Sustainable Quality-Incentive Contract Design of Public Technology Innovation Procurement under Asymmetry Information

Abstract

Public technology innovation procurement plays an essential role in alleviating current major social challenges. In the process of government procurement, the hidden adverse selection and moral hazard caused by the unobservable technology types and efforts of enterprises are not conducive to the sustainable improvement of technology innovation quality. To sustainably encourage enterprises to improve the quality of public technology innovation procurement, based on principal-agent and incentive regulation theories, this paper designs quality-incentive contracts under single- and dual-asymmetric information conditions. We discuss the impact of various relevant factors on contract design and the level of effort by solving and analyzing the model. Furthermore, we validate the effects of the proportion of enterprise technological type, the uncertainty of technological innovation, and the quality-benefit coefficient on the contract parameters and the expected profits of both parties through numerical simulation. The results show that under dual-asymmetry information, the government can motivate enterprises to realize self-selection and improve the quality of technological innovation by designing information screening contracts. The government’s revenue is closely related to the proportion of enterprises’ technology types in the market, and information rents can swamp the government’s expected revenues when the market proportion of high-type enterprises is small. The uncertainty of technological innovation will reduce the effort of enterprises and the incentive effect of the contract. The quality-benefit coefficients of the government and enterprises have different impacts on the intensity of contract incentives with higher quality-benefit coefficients of the government, therefore having better incentive effects for enterprises. The research conclusion provides a reference for the government to design a sustainable incentive contract to improve the quality of public technology innovation.

1. Introduction

Technological innovation plays an important role in supporting and guiding humanity towards sustainable development [1]. Today’s scientific and technological development has shown a multi-point and cluster breakthrough, and a new round of scientific and technological revolution is being born, which will strongly support the sustainable development of the economic, social and ecological environment [2]. In particular, many public areas, such as resources, environment and health, are facing new major challenges, which need to be led by scientific and technological innovation support. Therefore, how to achieve high-quality technological innovation is an urgent problem to be solved. The purpose of this paper is to design sustainable quality-incentive contracts for public technology innovation procurement under information asymmetry to motivate enterprises to provide high-quality products or services, and to promote a practical solution for technological innovation and economic growth.

Public procurement has long played an essential role in driving innovation, meeting human needs, and solving social problems [3]. In most OECD countries, government spending accounts for 40% to 55% of GDP, making government procurement have a strong demand-side impact. Especially after the financial crisis in 2008 [4], many countries have formulated policies that focus on public procurement as an innovative policy and a strategy to increase the productivity of public spending on health, safety, transport, energy, and the environment [5,6]. Public procurement is often combined with specific sector developments, particularly in the defense (Australia, the United States) and energy (Brazil, Sweden) industries. In the field of defense technology, the DOD awards 500 billion dollars in procurement contracts annually, representing a significant portion of the economy [7]. The DOD should utilize commercial solutions (including integrated services, systems, subsystems, components, and building block technologies) derived from commercial procurement practices to meet its defense modernization needs as much as possible [8].

Public procurement generally promotes commercial innovation by supporting the formation of markets for products, technologies and services [9], which can be roughly divided into three aspects: product procurement, innovative procurement (new products, services, systems), and functional procurement (products with problem-solving functions) [10]. Public innovative procurement refers to procurement practices developed when the solutions or products procured do not yet exist but can be developed within a certain period of time by requiring contractors to innovate to meet public needs. Conventional public procurement focuses on general existing products, technologies, or services [11]. When a public institution purchases off-the-shelf products without involving technological research and development, it is generally referred to as public procurement. The existing research shows that public innovative procurement has played a positive role in the value-added growth of enterprises [12]. According to the public innovation procurement program, public institutions can specify the characteristics of innovative products, technologies, or services through the form of procurement contracts (price, quality, and performance). This clear public demand has a strong incentive effect on contractors, reduces market risk, and encourages them to realize economies of scale and learning effects, which helps to improve production efficiency and product quality [13].

At the level of government policy, to encourage enterprises to carry out sustainable public technological innovation, a large number of market-oriented and legalized means have been used to carry out supply side reform. However, the existing policies still have some limitations in improving the innovation effectiveness of technology quality [14]. It is generally believed that this is because those demand-side policies are more effective in promoting and disseminating innovation than supply-side policies. Therefore, governments and scholars have turned their attention to demand-side tools, such as public procurement. Over the past few years, public procurement has been adopted in Europe, focusing on issues concerning the type of technology and the exchange of information between the parties involved in procurement. The process of public procurement in the Netherlands is seen as a new step for stakeholders to share the uncertainties of new technologies and issues arising from the complex process of public innovation procurement [15]. Issues, such as information asymmetry and technology path dependence, hinder the market entry of potential suppliers and the diffusion of innovative technologies in public technology procurement. For enterprises, the purpose of innovation is to obtain higher profits, whereas public technological innovation often requires a lot of effort to improve product quality [16]. In addition, the uncertainty and high-cost risk of technological innovation will weaken their motivation to improve quality. For the government, the purpose of carrying out innovation is to improve the public interest. It is difficult for the government to accurately grasp the type of technology of enterprises (ex-ante) and their efforts to improve quality (ex-post). Therefore, due to the adverse selection and moral hazard caused by information asymmetry between the government and enterprises, the design of a government incentive mechanism is crucial to sustainably improve the quality of public technology innovation [17].

Existing research on public technology innovation procurement mainly focuses on the theoretical significance and influence mechanism, and the research methods used are mostly case studies and data analysis. This paper aims to fill the research gap in this area and provide support for the design of public technology innovation incentive contract mechanism.

The design of existing incentive mechanisms often focuses on reducing product costs [18,19,20] or increasing production [12]. Most studies ignore the dual-asymmetry information of adverse selection and moral hazard, and only consider the problem of single-asymmetry information [21,22]. The relationship between the quality of technological innovation and the initial technology type and the degree of innovation effort of enterprises is not considered, and there is also a lack of research on the different degrees of influence of quality on government public benefits and enterprises benefits. Therefore, this paper constructs quality-incentive contract models under single- and double-asymmetry information, respectively, under the premise of considering the types of enterprise technology, the uncertainty of technology innovation, and different quality-benefit coefficients of both sides, in an attempt to solve the adverse effects of information asymmetry on the quality improvement of public technology innovation, and encourage enterprises to make more efforts to sustainably improve quality. It provides a reference for the government to further optimize and improve the policy of public technology innovation.

