Appendix A. Additional estimation results for section 5.

Transcription

1 Appendix A. Additional estimation results for section 5. This appendix presents detailed estimation results discussed in section 5. Table A.1 shows coefficient estimates for the regression of the probability of a contract offer being accepted (vs. being rejected or receiving a counteroffer) on the proposer s stage I contribution. Predictive margins in figure 3 are computed using this specification. Dependent Var.: Response Table A.1: Effects of proposer s stage I contribution on contract acceptance decisions Sample: EQUAL offers Sample: THRESH VESTING offers Sample: DIFF VESTING offers Sample: PROP offers Accept contract (baseline) (baseline) (baseline) (baseline) (Response = 0) Offer a different Proposer s ** contract contribution in stage I (0.083) (0.052) (0.060) (0.046) (Response = 1) Constant * (1.586) (2.089) (1.509) (1.273) Reject contract Proposer s * (Response = 2) contribution in stage I (0.054) (0.050) (0.044) (0.037) Constant (0.969) (1.796) (1.024) (0.693) Observations Dependent variable is the response to a contract offer (0: Accept, 1: Offer a different contract, 2: Reject). Estimation is conducted using Multinomial Logit model, standard errors clustered at subject level. Each column uses observations in which a given contract type was offered. Coefficients are reported in relative risk ratio format. Age, gender and period are controlled for. A-1

2 Appendix B. Additional estimation results for section 6. This appendix presents detailed estimation results discussed in section Table B.1 shows coefficient estimates for the regression of the probability of a subject expressing a preference for a certain contract form and of a subject selecting a certain contract on the subject s type. Table B.2 shows coefficient estimates for the regression of effort on both contracts and subject type. Table B.3 shows within-type effort changes between contracts and type-specific response to partner effort. In all three tables estimation is conducted using experimental data from experimental rounds 4-8 (to separate the analysis of type behaviors from type assignment for which rounds 1-3 data was used). For robustness the analyses presented in tables B.1- B.3 have been replicated using experimental data from rounds 1-8. In a further robustness check we regressed effort on type and contract variables and all pair-wise interactions between contracts and types. For further robustness, we repeat the analysis interacting the type variable with the incentive strength of the contract (taking the value 1 for EQUAL, 2 for VESTING and 3 for PROPORTION contract). These robustness checks confirm our results. Table B.1: Contract preferences and contract choices, by type. Contract Dependent variable: Dependent variable: Expressed contract preference Final contract EQUAL Conditional contributor *** (0.904) (0.630) High contributor *** *** (0.905) (0.718) Constant ** (1.279) (1.413) VESTING (baseline) (baseline) PROPORTION Conditional contributor ** * (0.835) (0.662) High contributor (0.909) (0.772) Constant Subjects Observations Tests of linear combinations of coefficients EQUAL High contributor NA NA conditional contributor PROPORTION High contributor 7.664*** 5.825*** conditional contributor (4.477) (3.317) Dependent variable is the expressed preference for a contract form (column 1) and final contract selected by the team (column 2). Preference for a contract is measured as the first offer made in negotiations. Estimation is conducted using Multinomial Logit model, standard errors clustered at subject level. Coefficients are reported in relative risk ratio format (i.e. the ratio of type-specific choice probabilities for different contracts). V EST ING contracts and Low contributors are used as the baseline. All coefficients are estimated using data from experimental rounds 4-8 (to separate type identification conducted in rounds 1-3 from type behavior). The bottom panel of the table shows tests of linear combinations of coefficients (again using the risk ratio format). NA denotes tests for which there is an insufficient number of observations of a type in a certain contract. Age, gender and experimental period are controlled for. * p < 0.1, ** p < 0.05, *** p < B-1

3 B-2 Table B.2: Effort, by contract and type. Dependent variable Stage I effort Stage II effort Total effort VESTING *** *** *** (7.354) (8.860) (6.885) PROPORTION *** *** *** (7.811) (9.005) (7.491) Conditional contributor ** * (9.174) (8.235) (8.602) High contributor * ** ** (10.012) (9.620) (9.758) Constant (15.345) (14.848) (13.875) Observations Subjects Tests of linear combinations of coefficients VESTING ** *** *** PROPORTION (3.651) (3.630) (2.895) High contributor Conditional contributor (6.504) (7.063) (6.725) Dependent variable is effort (stage I effort in column 1, stage II effort in column 2, total effort in column 3). Baseline is low contributor and EQUAL contract. Estimation is conducted using random effects regression model. All coefficients are estimated using data from experimental rounds 4-8 (to separate type identification conducted in rounds 1-3 from type behavior). Standard errors are clustered at subject level. Age, gender and experimental period are controlled for. * p < 0.1, ** p < 0.05, *** p < 0.01.

4 B-3 Table B.3: Within-type, between contract effort comparisons. Dependent variable: Stage II effort Sample: Low Conditional High Low Conditional High contributors contributors contributors contributors contributors contributors EQUAL (baseline) (baseline) NA (baseline) (baseline) NA VESTING ** *** (baseline) ** *** (baseline) (13.831) (11.219) (13.532) (11.419) PROPORTION *** *** ** *** (15.719) (11.394) (3.325) (16.414) (11.895) (3.121) Partner stage I *** contribution (0.320) (0.212) (0.262) Constant * * ( ) (14.900) (26.221) ( ) (15.168) (25.390) Observations Subjects Tests of linear combinations of coefficients VESTING *** NA ** NA PROPORTION (13.860) (4.578) NA (13.630) (4.642) NA Dependent variable is stage II effort. Baseline for low and conditional contributors is EQUAL contract. Baseline for high contributors is VESTING contract (there is not a sufficient number of observations of high contributors in EQUAL contracts). Estimation is conducted using random effects regression model. All coefficients are estimated using data from experimental rounds 4-8 (to separate type behaviors from type identification conducted in rounds 1-3). NA denotes tests for which there is an insufficient number of observations of a type in a certain contract. Standard errors are clustered at subject level. Age, gender and experimental period are controlled for. * p < 0.1, ** p < 0.05, *** p < 0.01.

