Theoretical Review

The study of investment strategy fundamentally involves contrasting the operational dynamics of a project under commitment-based and outcome-based modes. When a project represents the interests of superiors but its success hinges on the efforts of subordinates, a potential misalignment of interests between these two parties can arise [32]. Subordinates might prioritize their personal interests, thereby not fully committing to the project’s objectives. In such scenarios,a significant challenge is to design effective institutional mechanisms that align the actions of subordinates with the goals of superiors [33]. The principal-agent model is designed to examine decision-making and incentive issues within this framework. It is extensively utilized in academic research to analyze strategic choices, assess incentive constraints, and design optimal contracts [34]. This model offers valuable insights into how different investment strategies, such as commitment-based and outcome-based modes, can influence the alignment of interests between different hierarchical levels within an organization or a project.

Principal-agent theory, as a fundamental aspect of contract theory, has garnered increasing scholarly attention since the early 1970s, particularly in the context of information asymmetry and incentive issues. This focus aims to demystify the ‘black box’ mechanisms operating within firms. At its core, the principal-agent model seeks to unravel how, in scenarios marked by conflicting interests and information asymmetry, a principal (such as an investor) can devise optimal contracts or guidelines to effectively influence or regulate the behavior of an agent (such as a corporation) [35]. Sappington [36] further elaborated on this theory by outlining its basic procedural framework: initially constructing an agency problem based on the assumptions of conflicting interests and information asymmetry; subsequently identifying the inherent constraints of the problem; and finally, determining the decisions the principal needs to make to maximize utility. This structured approach offers a systematic method for analyzing and resolving the complexities inherent in principal-agent relationships.

In the investigation of incentive behaviors and strategic responses within hierarchical principal-agent relationships, game theory research emerges as the most prevalent and effective methodology [37]. Including commitment mechanisms, scholars have been using game theory to find methods that enhance performance in bureaucratic systems. Jayasekara [38] utilized game theory to characterize the principal-agent relationship between bank managers and employees, seeking ways to maximize overall corporation profits while minimizing costs. Chen [39] explored the feasibility of resolving information asymmetry and moral hazard issues in principal-agent problems through new technologies. Kjell [40] applied principal-agent theory and game theory to the Precautionary Principle to investigate changes in utility.

In theoretical research concerning ESG (Environmental, Social, and Governance) and CSR (corporation Social Responsibility) and their impact on social benefits, equal attention is given to the exchange of information and signaling between hierarchical levels: Gimpel [41] used game theory methodologies to study how organizations ultimately decide to incorporate sustainability into their strategic planning to gain advantages. Friedrich [42] examined the strategic use of corporate social responsibility (CSR) in Cournot competition and showed that the more efficient firm chooses a higher CSR level, reinforcing its dominant position. Uyar [43] explored the validity of the signaling theory and the greenwashing tendency in the logistics sector. Nirino [44] suggested that, from a corporation’s structural perspective, ESG practices are important for addressing stakeholders’ needs.

In summary, given the widespread application of the principal-agent model in related fields, its capability to elucidate the motivations of both hierarchical levels, and its effectiveness in determining optimal strategies under resource constraints [45], this paper adopts this model to delve into the effects and mechanisms of commitment-based investment strategy. Our objective is to offer a novel theoretical perspective for research applications in relevant areas. By doing so, we aim to contribute to a deeper understanding of these complex investment dynamics and assist in guiding more informed decision-making in the realms influenced by these strategies.

Research Hypotheses

In their interactions with investors, corporations may, at times, engage in deceptive practices. These deceptive practices can include exaggerating the use of green materials, concealing environmentally harmful production processes, or presenting products in a misleading manner. These actions are primarily driven by the corporation’s desire to appear more favorable than other companies in the ‘commitment competition’ to secure green investments or other resources. The more intense the competition, the stronger the motivation for corporations to engage in deception [46], and this phenomenon can be attributed to the higher embeddedness of environmental commitments in these contexts.

The commitment-based mode fundamentally differs from the outcome-based mode in terms of the timing and focus of their impact. While the outcome-based mode takes effect only after the completion of a project, assessing its success or failure based on tangible results, the commitment-based mode plays a critical role at the project’s initiation phase. It directly influences whether a project receives the green light, with commitments often serving as a key determinant in securing necessary support and resources. Given the high embeddedness of the commitment-based mode and the information asymmetry between different levels, it is more prone to information distortion [47]. Based on this, we propose Hypothesis 1: – Hypothesis 1: The commitment-based mode

functions as a significant medium for signal

transmission. It can carry the corporation’s genuine

commitment to the level of carbon footprint

reduction of the project or their exaggerated false

commitment to the level for additional benefits.