The rest of this paper is organized as follows. Section 2 reviews the related literature. Section 3 constructs the quality-incentive and constraint models under single- and dual-asymmetry information, respectively. Section 4 analyzes the quality-incentive contract and the key influencing factors. Section 5 is numerical simulation analysis. Finally, the conclusion and future research directions are provided in Section 6.

2. Literature Review

At present, countries around the world consider public innovation procurement as a common tool to promote innovation [23]. As a policy tool, public procurement can sustainably promote regional innovation, entrepreneurship, and growth. Especially for innovative public procurement, public procurement can more effectively stimulate innovation than R&D subsidies [24,25]. Public procurement stimulates innovation is mainly reflected in the following aspects. Firstly, public procurement provides large customers or markets for innovative products (technologies, services, systems) [26]. In addition, public procurement can effectively stimulate the creation of leading markets and facilitate the market to develop new technologies or products needed by society [23,27]. Public procurement can legalize product standards, while introducing supplementary policies and measures to create favorable conditions for product standards and regulations to create new markets or expand existing ones [3,28]. Public procurement can also help accelerate the development of new technologies and lead to potential changes in the economic structure. In conclusion, innovation-oriented public procurement can play an essential role in building an innovation-friendly environment and creating the necessary conditions for promoting the creation and development of new markets [29].

As an essential part of public procurement, public technology innovation procurement has been studied by some scholars. Edquist [30,31] first proposed the concept of public technology procurement and divided public technology procurement into two categories: technology development procurement and technology diffusion procurement. Edquist and Zabala-Iturriagagoitia [11] further found that public procurement can help private enterprises accelerate the commercialization and diffusion process of innovative products. Malacina et al. [32] regarded the value creation of public procurement as a dynamic process involving collaboration between different stakeholders. However, existing public procurement laws constitute barriers to the use of public technology procurement as a means of stimulating and supporting technological innovation [31]. Rolfstam [33] discussed and described the problems existing in the institutional aspects of innovative public procurement policies by studying the innovation policy system and the institutional determinants of innovation performance. Caravella and Crespi [34] focused on the impact exerted on private R&D expenditures by regular and innovative public procurement when taken in combination or insolation with supply push measures. Talebi et al. [35] provided evidence of a dynamic path in the creation of diverse types of value in a collaborative process of public procurement of innovation where start-ups are engaged. The above literature indicates that public technology innovation procurement has great practical value as an innovation policy tool, but the main research focuses on case studies and theoretical analysis. In addition, public technology innovation procurement is also neglected in the economic policy formulation of most governments [31].

The quality of public goods is often closely related to the development and national comprehensive strength of a country. Therefore, the government, as a regulator, usually pays more attention to quality than ordinary organizations. In particular, the DOD is known for its emphasis on quality performance rather than cost. The FAR stipulates that the final quality performance should be an important factor in commercial project evaluation and contract award. The common use of fixed-price contracts can lead to trade-offs in reliability and discourage improvement and innovation [36]. Gao et al. [37] considered the coordination of quality improvement in two-stage decentralized supply chain procurement with partial cost allocation contracts. Babica and Sceulovs [38] elaborated on the methods of innovation measurement and quality evaluation in public innovation procurement and designed a framework for evaluating the quantity and quality value of innovation proposals. Gao et al. [17] established a game theory model to study quality-incentive contracts under symmetric and asymmetric product manufacturability information. Quality is often difficult to observe and measure in procurement [39,40]; thus, research on innovation quality needs to be further explored. This paper mainly focuses on the role of technological innovation in improving the quality of product performance and meeting public demands.

So far, the research on incentive contract theory for reducing cost is relatively extensive. Laffont and Tirole [41] studied the optimal procurement contracts for government purposes. The government tended to award the program to the enterprise with the lowest expected cost. Cost-plus contracts (CPIF), widely used in defense contracts, also provided incentives to reduce costs and improve efficiency from a cost-reduction perspective [36]. Suet et al. [42] applied the principal-agent theory and incentive regulation to design the contract to maximize the interests of the principal on the premise of satisfying the incentives and constraints of the agent. In the case of experience goods, there is an inherent conflict between the incentive to provide high-quality products and the reduction of production costs. A high-intensity incentive scheme may induce firms to reduce costs, but raise the perceived costs of providing high-quality products for firms. This crowding-out effect means that the more important the quality, the lower the intensity of the optimal incentive scheme [43]. The above literature mainly focuses on the design of incentive mechanisms to reduce production costs. However, there is still little research on quality-incentives, especially the quality of technological innovation. In this regard, we combine quality-based contract incentives with innovation incentives to design contracts for government procurement of technology.

General research on quality issues in R&D procurement mainly considers the dimensions of moral hazard, asymmetry information, and product pricing [40]. Xiao et al. [44] argued that the government’s role in technological innovation performance often depends on the types of technological characteristics of enterprises. The asymmetry of technological information has brought significant protection to suppliers, and the government faces a dual uncertainty of market and technology [45]. Suppliers often know more about technological processes than the government, so they can capture private information about production costs, and reduce costs during technology development [46]. Especially for technologically complex products, suppliers often master lots of private information [47]. Suppliers with private information can usually make more profits [48]. Therefore, when selecting contractors in public procurement, the government should consider the adverse selection problem caused by the asymmetry information of enterprises. In the public procurement of technology innovation, the government is exposed to quality risks due to the inability to observe suppliers’ efforts [49]. To solve the moral hazard problem caused by insufficient efforts of suppliers, the government should put forward effective quality-incentive contracts to encourage suppliers’ quality efforts [50]. The quality of technology depends not only on the efforts expended in the R&D process but also on the uncertainty determined at the product design stage [17]. When contractors develop innovative technologies that have not yet been implemented, technological uncertainty will be higher because the probability of success of the innovation is relatively low [11,51]. The main difference between public and private technology procurement is that in private technology procurement, the buyer is a private organization rather than a public institution. From the perspective of enterprises, their motivation is to obtain the maximum profits, but from the perspective of the government, its purpose is often reflected in the improvement of public interests, such as the improvement of public medical level, environmental pollution, national defense combat effectiveness, and so on. Therefore, the starting point of the application of public technology procurement must be to satisfy the real social needs. Thus, in the procurement of public technology innovation, the different impacts of quality improvement on public interests and private interests should also be discussed separately.