5 Appendix S1 (Supplementary materials). Equilibrium analysis. In this supplementary document we describe the equilibrium structure in each contract. Before presenting the analysis it is useful to list the variables and the parameters used in our model and experiments. These are summarized in table S1.1 below. Without loss of generality, we consider the problem from the perspective of founder i and refer to i s partner as j. In the analysis presented below we assume that both partners are risk-neutral own payoff maximizers. Following the backward induction logic we first determine the optimal strategies in stage Table S1.1: Model components Variable label Variable description Variable expression e is m is Effort invested into the startup by player i in stage s {1, 2} Return on effort invested into the startup in by player i in stage s e is [0, E], determined by player i 0.5 with prob. 0.25, 1 with prob. 0.5, 2 with prob c is Contribution of player i in stage s {1, 2} m is e is V s Value generated by the team in stage s {1, 2} c is + c js V Final Value of the startup V 1 V 2 π i Individual profit of player i under contract X σ X i V + K(2E e i1 e i2 ) Parameter label Parameter description Parameter value K Return on effort invested privately 5 E Effort endowment in each stage 10 c T HRESH Minimal contribution requirement in THRESH VESTING contracts c DIF F Minimal contribution requirement in DIFF VESTING contracts σ EQUAL i Player i s share of V under EQUAL contract 0.5 T HRESH,UP F RONT σi DIF F,UP F RONT σi P ROP ORT ION,UP F RONT σi T HRESH,DELAY ED σi DIF F,DELAY ED σi P ROP ORT ION,DELAY ED σi Player i s share of V under THRESH VEST- ING contract and UPFRONT contracting Player i s share of V under DIFF VESTING contract and UPFRONT contracting Player i s share of V under PROPORTION contract and UPFRONT contracting Player i s share of V under THRESH VEST- ING contract and DELAYED contracting Player i s share of V under DIFF VESTING contract and DELAYED contracting Player i s share of V under PROPORTION contract and DELAYED contracting if vest, 0.4 if fail to vest in exactly one of the stages, 0.3 if fail to vest in both stages 0.5 if vest, 0.4 if fail to vest in exactly one of the stages, 0.3 if fail to vest in both stages c i1 +c i2 c i1 +c i2 +c j1 +c j2 0.5 if both players vest, 0.3 if fail to vest in stage if both players vest, 0.3 if fail to vest in stage 2 c i2 c i2 +c j2 S1-1

6 S1-2 II, in which player i faces the following problem: max e i2 Eπ i (X, e i2, e j2 S 2 ) = Eσ X i V 1 V 2 + 5(10 e i2 ) = 5(10 e i2 ) + (m i1 e i1 + m j1 e j1 )Eσ X i (m i2 e i2 + m j2 e j2 ) (S1.1) where the state of the game in stage II, S 2 is defined by the efforts invested by the team in stage I, e i1 [0, 10] and e j1 [0, 10], and by the returns to those efforts, m i1 {0.5, 1, 2} and m j1 {0.5, 1, 2}. After determining the best response strategies in stage II we examine stage I strategies given optimal continuation behavior in stage II. UPFRONT treatment EQUAL contracts Because EQUAL contracts do not tie equity allocation to either effort or contribution, optimal stage II decisions will be fully determined by V 1, regardless of how V 1 was earned. Stage II best response behavior can be further simplified to a single threshold-based strategy because Eπ i(equal,e i2,e j2 V 1 ) e i2 is strictly negative when V 1 < and strictly positive when V 1 > 8.888, and because 2 Eπ i (EQUAL,e i2,e j2 V 1 ) e i2 e j2 = 0. Therefore, for EQUAL contracts the best responses in stage II are given by 0 if V 1 < ( low state) e i2(v 1 ) = [0, 10] if V 1 = if V 1 > ( high state) (S1.2) We will next show that allocating all effort to the startup account is the best response to any partner action in stage I. The intuition for this result is as follows. Assume first that the partner, j invests no effort in stage I. Because the effort-contribution mapping is stochastic and given our model parameters player i cannot unilaterally guarantee that the high state will be reached. However, player i can increase the probability of the high state by investing more effort in stage I. Further, because the startup value V is multiplicative in its stage components V 1 and V 2, investing more effort in stage I increases payoffs if the high state is reached. Given our parameters, these considerations result in full effort being player i s best response to partner j s zero effort investment in stage I. In fact, full effort is the best response to any partner effort, because any increase in stage I partner effort will increase the probability of reaching the high state, which in turn increases the expected returns to effort for player i. Mathematically, it is straightforward to verify that Eπ i(equal,e i1,0,e i2,e j2 ) e i1 0 in the 0 e i1 < > 0 in the 8.888/2 e i1 10 range. Since the expected profit resulting from full effort investment is greater than the expected profit from zero effort, the best-response to zero partner effort is to invest full effort in stage I. Further, because the (expected) marginal returns to stage I effort increase in partner effort, full effort investment remains best response to any e j1. In sum, the equilibrium strategy for EQUAL contracts is {e i1 = 10; e i2 = 0 if V 1 < 8.888, e i2 [0, 10] if V 1 = 8.888, e i2 = 10 if V 1 > 8.888}. Notice that because both partners will invest full effort in stage I in equilibrium, the team can guarantee the high state of the world (V 1 > 8.888), so any effort levels below 10 imply off-equilibrium behavior /2 range and Eπ i(equal,e i1,0,e i2,e j2 ) e i1 NON-EQUAL contracts While the stage II best responses in the NON-EQUAL contracts are generally a function of four variables (own and partner stage I efforts and the returns to those efforts), we can specify behavioral predictions on the equilibrium path more concisely. In particular, there are cutoff values for V 1 that divide the stage II state space into three regions. Similarly to EQUAL contracts, there are two regions in which zero or full effort is a mutual best response (regardless of the efforts and the returns to those efforts in stage I). However, there is an additional region in which the best response depends on mutual stage I outcomes.

