The principal-agent model in venture investment based on fairness preference

Dongsheng Xu; Qingqing Liu; Xin Jiang; Dongsheng Xu; Qingqing Liu; Xin Jiang

doi:10.3934/math.2021132

AIMS Mathematics

2021, Volume 6, Issue 3: 2171-2195. doi: 10.3934/math.2021132

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Research article

The principal-agent model in venture investment based on fairness preference

School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, China

Received: 05 August 2020 Accepted: 29 November 2020 Published: 10 December 2020
MSC : 91B08, 91B43

The fairness preference in the principal-agent relationship is a vital factor that can even determine the success or failure of one program. Under normal circumstances, the capital invested by VC is often several times that of EN, which is one of the reasons for the profit gap between EN and VC. Therefore, when establishing a principal-agent model with fairness preferences, it is necessary to project the utility of VC to the level of EN and compare it with the utility of venture entrepreneurs, which will better reflect the profit gap between the two. On the basis of previous studies, this paper considers the amount of contribution of the participants, builds four principal-agent models to find the optimal distribution of income between the Venture Entrepreneur (EN) and the Venture Capital (VC) in a venture capital investment program, two without fairness preference and others with fairness preference. After the simulation we confirm that the fairness preference coefficient exerts a great impact on the distribution of income in both situations where information is symmetric and asymmetric, and a strong fairness preference will lead to a greater net profit gap between the EN and the VC. Thus, the EN should carefully choose the level of his efforts to realize the maximum return for him. In the case of information asymmetry, EN's optimal effort level decreases as the fairness preference coefficient increases.This will affect project revenue. And then affect the VC income.
- Venture Capital,
- principal-agent model,
- fairness preference
Citation: Dongsheng Xu, Qingqing Liu, Xin Jiang. The principal-agent model in venture investment based on fairness preference[J]. AIMS Mathematics, 2021, 6(3): 2171-2195. doi: 10.3934/math.2021132

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Abstract

The fairness preference in the principal-agent relationship is a vital factor that can even determine the success or failure of one program. Under normal circumstances, the capital invested by VC is often several times that of EN, which is one of the reasons for the profit gap between EN and VC. Therefore, when establishing a principal-agent model with fairness preferences, it is necessary to project the utility of VC to the level of EN and compare it with the utility of venture entrepreneurs, which will better reflect the profit gap between the two. On the basis of previous studies, this paper considers the amount of contribution of the participants, builds four principal-agent models to find the optimal distribution of income between the Venture Entrepreneur (EN) and the Venture Capital (VC) in a venture capital investment program, two without fairness preference and others with fairness preference. After the simulation we confirm that the fairness preference coefficient exerts a great impact on the distribution of income in both situations where information is symmetric and asymmetric, and a strong fairness preference will lead to a greater net profit gap between the EN and the VC. Thus, the EN should carefully choose the level of his efforts to realize the maximum return for him. In the case of information asymmetry, EN's optimal effort level decreases as the fairness preference coefficient increases.This will affect project revenue. And then affect the VC income.

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