To solve the above problems, scholars conducted the following studies. Lim [52] designed the quality control contract under the asymmetry information based on game theory. Chen et al. [53] used the principal-agent theory to design the supply chain technology investment contract with double-moral hazard. Poblete and Spulber [54] designed the optimal incentive contract under double-moral hazard and found that the incentive effect of technology R&D contracts will affect R&D cost and innovation quality. Baiman et al. [55] designed a dual-moral hazard model with incomplete information in a supply chain and found that incentive contracts existed to induce firms to make optimal quality choices. Yoo and Cheong [56] studied quality-dependent technology innovation reward contracts and discovered that when the principal set target quality to encourage the agent’s efforts, the quality-incentive contract would encourage the agent to respond to market changes in product quality decisions. Compared with the untargeted quality, the principal needs to give a higher reward to the agent. The results show that incentive strategies can improve supply chain performance. In the case of double-moral hazard and risk neutrality, linear contracts are usually optimal [57,58]. Information screening contracts can more effectively make agents reveal real information and play a better incentive effect [59,60]. Chao et al. [61] found that the use of the information screening contract by the principal can reduce the impact of asymmetry information, which can not only significantly reduce the cost of the contractor, but also improve the quality of the product.

Our paper differs from previous studies in that we consider quality-incentives in public technology innovation procurement. The study in this paper follows the quality models of Su and Wang [62], but we highlight the characteristics of public technology innovation procurement more, whose main purpose is to enhance the public interest and is distinctly different from general procurement. Therefore, we consider the quality-benefit coefficients of government and enterprises in the model design, reflecting the different effects of the improvement of technology innovation quality on the benefits of both parties. In addition, we consider the sustainability of public technological innovation quality-incentives and adopt a clearer way to analyze the nature of the contract, which provides a reasonable reference for achieving sustainable incentive effects.

The purpose of this paper is to design an incentive mechanism to encourage contractors to improve the quality of technological innovation. Considering the fact that the technology type and effort of enterprises are private information, we design the quality-incentive and constraint model based on the basic principal-agent incentive theory under the condition of single- and dual-asymmetry information. Especially in the case of dual-asymmetric information, we design an information screening contract to reduce the risk of information asymmetry. By solving the model, we obtain the optimal government fixed payment compensation, incentive and constraint coefficients, and government incentive contracts. Finally, we conduct numerical analysis on the proportion of enterprise technology type, the uncertainty of technological innovation, and the quality-benefit coefficient of both sides.

The main contributions of this paper are as follows. (1) Based on the main consideration of factors, such as the type of technology, uncertainty of technological innovation, and the different quality-benefit coefficients, a quality-incentive model for technological innovation under the condition of dual-information asymmetry is established. (2) We solve the incentive contract and analyze the influence of key parameters on the incentive contract. (3) This paper analyzes how the government utilizes incentive contracts for information screening to induce enterprises to realize self-selection and reduce the impact of information asymmetry. Our paper provides a reference for the government to select and encourage enterprises to improve the quality of public technology innovation.

3. Model Construction

The model considers a two-stage public technology procurement supply chain consisting of a risk-neutral government purchaser $(G)$ and a risk-averse enterprise contractor $(E)$. The government purchases certain public products from enterprises that require technological innovation and upgrading, such as defense weapons and equipment. We regard technological product quality as a combination of design quality and consistency quality [63]. In this process, the government designs contracts to encourage enterprises to upgrade technology to provide higher quality public goods, while enterprises choose their level of effort following the contract to conduct technology R&D and the production of products. The motivation of the government is to pursue the maximization of public interests, while the enterprise pursues the maximization of its profit.

The process of government procurement inevitably faces the dual-asymmetry information problem of adverse selection and moral hazard. One is that the government has no information about the technological type of enterprise before signing the contract. The other is that the government cannot observe the company’s efforts in the process of contract execution after the contract is signed. The government can only observe the quality of the R&D product at the posterior, and pay the price according to the R&D quality of the enterprise.

The time series diagram of public technology innovation procurement is shown in Figure 1.

The first stage is the contract design stage. The government designs contracts for public technology innovation procurement. Enterprises choose contracts according to their technology types. If the expected income of enterprises is greater than their retained income, they will choose to sign contracts, otherwise, they will give up.

The second stage is the research and development stage. The government completes the fixed payment of the enterprise according to the contract, and the enterprise selects the optimal degree of effort to complete the technological innovation project according to the contract.

The third stage is the transfer payment stage. After the successful R&D of the technology, the government verifies the quality of the project completion and pays the remaining contract price according to the contract requirements.

To further simplify the problem, we make the following assumptions.

Assumption 1.

Type of agent’s technology. The initial technology level type of the enterprise is $\beta$$(\beta >0)$. Consistent with the existing research [14,62], it is generally believed that the degree of effort to carry out technological innovation $(e(\beta ))$ is related to the technological type of the enterprise $(\beta )$. The R&D quality of the enterprise is shown as follows: $q(\beta )=\beta e(\beta )+\theta$. $\theta$ is a random disturbance variable subject to normal distribution $N(0,{\sigma }^2)$ [14,62].

Assumption 2.

Agent’s cost information. According to the existing research, the effort cost of an enterprise is closely related to the technological type [64]. Thus, the cost of the enterprise’s effort is $c(\beta )=\frac{k{e}^2(\beta )}{2\beta }$, that is, the more efforts the enterprise makes, the higher the cost it needs to pay, and the higher the technological level of the enterprise, the less the cost it needs to pay. $k$ represents the effort cost factor $(k>0)$. The enterprise is risk-averse. $\rho$ represents the risk coefficient $(\rho >0)$. Higher $\rho$ indicates more risk aversion. The utility function is generally expressed as a negative exponential function $U(\pi )=e^{-\rho \pi }$. The risk cost is $\frac{\rho b^2{\sigma }^2}{2}$ [62].

Assumption 3.