7 S1-3 Figure S1.1: Expected total payoff as a function of own and partner effort in stage I (a) Zero stage I partner effort (a) Full stage I partner effort EQUAL contract PROPORTION contract PROPORTION contract EQUAL contract Note. The expected profits are computed given risk-neutral own profit maximizing behavior and correct backward induction by both players. In particular, for PROPORTION contracts it can be shown that full effort is a mutual stage II best-response regardless of stage I efforts and returns to those efforts if V 1 > Further, zero effort is a stage II best-response regardless of stage II partner effort and regardless of stage I efforts and returns to those efforts if V 1 < Finally, in the V range the mutual best-response depends on the exact stage I effort levels and the returns to those efforts. In each possible state of the game there is a unique symmetric best-response strategy with either zero or full effort being the mutual best-response. Using these continuation strategies we can, again, show that exerting full effort is the unique best-response strategy in stage I. If the partner exerts no effort in stage I, the expected profit function is first decreasing in e i1 and then increasing in e i1. To determine the best responses for this scenario it suffices to compare expected profits at the corner solutions e i1 = 0 and e i1 = 10, with the latter allocation leading to higher profits. Further, similarly to EQUAL contracts, any increase in j s effort will increase the marginal returns to effort for player i, so full effort will remain the best response to any partner effort in stage I. Because maximum stage I effort will guarantee that the high state occurs with probability 1, on the equilibrium path both partners will, again, invest maximum effort in both stages. Figure S1.1 illustrates best response behaviors and the differences in expected profits in each scenario. The graphs show the expected profit as a function of stage I effort levels, assuming perfect backward induction by both players. Panel (a) shows an off-equilibrium path, in which the partner exerts no effort in stage I. Notice that while the best-response is to exert full effort in both contracts, PROPORTION contracts have a stronger incentive to do so. Panel (b) shows the consequences of different stage I effort allocations on the equilibrium path (That is, maximum partner effort). In this scenario, EQUAL contracts dominate PROPORTION contracts in terms of expected profits for any less-than-maximal effort level. However, when both partners exert full effort, expected profits are identical between the contracts because the differences in share allocation cancel out in expectation. With VESTING contracts best response behavior remains similar to PROPORTION contracts. In stage II the best response is a function of stage I efforts and of the returns to those efforts, and there are three regions with different predictions for stage II effort investment. Zero effort is the unique best-response in the low region (V 1 < v 1 ). Both zero and full effort are possible in

8 S1-4 Table S1.2: Equilibrium predictions EQUAL THRESH VESTING, UPFRONT DIFF VESTING, UPFRONT PROPORTION, UPFRONT THRESH VESTING, DELAYED DIFF VESTING, DELAYED PROPORTION, DELAYED Stage I Best response strategy Invest full effort Invest full effort Invest full effort Invest full effort Invest full effort Invest full effort Invest full effort Range of V 1 where Invest 0 is best response Stage II Range of V 1 with multiple best response strategies Range of V 1 where Invest full effort is best response [0, 8.888) [8.888] (8.889, 400] [0, 6.015) [6.015, 9.640] (9.640, 400] [0, 6.350) [6.350, ] (10.289, 400] [0, 4.444) [4.444, 6.966] (6.966, 400] [0,6.350) [6.350,7.142] (7.142, 400] [0,6.350) [6.350,7.955] (7.955, 400] [0, 4.444) [4.444] (4.444, 400] the middle region (v 1 V 1 v 1 ). Full effort is the unique best-response in the high region (v 1 < V 1 ). The differences between VESTING and PROPORTION contracts are the locations of the cutoff values, v 1 and v 1. Specifically, because VESTING contracts impose only a mild penalty for low effort, the middle region is extended relative to PROPORTION contracts (See table S1.2 for the exact cutoff values). Further, similarly to the other contracts, both partners will exert full effort levels in both stages on the equilibrium path. DELAYED contracting Because the mapping between partner contributions and share allocation is different with each contract form and with each contracting time, the returns to investing effort in stage II will be different in each of those regimes, too. Therefore, while the structure of optimal stage II responses will be similar, the cutoff values for V 1 will be different for the UP- FRONT and DELAYED scenarios, even conditional on the contract (The exact cutoff values for V 1 are reported in table S1.2). However, similarly to the UPFRONT scenario, predicted effort levels differ only in stage II and only on the off-equilibrium path. That is, full stage I effort remains mutual best response regardless of the contract, leading to full effort investment in stage II on the equilibrium path in each contract.

