is \(2p_{A}^22p_{A}2p_{B}^2+2p_{B} =2\left( p_{A}+p_{B}1 \right) \left( p_{A}p_{B} \right) \). This difference is strictly positive if \(p_{A}+p_{B}>1\). Therefore, the probability of bargaining success in case 2 will be higher for employment frame. For case 3, first consider \(\left( \pi ,w_{1},w_{2}\right) \) combinations for which bargaining failure occurs only when the players differ in their definition of fairness. The above argument shows that the employment frame will increase probability of bargaining success when \(p_{A}>p_{B}\) and \(p_{B}+p_{A}>1\). If \(\left( \pi ,w_{1},w_{2}\right) \) is such that bargaining success occurs only when both players define fairness with respect to outside options, then the employment frame will increase bargaining success as \(p_{A}>p_{B}\). Therefore, frame A will lead to a higher likelihood of bargaining success for both cases 2 and 3. \(\square \)
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Hossain, T., Lyons, E. & Siow, A. Fairness considerations in joint venture formation. Exp Econ 23, 632–667 (2020). https://doi.org/10.1007/s1068301909626x
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DOI: https://doi.org/10.1007/s1068301909626x