The principal’s contract design. Following previous research [62,65], we adopt a linear contract design model. In stage 1, the government signs linear quality-incentive contracts with enterprises. $T(\beta )$ is the contract price of the technology ultimately purchased by the government.

$$T(\beta )=a_0+nb(q-q_0)$$

(1)

$q_0$ is the government’s minimum constraint on the quality of enterprise R&D. Only when the quality of the enterprise in R&D reaches $q_0$, can it obtain a positive income. We make $a=a_0-nb{q}_0$, $a$ represents the fixed payment paid by the government to the enterprise for providing the initial technology, and $b$ is the incentive constraint coefficient of the contract. The government will pay fixed compensation to the enterprise whether it succeeds in R&D or not. $m$ and $n$ are the quality-benefit coefficient of government and enterprise, respectively, $(m>0,n>0)$, which are used to measure the different impacts of technology diffusion and a spillover effect on public benefits and private benefits.

The simplified contract expression can be obtained as follows.

$$T(\beta )=a+nb\beta e(\beta )$$

(2)

The expected income of the enterprise is ${\pi }_F$.

$${\pi }_F=a+nb\beta e(\beta )-\frac{k{e}^2(\beta )}{2\beta }-\frac{\rho b^2{\sigma }^2}{2}$$

(3)

The expected revenue for the government is ${\pi }_G$.

$${\pi }_G=(m-nb)\beta e(\beta )-a$$

(4)

The model design considers two situations: single-asymmetry information (moral hazard) and dual-asymmetry information (moral hazard, adverse selection), and establishes a quality-incentive contract model to study the design characteristics of quality-incentive contracts for technological innovation in government procurement under asymmetry information.

3.1. Quality-Incentive Contract under Single-Asymmetry Information

First, the model only considers the case of ex-post asymmetry information (moral hazard). Asymmetry information occurs after the government and the enterprise sign the contract. In this case, the government has all the information about the initial technological type of the enterprise, but it is not aware of the effort of the enterprise in the process of technological innovation. $IC$ is the incentive-compatible constraint condition. The enterprise will choose the degree of effort to maximize their profits for technological R&D. $IR$ is the individual rational constraint condition. The expected income of the enterprise must be higher than its retained income, otherwise, it will not conduct technological innovation. $\overline{\omega }$ is the retained income of the enterprise.

The basic model is built as follows.

$$\underset{\alpha ,\beta }{\max {\pi }_G}=(m-nb)\beta e-a$$

(5)

$$\underset{e}{\max {\pi }_F}=a+nb\beta e-\frac{k{e}^2}{2\beta }-\frac{\rho {\sigma }^2{b}^2}{2}(IC)$$

(6)

$${\pi }_F=a+nb\beta e-\frac{k{e}^2}{2\beta }-\frac{\rho {\sigma }^2{b}^2}{2}\ge \overline{\omega }(IR)$$

(7)

The contract $(a^{*},b^{*})$ can be obtained by solving the above Equations (5)–(7).

$$a^{*}=\overline{\omega }+\frac{\rho {\sigma }^{2}k-n^2{\beta }^3}{2k}{(b^{*})}^2$$

$$b^{*}=\frac{mn{\beta }^3}{\rho k{\sigma }^2+n^2{\beta }^3}$$

$$e^{*}=\frac{n{\beta }^2{b}^{*}}{k}$$

Proposition 1.

Under the condition of pure moral hazard, the government’s fixed payment$a(\beta )$is equal to the sum of the enterprise’s retained income and the difference between the risk cost and effort cost. The incentive constraint coefficient $b^{*}$has a positive incentive effect on the optimal effort $e^{*}$of enterprises.

Proof of Proposition 1.

$$a^{*}=\overline{\omega }+\frac{\rho {\sigma }^2{(b^{*})}^2}{2}-\frac{n^2{\beta }^3{(b^{*})}^2}{2k}$$

Due to the high uncertainty of technology R&D, the enterprise is often faced with relatively great risks. It is assumed that the risk cost of R&D is higher than its effort cost. That is $\rho {\sigma }^{2}k>n^2{\beta }^3$. Therefore, the fixed payment of the government not only satisfies the retained income of the enterprise, but also compensates for the risk cost of R&D, which can better encourage enterprises to carry out technological innovation of quality improvement.

$$\frac{\partial e^{*}}{\partial b^{*}}=\frac{n\beta }{k}>0,\frac{\partial b^{*}}{\partial \beta }>0$$

$$\frac{\partial e^{*}}{\partial \beta }=\frac{\partial e^{*}}{\partial b^{*}}\frac{\partial b^{*}}{\partial \beta }>0$$

Comparative static analysis of $e^{*}$ can show that the promotion of $b^{*}$ can motivate the enterprise to improve its efforts. The optimal incentive coefficient of the government is positively correlated with the type of technology, and the enterprise with a high level of technology will make more efforts. □

3.2. Quality-Incentive Contract under Dual-Asymmetry Information

The government often faces the problem of dual-asymmetry information in public technology procurement projects, namely, adverse selection and moral-hazard coexist. Before signing the contract, the government could not observe the initial technological experience level of the enterprise. After signing the contract, the government could not have access to information about the level of effort. To solve this problem, we find that according to the display principle [66,67], under dual-asymmetry information, the government can induce the enterprise to disclose its technological type by designing the information-screening contract to reduce the adverse impact of asymmetry information, while the contractor can obtain the highest expected profits through the separated balanced contract menu.

The technological level of enterprises in the market can be divided into two types: high $({\beta }_H)$ and low $({\beta }_L)$$({\beta }_H>{\beta }_L)$. The proportion of these two types of enterprises (prior probability) is public knowledge, which can usually be obtained according to previous experience and analysis. The proportions of high-type and low-type enterprises are $p$ and $1-p$$(0\le p\le 1)$, respectively.

The government designs two kinds of contracts $({\alpha }_L,{\beta }_L)$ and $({\alpha }_H,{\beta }_H)$ for different types of enterprises to choose from, to induce enterprises to disclose their real capability information and encourage them to make the best efforts to complete the task of technological innovation under dual-asymmetry information. The design of the model should encourage enterprises to truthfully report their technological type, that is, enterprises will obtain higher returns when they honestly report their technological type. At the same time, the design of the contract must satisfy the individual rational constraint condition, that is, the profits of the enterprise must be greater than its retained earnings. To encourage enterprises to choose the best degree of effort for technological innovation, the contract design needs to satisfy the incentive-compatible constraint condition of the enterprise’s profit maximization. Therefore, by designing the information-screening contract, the government makes enterprises of different technical levels have no motivation to pretend to be of other types. Through the different choices of enterprises in signing contracts, the government can realize the screening of enterprises of different information types and achieve the purpose of incentive.