9 Appendix S2 (Supplementary materials). Instructions for UPFRONT treatment, exact transcript. You and your partner have identified a potential new business start-up that you can develop as a team. Its success depends on decisions that you and your partner will make as well as on luck. There will be two sets of decisions you will have to make. Contract Negotiations. In the contracts negotiations phase you and your partner will together decide on a contract. This contract will establish how the value generated by your future startup will be divided. Startup Work. In the startup work phase you will make decisions that will affect the value of the startup. Then you will find out what the value is and divide it according to the negotiated contract. Let s first look at the decisions you and your partner will make in the startup work phase. During the startup work phase you will be asked to divide your time between the start-up (with an uncertain pay-out, as explained on the next screens) and an alternative task that pays you (individually, this pay is not shared with your partner) a fixed dollar amount per unit of time invested. Your partner faces the same choice. You do not yet know what the actual value of the start-up will be, or how much effort your partner will allocate to working on it relative to his/her private task. Your partner faces a similar level of uncertainty about your actions. Work on the startup involves two periods. In each period you have 10 hours to allocate between the start-up and your private task. You will choose how many hours to allocate to the start-up, and the remainder will be allocated to your private task. For example, if you do not allocate any hours to the start-up then 10 hours will be allocated to the private task. If you allocate 10 hours to the start-up you will allocate 0 hours to the private task. In general, if you allocate H hours to the start-up you will allocate (10 H) hours to the private task. As mentioned earlier, the amount you will be paid at the end of the experiment depends on the number of points you accumulate during a randomly chosen round of the experiment: - For each hour you allocate to your private task you get 5 points. - The number of points you get for investing in the start-up is not known with certainty until the end of the second period. Here is how it is determined: The value of the start-up depends on the contributions that you and your partner make in each of the two periods. In each period, your contribution to the project will be the hours you dedicate to it multiplied by one of three numbers: - 1/2H with probability 1/4 - H with probability 1/2-2H with probability 1/4 This means, the most likely case is that the hourly value of your effort for the startup is 1. However, there is a possibility that this value is only 0.5, or that it is 2. After you and your partner make your allocation decisions in period 1, the period 1 value of the start-up is the sum of your contributions. We will refer to the period 1 value as V 1. Example: Suppose in period 1 you decide to spend 6 out of 10 hours on the start-up. The randomly determined value of your effort is 1/2 so your contribution to the project is (1/2) (6) = 3. You also accumulate (10 6) hours 5 = 20 points for your private task. You are told that your partner s contribution to the project is 9, but recall that you cannot observe how many hours he/she spent on the startup. In this example this means he/she could have invested 4.5 hours and each hour was worth 2, or 9 hours and each hour was worth 1. Then, the intermediate value of the project V 1 = = 12. S2-1

10 S2-2 After period 1 has ended, and you have seen your partner s contribution and the period 1 value of the project, you (and your partner) will make your period 2 decisions. Just as in period 1, in period 2 you have 10 hours to invest in the start-up or private task, and each hour you invest in the start-up is multiplied by a random number (1/2 with prob. 0.25, 1 with prob. 0.5 or 2 with prob. 0.25) to determine your contribution to the project. The same is true for your partner. Similarly to the first period, the period 2 value of the start-up, V2, will be the sum of your and your partner s period 2 contributions. The final value of the start-up, V and the basis on which you and your partner will be paid, is the product of period 1 and period 2 values: V = V 1 V 2. Notice that the highest number of points you can jointly collect in one period is = 40 so the most your team can earn in the end is = The lowest possible team profit is 0 which would occur if neither of you invest any effort in the joint project in one period (Notice that multiplying 0 with any number equals 0). Once the total team profit is determined it will be divided between you and your partner according the contract (Contracts will be discussed shortly) Example (continued): In the previous example you invested 6 hours in the start-up in period 1, resulting in a contribution of 3 to V 1. Your partner contributed 9 so V 1 = 12. You also accumulated 20 points from investing 4 hours in your private task. Suppose that In the second period you decide to invest 5 hours in the start-up, and it is randomly determined that each hour is worth 2 units, so your contribution is 10. You invest 10 5 = 5 hours in your private task, earning an additional 5 5 = 25 points. You learn that your partner s contribution to V 2 is 4. So, V 2 = = 14. How much will you earn? The start-up is worth V 1 V 2 = = 168 points. Suppose that you are dividing the startup value evenly. Then each of you will receive 168/2 = 84. Recall that you have allocated a total of 9 hours to your private task, each of which is multiplied with 5 so your total take-home will be 45 (private task) + 84 (start-up) = 129 points. Figure S2.1: Quiz (Printed screen shot) Note. The figure shows a screen print of the quiz. Subjects were not allowed to proceed to the game prior to correctly answering each question in the quiz.

11 How will you decide on the contract? In the previous examples the value V generated by the startup was split regardless of how much each partner contributed. However, there are alternative ways to divide the startup value. Before you make contribution decisions you and your partner will select one of the 4 contract options. If you and your partner fail to agree on a contract your hours will be automatically allocated to your private account and the startup value will be 0. What are the 4 contract options? Performance dependent. Each partner gets the share of the startup value V proportional to the SUM of his contributions in two periods. In other words, the percentage a partner gets will be equal to the sum of his/her contributions divided by the sum of total contributions , unless contribution difference > 5. Each partner gets 50% of the startup value V if contributions in each period differ by no more than 5 points. If contributions differ by more than 5 in one period, the split is in favor of the partner who contributes more. If this happens and one partner contributes more each time, the split is in his/her favor , unless individual contribution < 5. Each partner gets 50% of the startup value V if his/her contribution is at least 5 points in each period. If one of the partners contributes less than 5 in one period, the split is in favor of the partner who contributes more. If this happens twice and one partner contributes more each time, the split is in his/her favor , always. Each partner gets 50% of the startup value V regardless of the contributions. S2-3 Figure S2.2: Contract negotiations (Printed screen shot) Note. The figure shows a screen seen by subjects during the negotiations. Subjects were able to select one of the four contract alternatives, reject an offer made by their partners, or accept an offer. They were also able to review the description of contract alternatives. Teams were given 4 minutes in the initial two rounds of the experiment and 2 minutes in the later rounds of the experiment to agree on a contract.

