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The development of new venture enterprise is the result of joint efforts of entrepreneurs and venture capitalists who collaborate based on complementary resources. In this paper, we analyze a venture capital incentive contracting model in which a venture capitalist interacts with an entrepreneur who is risk neutral and fairness concerned, offering him an equity contract. We solve the venture capitalist’s maximization problem in the presence of double-sided moral hazard. Our results show that fairness concerns change the structure of the optimal contract. More importantly, we show that the solution to the contract regarding the optimal share given to the entrepreneur is nonlinear and is a fixed point between 0 and 1. Further, we simulate the model under the assumption that venture project’s revenue is a Constant Elasticity of Substitution (CES) function and obtain the following results. (1) When the two efforts are complementary, the venture capitalist’s effort does not monotonically decrease in the share allocated to the entrepreneur, while the entrepreneur’s effort does not monotonically increase in his share. (2) Relative to the benchmark case where the entrepreneur is fairness neutral, the optimal equity share allocated to the fair-minded entrepreneur is larger than 1/2, and as the degree of efforts complementarity increases, the optimal equity share tends to 60%. In this scenario, for a given efforts substitution parameter, the fair-minded entrepreneur provides a higher effort level than the venture capitalist.

Venture capital is the primary means through which innovative ideas are financed, nurtured, and brought to fruition and therefore plays a crucial role in economic growth. Over the past 30 years, venture capital has been an important source of financing for innovative firms. Many highly successful companies, such as Facebook, Google, Amazon, Apple, FedEx, Starbucks, and Alibaba, have all been backed by venture capitalist (VC). Gornall and Strebulaev [

This paper studies the optimal contracting problem of an early start-up seeking venture capital finance within the context of two noncontractible efforts, entrepreneurial (denoted by EN) effort and VC effort, which are crucial for the success of start-up. An EN possesses an innovative idea for a new venture but may lack the personal funds and business expertise needed to get the business started. In addition to financing, VC provides advice and expertise in management, commercialization, and development which enhance the value, success, and marketability of high-risk, high return projects. Further, VC often places members of the venture capital team on the firm’s board. VC and EN both play an important and irreplaceable role in VC-backed innovative startups. In the case of incomplete information, the EN and the VC exert unobservable efforts to improve the profitability of a venture project, and the asymmetry of efforts and the arrangement of the residual claims make both parties have the motive to seek private benefits. Therefore, the start-up firms are faced with double-sided moral hazard. In this case, the incentive problem is particularly prominent, and double-sided moral hazard has become the research direction of venture capital financing contract [

A unique feature in the VC-EN relationship results from the role of VC as active investors, which ideally goes far beyond the traditional principal-agent context. Casamatta [

In the study of how to guard against the moral hazard caused by information asymmetry, most scholars choose the perspective of contract instruments to stimulate the efforts of both parties. More recently, Vergara et al. [

The existing financial contracting models assume that decision makers are self-interested in that their utility function depends only on their own material payoffs [

It is observed that other-regarding preferences may have a positive role in moral hazard situations [

If the agent’s preference indeed does exhibit fairness concern, then the optimal contract design must take this into account. How is the structure of the optimal contract changed if the agent is no longer selfish but concerns about fairness? Furthermore, what are the implications for incentive provisions? To solve these questions, we consider a double-sided moral hazard model of venture financing with a fairness concern agent. In the model, a VC who is self-interested and profit maximizing hires an EN to implement a potentially profitable project. The EN is a utility-maximizing agent who is fairness concerned towards his principal. A contract specifies a share of the total output for each of the contracting parties. Hence, we investigate an equity contract according to the corporate finance literature.

In the present study, we discuss how incorporating behavioral biases in the analysis of incentives may affect the predictions of the classical moral hazard model. The VC maximizes his own profit whereas the EN maximizes his utility depending on the profits of both members. The optimal contract under moral hazard takes into account the acceptance condition for the EN and his choice of effort. Moreover, it is often the case that arbitrarily low or high payments are not feasible, which would introduce additional constraints into the VC’s optimization program.