The profits expressions of the two types of enterprises are ${\pi }_{LL}$ and ${\pi }_{HH}$.

$${\pi }_{LL}=a_L+n{b}_L{\beta }_L{e}_L-\frac{k{e}_L^2}{2{\beta }_L}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}$$

(8)

$${\pi }_{HH}=a_H+n{b}_H{\beta }_H{e}_H-\frac{k{e}_H^2}{2{\beta }_H}-\frac{\rho {\sigma }^2{b}_H{}^2}{2}$$

(9)

The enterprises of different technological levels choose the effort level $e_L^{*}$ and $e_H^{*}$ under the expectation of profit maximization.

$$\frac{\partial {\pi }_{LL}}{\partial e_L}=n{b}_L{\beta }_L-\frac{k{e}_L}{{\beta }_L}=0$$

(10)

$$\frac{\partial {\pi }_{HH}}{\partial e_H}=n{b}_H{\beta }_H-\frac{k{e}_H}{{\beta }_H}=0$$

(11)

$$e_L^{*}=\frac{n{b}_L{\beta }_L^2}{k},e_H^{*}=\frac{n{b}_H{\beta }_H^2}{k}$$

(12)

Firstly, we bring the effort level $e_L^{*}$ and $e_H^{*}$ into the model, and then construct the objective function to maximize the government’s benefits as follows. ${\pi }_G$ represents the government’s expected return function.

$$\underset{a_H,b_H,a_L,b_L}{\max {\pi }_G}=p[(m-n{b}_H)\frac{n{b}_H{\beta }_H{}^3}{k}-a_H]+(1-p)[(m-n{b}_L)\frac{n{b}_L{\beta }_L{}^3}{k}-a_L]$$

(13)

$$s.t.\left\{\begin{array}{l}\max {\pi }_{LL}=a_L+\frac{n^2{b}_L^2{\beta }_L^3}{2k}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}\ge \max {\pi }_{LH}=a_H+\frac{n^2{b}_H^2{\beta }_H^2(2{\beta }_L^2-{\beta }_H^2)}{2k{\beta }_L}-\frac{\rho {\sigma }^2{b}_H{}^2}{2}\\ \max {\pi }_{HH}=a_H+\frac{n^2{b}_H^2{\beta }_H^3}{2k}-\frac{\rho {\sigma }^2{b}_H{}^2}{2}\ge \max {\pi }_{HL}=a_L+\frac{n^2{b}_L^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2)}{2k{\beta }_H}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}\\ {\pi }_{LL}=a_L+\frac{n^2{b}_L^2{\beta }_L^3}{2k}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}\ge \overline{\omega }(I{R}_1)\\ {\pi }_{HH}=a_H+\frac{n^2{b}_H^2{\beta }_H^3}{2k}-\frac{\rho {\sigma }^2{b}_H{}^2}{2}\ge \overline{\omega }(I{R}_2)\end{array}\right.$$

(14)

We solve the objective function under the constraint conditions.

Proposition 2.

If the profits of low-type enterprises are greater than retained earnings, the profits of high-type enterprises must be greater than retained earnings.

Proof of Proposition 2.

By comparing the profits of high-type and low-type enterprises, we can obtain the following results.

$$\begin{array}{l}{\pi }_{HH}=a_H+\frac{n^2{b}_H^2{\beta }_H^3}{2k}-\frac{\rho {\sigma }^2{b}_H{}^2}{2}\\ \ge {\pi }_{HL}=a_L+\frac{n^2{b}_L^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2)}{2k{\beta }_H}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}\\ ={\pi }_{LL}+\frac{n^2{b}_L^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2-{\beta }_H{\beta }_L)}{2k{\beta }_H}\\ \ge {\pi }_{LL}\end{array}$$

(15)

According to Equation (15), the profit of high-type enterprises must be greater than or equal to that of low-type enterprises. It’s easy to get that if the condition $I{R}_1$ is satisfied, $I{R}_2$ must be satisfied.

In light of Proposition 2, we can ignore the constraint of $I{R}_2$. The objective function in the model is a typical two-layer programming problem. We introduce Lagrange coefficients $\lambda$, $\mu$, $\eta$ and solve the contract coefficient by using Kuhn–Tucker optimal condition.

$$\begin{array}{l}L=p[(m-n{b}_H)\frac{n{b}_H{\beta }_H{}^3}{k}-a_H]+(1-p)[(m-n{b}_L)\frac{n{b}_L{\beta }_L{}^3}{k}-a_L]\\ +\lambda [a_L+\frac{n^2{b}_L^2{\beta }_L^3}{2k}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}-a_H-\frac{n^2{b}_H^2{\beta }_H^2(2{\beta }_L^2-{\beta }_H^2)}{2k{\beta }_L}+\frac{\rho {\sigma }^2{b}_H{}^2}{2}]\\ +\mu [a_H+\frac{n^2{b}_H^2{\beta }_H^3}{2k}-\frac{\rho {\sigma }^2{b}_H{}^2}{2}-a_L-\frac{n^2{b}_L^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2)}{2k{\beta }_H}+\frac{\rho {\sigma }^2{b}_L{}^2}{2}]\\ +\eta [a_L+\frac{n^2{b}_L^2{\beta }_L^3}{2k}-\frac{\rho {\sigma }^2{b}_L{}^2}{2}-\overline{\omega }]\end{array}$$

(16)

Letting the partial derivatives of $a_L$, $a_H$, $b_L$, $b_H$ to zero, we can obtain the following equations combination.

$$\left\{\begin{array}{l}\frac{\partial L}{\partial a_H}=\mu -\lambda -p=0\\ \frac{\partial L}{\partial a_L}=p+\lambda -\mu +\eta -1=0\\ \frac{\partial L}{\partial b_H}=0\\ \frac{\partial L}{\partial b_L}=0\\ \lambda ({\pi }_{LL}-{\pi }_{LH})=0\\ \mu ({\pi }_{HH}-{\pi }_{HL})=0\\ \eta ({\pi }_{LL}-\overline{\omega })=0\\ \lambda \ge 0,\mu \ge 0,\eta \ge 0\end{array}\right.$$