12 Appendix S3 (Supplementary materials). Contracts Designed by Subjects in the Pilot Treatment. In this appendix we document the contracts designed by subjects in the pilot treatment. 73% of the teams chose equal splits ( 50-50, Each partner gets equal share, Each partner gets the same ). The exact transcripts of the remaining contracts are presented below (omitting identical and near identical contracts). As long as both partners contribute to the project they both equally share the gains made. If one partner doesn t contribute to the project (i.e. partner 1) then he will lose 1/3 of this private gains and they will be reallocated to his partner. Split gains made from joint project evenly as long as both partners have contributions that are 5, 10, or payoff for the joint contribution for about equal contribution. If one person s effort points exceed the other s by 3 the payoff should be 70/30 in their favor. If the difference in profits is lower or equal than 15 points then evenly. If the difference in profits is greater than 15 points, the person with lower points gets 30%, the person with higher points gets 70% of the profits. 60% for person with higher value of contribution, 40% for person w lower value of contribution. If the point spread in each round is 15 points or lower in each individual round then we split evenly. If the point spread is greater than 15 on either or both of the stages then the lower points person gets 20%, the higher points person gets 80%. If difference is less than 10 then split evenly. If not person with higher value gets 705, and person with lower gets 30%. After period 1 and 2 add each person s project contribution. Whoever has the highest total shared contribution value will get 60% of the total project value. The other person gets 40%. If equal, We will split person with the highest roll total gets 55 and the other person 45. We promise both putting our times (10 hours) to our joint projects for both series and will divide the gains The shares depend on the percentage of the total individual contributions to total profits. For example 507 [subject id] contributes X over 2 periods and 506 [subject id] contributes Y over 2 periods, so total is X + Y. The percentage that X gets is X/(X + Y ) and 506 [subject id] gets Y/(X + Y ) of total profit. We will divide the gains based on points each individual earns over total points (taking the sum of the individual contributions). S3-1

13 Appendix S4 (Supplementary materials). Construction of Utility Functions, Type Assignment and Type Behaviors Across Treatments. In this supplementary document we describe the assumptions and methodology behind the utility analysis presented in section 6 of the paper and the implications for type behaviors in each treatment. Methodology Utility function To characterize each type s preferences we estimate Conditional Logit models with the dependent variable being the joint probability of choosing a contract and an effort level (the discussion of type assignment is postponed until later). We model contract and effort choices as noisy solutions to a discrete choice problem, with each subject choosing effort e i {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and at the same time choosing contract X {EQUAL, THRESH VESTING, DIFF VESTING, PROPORTION}. Each of the resulting 44 alternatives is valued by the (expected) utility it generates. The probability of choosing an alternative is proportional to the utility it generates relative to the remaining alternatives. The objective of the Conditional Logit model is to choose the weights (also referred to as behavioral parameters or coefficients) on the components of the utility function that lead to the highest likelihood of the observed contract and effort choices of each type. 1 In particular, subject i s utility (conditional on type) from choosing alternative k K, where K is the set of all {contract effort} combinations, in period t is given by U ikt θ = z iktα θ + ɛ ikt, (S4.1) where θ {low, cond, high} denotes the subject s type and ɛ ikt is the random component of utility, assumed to be independent and identically distributed with Gumbel distribution (McFadden, 1973). The non-random component of the utility function, z iktα θ is the inner product of the vector of decision attributes, z ikt and the parameter vector α θ. We next discuss the model components in more detail. Model components The mathematical objects used in each of the examined models are described in table S4.1. After discussing the model components we will demonstrate the workings of the models with a simple example. Additional notation In the analysis presented below we will denote the contractual share of profit by σ i (X, e i, ê j (X, I it )) to make explicit the dependence of σ i on the contract X, efforts e i, ê j and the information set I it (The construction of information sets will be discussed later). Notice that the subscript of the expressions for own and partner effort does not include the contribution stage. The reason is that we will use e i and ê j to denote all effort variables that will be affected by the current decision, given the timing of the contracting. That is, in the UPFRONT scenario e i = {e i1, e i2 } and ê j = {ê j1, ê j2 } because contracting happens prior to effort provision. In DELAYED e i = e i2 and ê j = ê j2 because contracting happens prior to stage II but after stage I, so only stage II outcomes are affected. 1 We use the final contract selected by the team as the subject s contract choice in a given period. Notice that the final contract is a noisy measure of contract preferences, because it reflects team consensus rather than individual desires. Alternatively, one may use the first proposed contract to measure contract preferences. The disadvantage of the latter approach is that we only observe effort decisions in final contracts and not in proposed contracts, so evaluation of joint effort and contract choices is not always possible. Still, we explore the latter approach in robustness analyses and find similar results. Further, to make the effort data amenable to a discrete choice model non-integer effort values are rounded to the nearest integer. S4-1