This paper thus focuses on how the complementarity of efforts between a VC and an EN affects the equity share that the VC is willing to allocate to the EN. We investigate the combined impact of double-sided moral hazard and the EN’s fairness concerns on VC/EN contracting. Following the approach of [

Our model is similar to that in [

Another paper closely related to our work is that of Fairchild [

The remainder of the paper is structured as follows: in Section

We consider a setting in which an EN has initially formed a firm to develop a potentially profitable project, requiring start-up funds

Due to the high levels of uncertainty involved, it is difficult for startups to seek support from traditional financial intermediaries (such as banks); EN may not have sufficient bargaining power in the process of seeking financial support from VC. Different from the hypothesis of [

When the project is successful, the VC offers the EN an equity share

As a benchmark, let us first determine the optimal level of effort for both EN and VC when their efforts are observable and verifiable. According to the classic principal-agent theory, this corresponds to the first-best solution that maximizes the social value of the venture project.

The social value of the project is expressed as

This means that the financing strategy is irrelevant; in other words, it does not matter who funds the project. However, when EN and VC cannot observe each other’s level of effort, the form of funding and how the project cash flows are distributed affecting the way in which efforts are made, resulting in what is called double-sided moral hazard in the literature.

In this paper, our objective is to catalyze the research agenda by developing the formal game-theoretic model to incorporate fairness preference and double-sided moral hazard into VC/EN financial contracting.

We model the interaction between a profit-maximizing VC (principal) and a utility-maximizing EN (agent). In our model, both EN and VC make efforts that are not observable to each other. Therefore, this is a double-sided moral hazard problem. The sequence of events in the development of the business is as follows. At date 0, a wealth-constrained EN has in mind a positive net present value project, which requires an initial capital outlay

At date 1, the VC offers an ultimatum proposal regarding the equity allocation

In data 2, the EN and the VC make simultaneous, nonobservable efforts to develop the business. After the success or failure of the project is disclosed at date 3, both partners are paid according to the financial contract that was signed at date 1, and the game ends.

The payoff function of the VC and the EN can be expressed respectively as

It is assumed that the VC is a self-interested profit maximizer and his expected utility is given by

In this study, we assume that the EN is risk neutral but inequity averse towards the VC in the sense of Fehr and Schmidt [

At the same time, many scholars proved that the decision maker is more caring about the envy than the compassion [

We solve the game-theoretic model using backward induction. That is, we firstly solve for VC’s and EN’s optimal data 2 effort levels, given the agreed equity stakes, and then move back to solve for VC’s optimal data 1 equity offer. It is important to highlight that we do not impose any specific functional form for the project revenue function or the cost of the two players’ efforts. In the next section, we simulate the model under the assumption that venture project’s revenue is a CES function and assume that the disutility of the players’ efforts is quadratic function.

Given that the VC has proposed equity allocation

That is, the VC maximizes his expected profit based on his share of the revenues as stipulated in the contract

In the similar way, the EN also chooses his level of effort based on his incentive-compatibility constraint:

Given the assumptions upon, the principal-agent problem faced by the VC is

The main difficulty in solving the above principal-agent problem is related to the fact that the incentive-compatibility constraint is itself a maximization problem. That is to say, the VC’s maximization problem includes two additional optimization problems expressed in (

The incentive-compatibility equations (

When

According to (

(a) The EN’s participation constraint is binding because

The Lagrangian of the VC’s maximization problem is defined as follows:

(1) The First Order Condition for the VC’s investment level

(2) The First Order Condition for the EN’s effort

(3) The First Order Condition for the VC’s effort

(4) At a given equity participation level

Given (

Equation (

The next theorem provides the equity share given to the EN that maximizes the VC’s problem.

When the EN is concerned with fairness, the optimal equity participation level given to the EN that solves the VC’s problem is nonlinear and at a fixed point takes the form of

Using (

then

where

Equation (

Note that under the assumptions of [

According to (

The expression of the optimal equity share is complex, so the analysis of Theorem

In this section, we discuss the effects that the degree of complementarity of efforts, the efficiency of the EN’s efforts and the VC’s efforts, and the fairness preference of the EN all have on the dynamics of the effort best-response functions and on the optimal equity participation level expressed in (

The CES function is a well-known function widely used in the production part of the microeconomics and operational research literature. Leontief, linear and Cobb-Douglas production functions are special cases of the CES production function [

Both efforts are costly. We will also assume that the cost of the EN’s effort is given by

According to the incentive-compatibility constraints, we obtain the best-response functions concerning the equity share assigned to the EN at date 1 of the game. As the production function is CES, and given the assumptions of the cost of efforts, the effort dynamics of the EN and the VC are expressed as follows (see Appendix

Under the condition that the two levels of efforts are perfect substitutes: the equity share