(17)

By solving the above equations combination, we can get the following results.

$$\lambda =0,\mu =p,\eta =1$$

$$b_H^{*}=\frac{mn{\beta }_H^3}{\rho {\sigma }^{2}k+n^2{\beta }_H^3}$$

$$\begin{array}{l}{b}_L^{*}=\frac{(1-p)mn{\beta }_H{\beta }_L^3}{(1-2p)n^2{\beta }_H{\beta }_L^3+(1-p)k\rho {\sigma }^2{\beta }_H+p{n}^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2)}\\ =\frac{mn{\beta }_L^3}{n^2{\beta }_L^3+k\rho {\sigma }^2+\frac{p}{1-p}\frac{{\beta }_L^2}{{\beta }_H}{n}^2(2{\beta }_H^2-{\beta }_L^2-{\beta }_L{\beta }_H)}\end{array}$$

$$a_H^{*}=\overline{\omega }+\frac{n^2{(b_L^{*})}^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2-{\beta }_H{\beta }_L)}{2k{\beta }_H}-\frac{n^2{\beta }_H^3{(b_H^{*})}^2}{2k}+\frac{\rho {\sigma }^2{(b_H^{*})}^2}{2}$$

$$a_L^{*}=\overline{\omega }-\frac{n^2{\beta }_L^3{(b_L^{*})}^2}{2k}+\frac{\rho {\sigma }^2{(b_L^{*})}^2}{2}$$

□

Proposition 3.

Under dual-asymmetry information, the two types of enterprises will have different contract incentive intensities, optimal effort levels, and expected benefits.

Proof of Proposition 3.

We compare the incentive and constraint coefficients, optimal effort levels, and expected profits of two types of enterprises.

$$\frac{b_H^{*}}{b_L^{*}}-1=\frac{(1-p)k\rho {\sigma }^2({\beta }_H^3-{\beta }_L^3)+p{n}^2{\beta }_L^2{\beta }_H^2(2{\beta }_H^2-{\beta }_L^2-{\beta }_H{\beta }_L)}{(1-p){\beta }_L^3(\rho k{\sigma }^2+n^2{\beta }_H^3)}>0$$

$$\frac{e_H^{*}}{e_L^{*}}=\frac{b_H^{*}}{b_L^{*}}\frac{{\beta }_H^2}{{\beta }_L^2}>1$$

$${\pi }_{HH}^{*}=\overline{\omega }+\frac{n^2{(b_L^{*})}^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2-{\beta }_H{\beta }_L)}{2k{\beta }_H}>{\pi }_{LL}^{*}=\overline{\omega }$$

By comparison, we can get $b_H^{*}>b_L^{*}$, $e_H^{*}>e_L^{*}$, and ${\pi }_{HH}^{*}>{\pi }_{LL}^{*}$. Therefore, under dual-asymmetry information, the government will provide higher incentive intensity to the high-type enterprises. The high-type enterprises tend to exert more effort and obtain more benefits than low-type enterprises. □

Proposition 4.

The government can infer the real technology type of the enterprises through the selection of information screening contracts.

Proof of Proposition 4.

According to Equations (14) and (15), we can obtain ${\pi }_{LH}^{*}<{\pi }_{LL}^{*}$. The proof is as follows.

$$\begin{array}{l}{\pi }_{LH}^{*}={\pi }_{HH}^{*}+\frac{n^2{(b_H^{*})}^2{\beta }_H^2(2{\beta }_L^2-{\beta }_H^2-{\beta }_H{\beta }_L)}{2k{\beta }_L}\\ =\overline{\omega }+\frac{n^2{(b_L^{*})}^2{\beta }_L^3(2{\beta }_H^2-{\beta }_L^2-{\beta }_H{\beta }_L)+n^2{(b_H^{*})}^2{\beta }_H^3(2{\beta }_L^2-{\beta }_H^2-{\beta }_H{\beta }_L)}{2k{\beta }_H{\beta }_L}<\overline{\omega }={\pi }_{LL}^{*}\end{array}$$

The low-type enterprise makes more profits when it tells the truth about its technology type than when it lies about being high-type. Due to $\mu =p$, we can obtain ${\pi }_{HH}^{*}={\pi }_{HL}^{*}$. The profits earned by a high-type enterprise for reporting its technology type are equal to the profit earned if it lied about being low-type. Thus, no matter what type of enterprise has no incentive to lie about its technology type, only by choosing contracts that match its true type, can it make the maximum profits. The information-screening contract designed by the government has the function of making enterprises report exactly what type of technology they have. □

Proposition 5.

Under dual-asymmetry information, the low-type enterprise can only obtain retained income, while the high-type enterprise can not only obtain retained income but also obtain additional information rents.

Proof of Proposition 5.

According to the proof of Proposition 3, we can get the following results.

$$△\pi ={\pi }_{HH}^{*}-{\pi }_{LL}^{*}=\frac{n^2{(b_L^{*})}^2{\beta }_L^2(2{\beta }_H^2-{\beta }_L^2-{\beta }_H{\beta }_L)}{2k{\beta }_H}>0$$

$$\frac{\partial △\pi }{\partial b_L^{*}}>0,\frac{\partial b_L^{*}}{\partial p}<0$$

$$\frac{\partial △\pi }{\partial p}=\frac{\partial △\pi }{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial p}<0$$

$$\frac{\partial {\pi }_{LL}^{*}}{\partial p}=0$$

$$\frac{\partial {\pi }_{HH}^{*}}{\partial p}=\frac{\partial {\pi }_{LL}^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial p}<0$$

It can be seen that the government needs to pay extra information rents to prevent high-type enterprises from taking advantage of information advantages to seeking rents. With the increase in the proportion of high-type enterprises, the information rents and the profits of high-type enterprises will decrease, but the profits of low-type enterprises will not be affected. As the initial experiential capacity information gradually becomes public information, the government will not pay additional information rents. □

4. Analysis of Quality-Incentive Contract Characteristics

Proposition 6.

The contract parameters and efforts of different types of enterprises are affected by the proportion of enterprises in the market.

Proof of Proposition 6.