14 S4-2 model 1 model 2 model 3 model 4 model 5 model 6 model 7 model 8 Table S4.1 Model components Parameter Factors assumed to be driving Attribute vector z vector α ikt θ behaviors [ ] [ αown,θ Eπi (X, e i, ê j (X, I it )) ] Own profit [ αown,θ ] [ ] Eπ i (X, e i, ê j (X, I it )) α erc,θ E 0.5 σ i (X, e i, ê j (X, I it )) [ αown,θ α aed,θ α own,θ α erc,θ α aed,θ [ αown,θ α ed,θ α own,θ α erc,θ α ed,θ [ αown,θ α eratio,θ ] [ ] Eπi (X, e i, ê j (X, I it )) e i ê j (X, I it ) Eπ i (X, e i, ê j (X, I it )) E 0.5 σ i (X, e i, ê j (X, I it )) e i ê j (X, I it ) ] [ ] Eπi (X, e i, ê j (X, I it )) e i ê j (X, I it ) α own,θ α erc,θ α eratio,θ Eπ i (X, e i, ê j (X, I it )) E 0.5 σ i (X, e i, ê j (X, I it )) e i ê j (X, I it ) ] [ ] Eπi (X, e i, ê j (X, I it )) e i e i +ê j (X,I it ) Eπ i (X, e i, ê j (X, I it )) E 0.5 σ i (X, e i, ê j (X, I it )) e i e i +ê j (X,I it ) Own profit; Payoff inequality Own profit; Abs. value of effort differences Own profit; Payoff inequality; Abs. value of effort differences Own profit; Effort relative to partner (diff) Own profit; Payoff inequality; Effort relative to partner (diff) Own profit; Effort relative to partner (ratio) Own profit; Payoff inequality; Effort relative to partner (ratio) Note. Own effort is denoted by e i. Estimate of partner effort in contract X is denoted by ê j(x, I it), where I it is the information set of individual i in the experimental period t. The share of equity allocated to individual i after choosing contract X and after the team exerting efforts e i and ê j is denoted by σ i(x, e i, ê j(x, I it)). In UPFRONT own expected profit is computed prior to stage I: Eπ i(x, e i, ê j(x, I it)) = E[σ i(x, e i, ê j(x, I it))v (e i, ê j(x, I it))] + 5(20 e i1 e i2) where V (e i, ê j(x, I it)) is the final value generated by the team and e i1 and e i2 are subject i s stage-specific effort values. In DELAYED own expected profit is computed after stage I and prior to stage II to allow updating of the information set: Eπ i(x, e i, ê j(x, I it)) = V 1E[σ i(x, e i2, ê j2(x, I it))v 2(e i2, ê j2(x, I it))] + 5(10 e i2). Self-interest The self-interested decision-maker will choose efforts and contracts to maximize her expected profit. We denote type θ s sensitivity to own profits by α own,θ. Model 1 assumes that each type cares solely about their own profits. Models 2-8 include the self-interest component among other components, nesting model 1 as a special case with the nonself-interest parameters set to 0. 2 When modeling the subject s sensitivity to changes in own profits, we need to construct the expected profits resulting from their decisions. In particular, the expected profit, Eπ i (X, e i, ê j (X, I it )) depends on the chosen contract, X and on the chosen effort level, e i. The subject s expected profit is also affected by her beliefs about the effort levels exerted by her partner in each contract. We model these beliefs by constructing information sets I it held by subject i in period t. The construction of these information sets is different in the UPFRONT and DELAYED treatments and will be discussed later in more detail. Further, notice that partner effort ê j (X, I it ) is an estimate, rather than a precise measure because subjects see noisy signals of each others effort (in form of contribution amounts), and not the exact initial efforts. 2 In our main analysis we assume that the self-interest parameter α own,θ may vary by type. For robustness we explore several models with the self-interest parameter being held fix across types, i.e. α own,low = α own,cond = α own,high. These specifications reduce the model fit substantially and are poor predictors of behavior.

15 Income differences Extensive work in experimental economics suggests that individuals may dislike discrepancies in payoffs and may prefer arrangements that lead to similar payoffs for them and their counterparts (Fehr and Schmidt, 1999; Bolton and Ockenfels, 2000). We denote the income discrepancy parameter by α erc,θ (The label ERC is borrowed from the Equity, Reciprocity and Competition model in Bolton and Ockenfels, 2000). We model the preference for equal splitting of rewards as the sensitivity to the deviation from the norm of the split implied by the contract and by the partners effort levels. We denote this deviation by 0.5 σ i (X, e i, ê j (X, I it )), where σ i (X, e i, ê j (X, I it )) is the share of equity implied by contract X and by the effort levels, e i and ê j (X, I it ). Notice that this parameter focuses on the attitudes towards relative differences rather than absolute differences in income. 3 In our setting, choosing an EQUAL contract will always lead to a payoff difference of zero because σ i = 0.5 regardless of the effort levels. With a VESTING contract σ i {0.3, 0.4, 0.5, 0.6, 0.7} depending on whether each partner vests in both, one or none of the two contribution stages. PROPORTION contracts will result in an income difference proportional to the difference in contributions between partners, so σ i can take any value between 0 and 1. Effort level differences Individuals may be sensitive not only to differences in income, but also to differences in effort levels. In particular, we explore three different flavours of attitudes towards effort discrepancies within the team. Individuals may prefer arrangements in which partner effort is similar to their own effort level, so that e i ê j (X, I it ) is low. We refer to this preference component as the sensitivity to absolute effort level differences and denote it by α aed,θ. Further, individuals may prefer to work less then their counterparts, even when this hurts their profits. In particular, they may care about the difference in effort levels, (e i ê j (X, I it )). We denote this parameter by α ed,θ. Alternatively, individuals may care about the ratio of their effort to the overall effort invested e by the team, i. We denote this parameter by α e i +ê j (X,I it ) eratio,θ. Construction of z ikt in UPFRONT and DELAYED We next discuss the construction of the attribute vector, z ikt in more detail. In particular, z ikt is constructed differently in the UPFRONT and DELAYED treatments because types operate with different information when making the contracting decisions. In the UPFRONT treatment subjects use their prior beliefs about effort levels ê j (X, I it ) in different contracts to evaluate the attractiveness of a contract. The beliefs about ê j (X, I it ) can be constructed using the true average effort levels in each contract, or they can be updated dynamically, in a Bayesian way over the course of the experiment, with the posterior values evolving with the efforts they see in the contracts. We use the former in our main analysis of the UP- FRONT data, and the latter as a robustness check. That is, in UPFRONT I it is identical for all subjects and does not change over time (the use of the subscript will become clear below, in the DELAYED discussion). Further, to reduce the number of modeled decisions, in UPFRONT we assume own and partner effort to not change between stage 1 and 2. That is, e i = e i1 = e i2 and ê j (X, I it ) = ê j1 (X, I it ) = ê j2 (X, I it ). In the DELAYED treatment we need to account for the effort signals exchanged by the team prior to contracting, when modeling their contract and effort choices. This additional information is captured in the information set I it. In particular, the attractiveness of a contract and the attractiveness of exerting (or not) effort is now different for each subject i and in each experimental round t. As in the UPFRONT treatment we assume that subjects hold (correct) prior beliefs about effort levels in each contract, but in addition they use their partners stage 1 effort signals to predict stage 2 effort. In particular, ê j2 = ê j1 M X, where M X is the (true empirical) multiplier that S4-3 3 We focus on the difference in publicly observable payoffs, i.e. differences in equity. Subjects also earn payoffs from their private effort investments, but these are made public. For robustness we examine an alternative specification in which we account for total (public + private) payoffs and obtain similar results. In our robustness analyses we explore several different flavours of difference aversion including absolute difference aversion (Fehr and Schmidt, 1999) and the more flexible lowest earner specification (Charness and Rabin, 2002).