If the two efforts are perfect substitutes, i.e.,

Theorem

In order to investigate the effect that the substitution parameter

Simulation parameters. Table

Parameter | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

| 0.5 | 0.5 | 0.5 | 0.5 |

| 0.5 | 0.5 | 0.5 | 0.5 |

| 30 | 30 | 30 | 30 |

| 30 | 30 | 30 | 30 |

| 1 | 1 | 1 | 1 |

| 0.7 | 0.7 | 0.7 | 0.7 |

| (0,0.8,1.8) | (0,0.8,1.8) | (0,0.8,1.8) | (0,0.8,1.8) |

| 1 | 0.5 | -1 | -10 |

Effort dynamics for different degrees of effort complementarity

It can be found from Figure

It is worth noting that when the EN does not have fairness concerns, as the degree of efforts complementarity increases, for instance case 4:

If efforts of the EN and the VC are complementary, then we have the following:

(a) There is an equity participation level

(b) There is an equity participation level

See Appendix

Figure

Equity share that maximizes effort, for different degrees of complementarity

According to Theorem

When

Notice that the equilibrium points of the functions

The results of Theorems

Optimal equity share for different degrees of complementarity

In this section, we investigate the influence of fairness concerns on the equilibrium result and the optimal effort levels through numerical analysis.

In case the two effort levels are perfect substitutes, i.e.,

It is easy to find

Table

Optimal equity share.

Parameter | | | |
---|---|---|---|

| 0.5 | 0.8077 | 0.8913 |

| 0.5 | 0.6980 | 0.7566 |

| 0.5 | 0.6128 | 0.6507 |

| 0.5 | 0.5777 | 0.5955 |

Substituting the optimal equity share level

Optimal effort levels.

Parameter | | | |
---|---|---|---|

| 0.0058 | 0.0152 | 0.0268 |

| 0.0058 | 0.0099 | 0.1490 |

| 0.0058 | 0.0073 | 0.0089 |

| 0.0058 | 0.0063 | 0.0070 |

| 0.0058 | 0.0022 | 0.0013 |

| 0.0058 | 0.0044 | 0.0041 |

| 0.0058 | 0.0056 | 0.0059 |

| 0.0058 | 0.0061 | 0.0065 |

Table

Providing incentives to an inequality-averse EN is often more costly than to a classical agent. The intuition is that as the project is more profitable, more inequality is created and it is more expensive to satisfy the incentive-compatibility constraint. The significance of our research is that if VC knows that the EN has inequality-aversion preference and that EN will compare the benefits between them, so VC will increase the incentive level to transfer some of the benefits to the EN. As EN sees VC’s kindness to him, he will also exert more effort to reward the VC.

Equity sharing is a common practice in joint ventures, and the VC often provides value-added services by influencing firm-level innovation and commercialization beyond mere capital infusion. Taking a global perspective, the most widespread incentive contracts are sharecropping contracts. We analyze in this paper a contracting problem within a double-sided moral hazard setting where the EN has limited wealth, which constrains his feasible range of actions as the EN’s effort induces both monetary and nonmonetary costs. We consider the case that the EN has fairness concerns, but the VC does not. Our analysis shows that incorporating fairness concerns into the analysis of optimal financing contract can improve our understanding of real world incentive schemes. If the EN exhibits an aversion towards inequitable distributions, the optimal contract has to balance the EN’s concern for fairness and the VC’s desire to provide adequate incentives.

The value-added services of VC and fairness concerns of EN have been studied in the literature independently, but these two factors are seldom studied simultaneously. In this study, we consider the VC’s value-added services and behavior regarding fairness concerns using the principal-agent theory. The decision problems are much more complex, but they are closer to reality. We examine the influence of the EN’s fairness concerns on the decisions of the two members, thereby demonstrating that their decisions differ from those under perfect rationality.

There are several directions deserving future research. First, we implicitly assume the information to be complete in the current paper. The VC knows the exact values of the EN’s fairness related factor

If

If we divide (

Substitute (

The derivative of (

Similarly, the derivative of (

If we set the expression above to zero and reorder, then

All data generated or analyzed during this study are included in this paper. The authors are willing to share the implementation scripts in the form of some MATLAB m-files with the interested reader.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was funded by the National Natural Science Foundations of China (Grant Nos. 71361003 and 71461003) and Natural Science Foundations of Guizhou Province (Grant No.