We perform a comparative static analysis of contract parameters.

$$\frac{\partial b_L^{*}}{\partial p}<0,\frac{\partial b_H^{*}}{\partial p}=0$$

$$\frac{\partial a_H^{*}}{\partial b_L^{*}}>0,\frac{\partial a_L^{*}}{\partial b_L^{*}}=\frac{\rho k{\sigma }^2-n^2{\beta }_L^3}{k}{b}_L^{*}>0$$

$$\frac{\partial a_H^{*}}{\partial p}=\frac{\partial a_H^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial p}<0,\frac{\partial a_L^{*}}{\partial p}=\frac{\partial a_L^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial p}<0$$

As the proportion of high-type enterprises in the market increases, the fixed payments of both types of enterprises are gradually reduced. The incentive-constraint coefficient of high-type enterprises ($b_H^{*}$) has nothing to do with the market share, but the incentive-constraint coefficient of low-type enterprises ($b_L^{*}$) is distorted downward. With the increase in the proportion of high-type enterprises, the distortion degree is intensified.

We perform a comparative static analysis of the optimal effort level.

$$\frac{\partial e_H^{*}}{\partial p}=0,\frac{\partial e_L^{*}}{\partial b_L^{*}}>0,\frac{\partial e_L^{*}}{\partial p}=\frac{\partial e_L^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial p}<0$$

The optimal effort degree of high-type enterprises has nothing to do with the market share, but the optimal effort degree of low-type enterprises will decrease with the increase of high-type enterprises in the market. □

Proposition 7.

The uncertainty of technological innovation will reduce the effort of enterprises and destroy the incentive effect of contracts.

Proof of Proposition 7.

In the innovation contract of public procurement, the uncertainty of technological innovation makes the final cost and innovation quality unpredictable, and consequently ${\sigma }^2$ is the key factor affecting the final decision. In the following, we analyze the interaction between the government’s contract design, the choice of enterprises, and the uncertainty of technological innovation under dual-asymmetry information.

$$\frac{\partial b_L^{*}}{\partial {\sigma }^2}<0,\frac{\partial b_H^{*}}{\partial {\sigma }^2}<0$$

$$\frac{\partial a_H^{*}}{\partial {\sigma }^2}=\frac{\partial a_H^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial {\sigma }^2}<0,\frac{\partial a_L^{*}}{\partial {\sigma }^2}=\frac{\partial a_L^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial {\sigma }^2}<0$$

$$\frac{\partial e_L^{*}}{\partial {\sigma }^2}=\frac{\partial e_L^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial {\sigma }^2}<0,\frac{\partial e_H^{*}}{\partial {\sigma }^2}=\frac{\partial e_H^{*}}{\partial b_H^{*}}\frac{\partial b_H^{*}}{\partial {\sigma }^2}<0$$

Through the above comparison, it is not difficult to find that with the increase in the degree of uncertainty in technological innovation, the effort degree and incentive intensity of the two types of enterprises will be weakened, and the fixed payment will also be reduced. This indicates that the uncertainty of technological innovation will inhibit the incentive effect of contracts and reduce the effort degree of enterprises.

When ${\sigma }^2\to 0$, we can obtain $b_H^{*}=\frac{m}{n}$ and $b_L^{*}=\frac{m}{n+\frac{p}{1-p}\frac{n}{{\beta }_H{\beta }_L}(2{\beta }_H^2-{\beta }_L^2-{\beta }_L{\beta }_H)}$. It is easy to identify $b_L^{*}<b_H^{*}$. With the increase in the proportion of high-type enterprises in the market, the gap between the incentive intensity of the two types of enterprises is increasing.

When ${\sigma }^2\to \infty$, we can obtain $b_H^{*}=0$ and $b_L^{*}=0$. At this time, due to the strong risk, the enterprises cannot bear the risk of technological innovation, and the government will not impose incentives on them.

$$\frac{\partial {\pi }_{LL}^{*}}{\partial {\sigma }^2}=0,\frac{\partial {\pi }_{HH}^{*}}{\partial {\sigma }^2}=\frac{\partial {\pi }_{HH}^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial {\sigma }^2}<0$$

By judging the impact of uncertainty on profits, we find that the maximum profit of low-type enterprises is retained earnings. Although the increase in uncertainty will lead to a decline of the profits of high-type enterprises, it will not affect the profits of low-type enterprises. □

Proposition 8.

Under dual-asymmetry information, the higher the technological level of the enterprise, the greater the corresponding incentive intensity. Enterprises with higher technological levels are willing to pay more effort.

Proof of Proposition 8.

We analyze the relationship between the level of effort and technology of the enterprise.

$$\frac{\partial e_H^{*}}{\partial b_H^{*}}>0,\frac{\partial b_H^{*}}{\partial {\beta }_H}>0,\frac{\partial e_H^{*}}{\partial {\beta }_H}=\frac{\partial e_H^{*}}{\partial b_H^{*}}\frac{\partial b_H^{*}}{\partial {\beta }_H}>0$$

$$\frac{\partial e_L^{*}}{\partial b_L^{*}}>0,\frac{\partial b_L^{*}}{\partial {\beta }_L}>0,\frac{\partial e_L^{*}}{\partial {\beta }_L}=\frac{\partial e_L^{*}}{\partial b_L^{*}}\frac{\partial b_L^{*}}{\partial {\beta }_L}>0$$

Enterprises with higher technological levels are willing to pay more effort. Improving the quality-incentive coefficient in the contract can also improve the enterprises’ level of effort.

$$\frac{\partial b_H^{*}}{\partial {\beta }_L}=0,\frac{\partial b_L^{*}}{\partial {\beta }_H}<0$$

The incentive and constraint coefficient of high-type enterprises ($b_H^{*}$) is not affected by the technological level of low-type enterprises (${\beta }_L$), but the incentive and constraint coefficient of low-type enterprises ($b_L^{*}$) is affected by the technological level of high-type enterprises (${\beta }_H$). With the increasing technological level of high-type enterprises, the government’s incentive intensity of low-type enterprises gradually decreases. □

Proposition 9.

With the increase of the risk avoidance coefficient or effort cost coefficient, the incentive intensity provided to the enterprise by the government will be reduced.

Proof of Proposition 9.