16 S4-4 characterizes the average change between stage I effort and stage II effort for contract X and ê j1 is the most likely effort level given the observed stage I contribution. 4 A simple example A simple binary choice example illustrates the trade-offs faced by the subjects in each treatment. We begin with the UPFRONT scenario and assume that subject i is choosing between two alternatives: invest 10 units of effort and choose EQUAL contract (labeled as k = 1) vs invest 10 units of effort and choose PROPORTION contract (labeled as k = 2). We further assume for the purpose of this example that the subject s behavior is characterized by model 2 in table S4.1. In our experimental data, average effort in PROPORTION contracts is substantially higher relative to EQUAL, leading to higher expected profits in PROPORTION contracts. However, EQUAL contracts result in a more egalitarian division of profits. Specifically, z i1t = [127 0] and z i2t = [ ] for model 2. The choice between the two options will then depend on the subjects behavioral parameter α θ. In all of our models subjects strictly prefer more money to less, i.e. α own,θ > 0. Further, if subject i is indifferent towards payoff inequality or enjoys greater pay inequality (α erc,θ 0) then she will prefer PROPORTION contracts, since U i1t < U i2t for her. But, if α erc,θ is sufficiently low, she may prefer EQUAL contracts because inequality concerns will outweigh self-interest. For example, if α own,θ = 1 it can be easily verified that U i1t > U i2t when α erc,θ < Next, consider the DELAYED treatment and assume that partner stage I contribution observed by subject i is 8, resulting in ê j1 = 8. The expected payoffs resulting from choosing EQUAL vs PROPORTION contracts are now closer together. Specifically, assuming model 2 again, z i1t = [182 0] and z i2t = [ ] making EQUAL contracts substantially more attractive relative to UPFRONT, even if the subject is only mildly disinclined towards payoff inequality. For example, if α own,θ = 1 it can be easily verified that U i1t > U i2t when α erc,θ < 216. This example demonstrates that when a subject sees high initial effort in DELAYED, her rank order of the contracts and effort choices may be subject to substantial changes relative to UPFRONT. Assignment of Types Assignment of Types in the UPFRONT Treatment In the UPFRONT treatment subjects signal their types by the offers they accept and reject in negotiations. As discussed in sections 4-6 of the paper, the preference for EQUAL contracts is associated with reduced effort, and the preference for PROPORTION contracts is associated with increased effort, relative to the remaining groups. We use this insight to assign subjects to types. In particular, our main analysis uses the initial 3 periods to rank the desirability of each contract for each subject and to assign subjects whose top choice is EQUAL (VESTING, PROPORTION) contract to the low (conditional, high) contributor type. More specifically, we generate the variables OF F EREDit X where X {EQUAL, THRESH VESTING, DIFF VESTING, PROPORTION}. These denote the contract subject i used as her initial offer in period t. Similarly, ACCEP T EDit X denotes the contract subject i accepts in period t. When a subject does not make any offers or does not accept any contracts, these variable are assigned zero value. The preference for contract X of subject i is then measured as P REF SCOREi X = (OF F t=1,2,3 EREDX it + ACCEP T EDit X ). Further, the two vesting contracts are pooled. The final type assignment is done by finding the preferred contract type (that is, the contract with the highest preference score), and assigning low (conditional, high) contributor type to the subjects who prefer EQUAL (VESTING, PROPORTION). 5 4 Alternatively, we split all possible partner stage I contribution levels into discrete categories and predict stage II effort based on the category of the observed stage I contribution. These robustness analyses yield similar results. 5 Our main specification uses the initial three periods to compute P REF SCOREi X. For robustness we repeat the analysis with the type assignment based on the initial two and based on the initial four periods and find similar results. We also examine alternative classification procedures, based on initial offers OF F EREDit X alone (omitting ACCEP T EDit X ), between-contract changes in effort levels and discrete cutoffs for score variables. These result in