When investors discover that a corporation has falsified its commitments, they too will implement punitive measures. These sanctions may manifest as withdrawal of investments, a decline in stock prices, or damage to the corporation’s reputation. Investors typically rely on the information provided by corporations to make investment decisions; therefore, when such information is proven to be false, this breach of trust can lead to severe consequences [48]. Furthermore, whether in outcome-based or commitment-based mode, investors will still compare a corporation’s performance commitments to actual outcomes, regardless of whether it may impact their investment decisions. When the disparities are significant, investors may still take actions such as divestment or selling stocks [49], resulting in losses for the corporation.

Based on the above facts, we propose Hypothesis 2 and Hypothesis 3: – Hypothesis 2: In the commitment-based mode,

when the corporation is found by the investor to have

made a false commitment or distorted information,

the corporation must face corresponding penalties

such as disinvestment. – Hypothesis 3: Both in the commitment-based

mode and the outcome-based mode, when there

is a significant gap between the actual outcomes

and commitment, the corporation must face

corresponding penalties.

Design of the Game Model Process

Consider a project designed to generate societal benefits, operating within a principal-agent framework that encompasses two hierarchical levels. At the upper level of this hierarchy is the investor, who faces a critical decision: choosing between an outcome-based and a commitment-based investment mode. The outcome-based mode relies on evaluating the project’s results post-completion, while the commitment-based mode focuses on upfront commitments made regarding the project’s goals and methodologies.

Symbols and Definitions

The symbols used in the model in this article are defined as shown in Table 1.

The Model

In our model, a corporation project is characterized by two key indicators: quantity (scale) and quality (level of carbon footprint reduction [50]). The scale of the project, denoted as e, is public information, observable by both the corporation and the investor. In contrast, the level of carbon footprint reduction chosen by the corporation, denoted as i, is private information that the investor cannot directly observe. This distinction between public and private information introduces a layer of complexity in the investor’s decision-making process, as it requires reliance on indirect signals or assessments to gauge the actual environmental impact of the project.

For the same project, different low-carbon-quality materials will have different cost coefficients, denoted as b. Let’s define c(i, e) as the cost incurred by the corporation to complete a project of scale e with a low-carbon quality i.

Note: For all j>i, it holds that b_j>b_i.

Similarly, the investor funds the project. For the same project, different low-carbon qualities will adopt different investment coefficients, denoted as β. Define r_i(e) as the amount of investment for a project of scale e with low-carbon quality i:

Note: For all j>i, it holds that β_j>β_i. Where w_i represents the startup cost under the low-carbon quality i and β_ie represents the operational cost related to the project scale under that quality.

For the corporation, in addition to the incentives from the investor, it can also obtain benefits p(i) (such as industry reputation, consumer favor, etc.) by working hard on the project. In summary, the investment, the corporation’s effort cost, and the corporation’s benefits from the project together constitute the corporation’s objective function π_l:

For the investor, the target is to maximize the social benefits brought by the project, mainly reflected in maximizing the difference between the project’s output results and the amount of investment. Without considering uncertainty, under the low-carbon level i, the benefit output of the project is directly proportional to the scale of the project. Therefore, the output results can, without loss of generality, also be represented by e. In this model, the objective function π_h for the investor can be expressed as:

Complete Information Scenario

First, we examine the optimization results of this model under the ideal scenario of complete information. This approach establishes a comparative benchmark, providing a foundational understanding of the model’s behavior and outcomes in a theoretically perfect information environment.

In this scenario, the investor can both know the scale e of the project and the low-carbon level i chosen by the corporation for the project. Then the only constraint for Formula (4) is the non-negative utility of the corporation. Therefore, the optimization problem can be transformed into:

By incorporating Formulas (1), (2), and (3), we can construct the Lagrangian function:

And

Under the condition of complete information, the optimal social benefit is:

Where

Incomplete Information Scenario Based on Outcome-Based Mode

In the outcome-based mode, corporations are also required to report their low-carbon targets to investors. However, the reporting stage in the outcome-based approach does not directly influence the investment decisions of the investor. The investor only evaluates the project based on the outcomes. But if there is a significant discrepancy between the commitment and the outcome (for instance, a commitment of j and an outcome of i, the investor will penalize the corporation by u( j–i) such as disinvestment, where u(0) = 0.

Given that π_l( j,e)>π_l(i,e) for all j>i, the corporation has an incentive to declare the level of carbon footprint reduction of the project i as j. Define π_l(i,j) as the utility:

Under these circumstances, the objective function for the investor π_h(i,e), can be expressed as:

Where

And

The optimal social benefit under the scenario of an outcome-based mode with incomplete information can be derived as:

Where

Note: A = 1 – u' (j–i).