17 Assignment of Types in the DELAYED Treatment In the DELAYED treatment individuals no longer signal their types solely by the contracts they offer. Rather, as shown in section 5.2 of the paper, their preferred contracts depend on the effort levels they see in stage I. To account for the differences in the information available to subjects prior to contracting we use the α θ parameters estimated using the UPFRONT contracting data to predict what each type would do in DELAYED, conditional on the partner contribution levels they see. We then choose for each subject in DELAYED the type whose predicted behavioral profile is closest to the subjects actual behavior. Methodologically, the closest approach to ours is type mixture modeling in the experimental economics literature on distributional preferences (see, for example, Bardsley and Moffatt, 2007 and Cappelen, Hole, and Sorensen, 2007). Specifically, recall that in DELAYED the attribute vector z ikt includes the additional effort information available to subject i in period t (captured in the information set I it ). Using the type-specific parameter vector α θ estimated from the UPFRONT data we can now combine the DELAYED effort data with the type preference structures to predict the probability of subject i choosing alternative k K in period t, conditional on the type. These probabilities are denoted by P (y ikt = 1 θ) and are computed as follows: S4-5 P (y ikt = 1 θ) = exp(z iktα θ ) l K exp(z ilt α θ) (S4.2) where α θ is ported from the UPFRONT estimation results and z ilt is constructed using the DE- LAYED data. After calculating these conditional probabilities we compute the posterior probabilities of each subject i being type θ given their effort and contract choices k in periods t = 1,..., T : P (θ y ik1,..., y ikt ) = T t=1 k K P (y ikt = 1 θ) I (y ikt =1) [ T ]. t=1 k K P (y ikt = 1 θ) I (y ikt =1) θ {low,cond,high} (S4.3) where I (.) is the indicator function taking the value 1 if the subscripted expression is true and 0 otherwise. 6 Results Table S4.2 presents the estimation results. The columns show the utility coefficients with each column assuming a different functional form of the utility function. The columns in table S4.2 correspond to the models defined in table S Column (1) is our benchmark model in which we assume behavior to be driven solely by the self-interest parameter α own,θ. The self-interest parameter is significant for conditional contributors and high contributors at p < 0.01, but only marginally significant for low contributors, p = That is, low contributors decisions are the least consistent with the standard profit maximization paradigm. Further, the self-interest parameter increases in magnitude as we go from low to similar type assignments. Further, we examine whether un-pooling VESTING contracts and creating separate types for each of the VESTING contracts generates a more informative taxonomy. However, there are few differences in behaviors between the individuals who prefer different VESTING contracts. 6 Equation S4.3 is equivalent to assuming equal prior probabilities of each subject being a particular type. Alternatively one may assume non-equal prior probabilities that can be imposed using the shares of types in the UPFRONT treatment or estimated directly from the DELAYED data, using the maximum likelihood approach. We use these approaches as robustness checks and arrive at similar results. 7 Table S4.2 uses UPFRONT data to estimate the utility parameters. Observations from periods 1-3 are discarded in order to separate type identification (which uses period 1-3 data) from the analysis of types behaviors (which uses period 4-8 data). For robustness we repeat the analysis using the full (period 1-8) data set and find similar results.

18 S4-6 Table S4.2 Estimation Results. (1) (2) (3) (4) (5) (6) (7) (8) Sensitivity to own profits α own,low 0.01* * *** 0.03*** 0.02*** 0.02*** α own,cond 0.02*** 0.02*** 0.02*** 0.02*** 0.02*** 0.02*** 0.01*** 0.02*** α own,high 0.04*** 0.03*** 0.04*** 0.03*** 0.04*** 0.03*** 0.04*** 0.03*** Sensitivity to pay diff α erc,low α erc,cond -7.84*** -8.59*** -8.73*** -6.16*** α erc,high Sensitivity to abs. effort diff α aed,low α aed,cond -0.27*** -0.27*** α aed,high Sensitivity to effort diff α ed,low -0.27** -0.39** α ed,cond 0.08* α ed,high Sensitivity to effort ratio α eratio,low -3.21** -3.10* α eratio,low 2.13*** 1.02 α eratio,low Subjects Observations AIC LL LR-test, p-value baseline Notes. Conditional Logit estimation results are presented. Periods 1-3 are discarded to separate type identification from the estimation of behavioral parameters. Columns correspond to the utility models described in table S4.1. Standard errors are clustered at subject level. * p < 0.1, ** p < 0.05, *** p < conditional and from conditional to high contributors. In fact, the parameters are significantly different between the low and high contributor types and between the conditional and the high contributor types (Wald test, p = 0.014, p = 0.026), but not significantly different between the low and conditional contributor types (p = 0.336). In column (2) we add the payoff inequality aversion parameter α erc,θ. The self-interest parameters are almost unchanged, relative to column (1). Further, conditional cooperators are sensitive to differences in payoff implied by the contract (p < 0.01), whereas the remaining types do not appear to be affected by it (p > 0.1). That is, conditional cooperators are the only ones who care about low payoff discrepancies (Wald tests confirm that these differences between types are significant, p < 0.05). Column (3) shows that conditional cooperators also care about the differences in effort levels. In particular, they dislike differences in effort levels within the team, with the utility difference parameter being significant for them at p < As before, the remaining types are shown to care only about their profits in this specification. Column (4) shows that this result holds even after controlling for the sensitivity to payoff inequality implied by the contract.