Incomplete Information Scenario Based on Commitment-Based Mode

In the commitment-based mode, the corporation is required to make a commitment about the low-carbon level i before receiving funding for the project. The investor assesses the probability of the project’s approval based on the project scale submitted by the corporation and the proposed level i. In this model, the higher the level proposed by the corporation, the higher the probability of getting the investment. That is, for all j>i, the probability with low-carbon level j, P(j), is greater than the probability with level i, P(i). This system inherently incentivizes corporations to propose higher levels of carbon footprint reduction in their commitments to increase the probability of receiving funding. Define the benefit coefficient resulting from the difference in probabilities as F(j−i)=πl(j)πl(i), where F(0) = 1.

As previously discussed, to tackle potential distortions in the information about the project’s carbon footprint reduction level, the investor undertakes a crucial step: a preliminary review of the commitment materials submitted by the corporation. If the corporation distorts information (exaggerating the low-carbon level of i to j>i), there is a probability ρ( j) that the investor will detect this. In such cases, the investor will be penalized with an intensity of υ( j–i), where υ(0) = 0. Additionally, similar to the outcome-based mode, if there is a significant discrepancy between the commitment and the outcome, the investor will penalize the corporation with u( j–i).

Given this context, the expected objective function for the corporation, when declaring the low-carbon level i as j, can be represented as E[π_l(i,j)]:

The incentive compatibility condition that ensures the corporation truthfully reports to the investor is:

By substituting Formulas (1) to (4), the incentive compatibility condition can be reformulated as:

Define:

Formula (18) can be reformulated as:

Specifically, Π(x,y) represents the benefit that the investor needs to achieve through institutional design to satisfy the incentive compatibility condition when the corporation declares the low-carbon level x as y. Therefore, when Π(i,i)≥Π(i,j) for all j≠i, it further implies:

And

Substituting (x,y) = (i,j), i = j, F′(0) = 0¹, we can derive Proposition 1:

– Proposition 1: In the commitment-based mode, to satisfy the incentive compatibility condition between the investor and the corporation, the investor’s verification capability should meet the condition ρ(j)≥p′(j)−u′(0)υ′(0).

Additionally, ρ(y) also represents the threshold value for the incentive compatibility condition. Thus, ρ'(y) indicates the incremental values of the commitment-based penalty u’ and the outcome-based penalty υ›, reflecting the efficiency of these two penalty mechanisms. Specifically:

Thus, only when p′(y)>(υ′(0)+△υ′)υ′(0)△υ′△u′+△υ′, we have ρ_υ'(y)>ρ_u'(y), from this, we derive Lemma 1:

– Lemma 1: In the commitment-based mode, the greater the benefits the corporation derives from the project, the more impactful the commitment-based penalties become. Conversely, when the benefits accruing to the corporation are relatively modest; outcome-based penalties tend to be more effective.

In the analysis of overall societal benefit, a critical factor to consider is the investor’s limited ability to accurately gauge the true extent of the corporation’s low-carbon initiatives during the commitment phase. To address this, it becomes essential for the investor to review the related materials submitted by the corporation. The process of this verification incurs a cost for the investor, which is determined by the unit verification cost f and scaled by the project size e. Therefore, the cost of verification fe becomes a significant component in the investor’s calculations. As a result, the objective function for the investor, which aims to optimize the balance between verification costs and the societal benefits of the investment, can be expressed as follows:

And

So we have

Compared with Formula (13), we can derive Proposition 2:

– Proposition 2: In the commitment-based mode, corporations choose a lower level of carbon footprint reduction for the project compared to the outcome-based mode. The reason for the decrease in their level is that the commitment-based approach subjects corporations to additional assessments and potential penalties without offering corresponding rewards for exerting extra effort or fulfilling their commitments. Subsequently, we can derive the optimal solution for the investor’s objective function under the incomplete information scenario for commitment-based mode:

Where

Compared with Formula (14), we can derive Proposition 3:

– Proposition 3: hether the investor’s benefit (societal benefit) ultimately increases due to the commitment-based mode is influenced by the relationship between the commitment-based verification capability and the verification cost. If ρ(j)υ′(j−i)2>f, then π^*_hx(i,e)>π^*_hp(i,e), indicating that the commitment-based mechanism enhances societal benefits. Conversely, π^*_hx(i,e)<π^*_hp(i,e), the commitment-based mechanism reduces societal benefits.

Considering the case where π^*_hx(i,e)>π^*_hp(i,e) and combining with Proposition 2, it is observed that even though the corporation’s effort level has decreased, the investor’s benefit ultimately increases within this range. By integrating Formulas (15) and (31), we can derive Lemma 2:

– Lemma 2: hen an investor adopts the commitment-based mode within a reasonable scope, even though the corporation chooses a lower level of carbon footprint reduction, investors can still amplify the societal benefits by avoiding unnecessary expenditures and improving investment utilization.