By comparative static analysis of parameters in the expression of incentive and constraint coefficients, we can obtain as follows:

$$\frac{\partial b_L^{*}}{\partial \rho }<0,\frac{\partial b_L^{*}}{\partial k}<0$$

$$\frac{\partial b_H^{*}}{\partial \rho }<0,\frac{\partial b_H^{*}}{\partial k}<0$$

(18)

With the increase in risk aversion coefficient and effort cost coefficient, enterprises need to bear more risks to carry out technological innovation. The amount of risk they are willing to take will be reduced, and so will the intensity of the incentive. □

5. Numerical Analysis

In the previous section, we analyzed the characteristics of quality-incentive and constraint contracts in public technology innovation procurement, investigated the influence of single- and dual-information asymmetry on incentive contracts and the degree of enterprise effort, and discussed the interaction between the optimal equilibrium result and the key parameters. In this section, we compare the equilibrium results under different conditions through numerical simulation analysis and focus on the proportion of enterprise technological type, the uncertainty of technological innovation, and the quality-income coefficient of both sides.

5.1. Analysis of the Proportion of Enterprises’ Technological Type

First, we examine the relationship between contracts and the proportion of enterprises technology types in the market. We set the parameters as follows: $\overline{\omega }=1$, $k=1$, $\rho =2$, ${\beta }_L=1$, ${\beta }_H=2$, ${\sigma }^2=2$, $m=1$, $n=1$. $p$ is assumed here as the industry consensus. $p$ belongs to $[0,1]$.

Low-type enterprises will choose the quality-incentive constraint contract $(a_L^{*},b_L^{*})$. According to Figure 2, with the increase in the proportion of high-type enterprises ($p$), the fixed payment of low-type enterprises ($a_L^{*}$) gradually decreases, and the incentive intensity ($b_L^{*}$) gradually weakens. Compared with $a_L^{*}$, the change in the proportion of enterprises has a greater impact on $b_L^{*}$.

High-type enterprises will choose the quality-incentive constraint contract $(a_H^{*},b_H^{*})$. As can be seen from Figure 3, the incentive and constraint coefficient $b_H^{*}$ is a fixed value, which indicates that for high-type enterprises, the expectation of participating in technological innovation is relatively large, while the fixed payment $a_H^{*}$ decreases with the increase of $p$. Finally, $a_H^{*}$ approaches to the retained income steadily. When $p$ is low, the government will provide a higher fixed payment to encourage high-type enterprises to participate in technological innovation.

The combination of Figure 2 and Figure 3 can reflect the phenomenon that high-type enterprises are not distorted, while low-type enterprises are distorted. That is, the incentive coefficient of low-type enterprises will be distorted downward, while the incentive coefficient of high-type enterprises will not be distorted. Additionally, the findings are in line with the discovery of Su and Wang [62], as well as Zhang and Xu [14]. As the proportion of high-type enterprises in the market increases and competition intensifies, fixed payments for both types of enterprises are decreasing.

As can be seen from Figure 4, the increase in the proportion of high-type enterprises does not affect their optimal effort degree, but the optimal effort degree of low-type enterprises decreases with the increase of $p$. When $p\to \infty$, $e_L^{*}\to 0$. Combining Proposition 4 and the findings of Alexander et al. [60], information screening contracts enable enterprises to choose the contracts that match their technology type. We can also obtain $e_H^{*}>e_L^{*}$ from Figure 4. High-type enterprises exert more effort than low-type enterprises.

With the increase of high-type enterprises, the information rent and the income of high-type enterprises decrease continuously, while the income of low-type enterprises remains unchanged (Figure 5). The expected income of the government first increases and then decreases with the changes of $p$. When $p=1$, there are no low-type enterprises in the market. Finally, the information rent drops to zero, and the profits of all parties are equal to the retained income.

5.2. Analysis of Technological Innovation Uncertainty

Combined with the analysis of technological innovation uncertainty in Section 4, this section conducts numerical simulation to test its characteristics, and mainly analyzes the impact of technological innovation uncertainty on contract design and profits.

As shown in Figure 6 and Figure 7, the greater the degree of uncertainty of technological innovation, the higher the risk of technological innovation, and the greater the possibility of innovation failure for enterprises. For risk-averse enterprises, their expected earnings will decline, and the degree of effort will also decline. For the government, it will judge that the enterprise is more likely to be low-type; thus, the government will provide relatively low-incentive intensity to the enterprise. However, the fixed payment has a process of first increasing and then decreasing as the technological uncertainty changes. Within a reasonable range of risks, the government will appropriately increase the fixed payment and encourage enterprises to perform technological innovation activities.

5.3. Analysis of the Quality-Benefit Coefficient

Different from existing work on quality-incentives for public innovation [14,62], the model in this paper focuses on the effect of quality benefit coefficients on the incentive effects of contracts. The quality-benefit coefficient of government and enterprise is also the key factor of contract design. The quality-benefit coefficient of the government reflects the degree of influence of technological innovation quality on public benefits, whereas the quality-benefit coefficient of the enterprise reflects the degree of influence of technological innovation quality on enterprise profits. Because the comparative static analysis of the quality-benefit coefficient is complicated and inconvenient to discuss, we observe its influence through numerical simulation here.

First, we assume that $n$ is unchanged, and analyze the influence of $m$ on contract design. As shown in Figure 8, the increase of $m$ will improve the incentive intensity of the government for enterprises. That is because the improvement of quality can bring more public benefits. Meanwhile, the government will reduce the fixed payment for high-type enterprises, because the increase of $b_H^{*}$ has already played a strong incentive effect. Obviously, the change of $m$ has a greater impact on the contract change of high-type enterprises than low-type enterprises. As shown in Figure 9, the increase of $m$ can increase the expected benefits for the government and enterprises. Especially for high-type enterprises, $m$ plays a positive role in increasing their profits. $m$ has a greater impact on the profits increase of high-type enterprises than on the government’s benefits. Since the influence of $m$ on the effort level is similar to that on the incentive coefficient, we will not be repeat it here. It is easy to find that $m$ has a positive effect on the effort level of the enterprises.

Similarly, we analyze the influence of $n$ on contract design and profits while keeping $m$ unchanged, shown in Figure 10 and Figure 11.

For low-type enterprises, the fixed payment will first increase slightly and then decrease with the increase of $n$. For high-type enterprises, the fixed payment will decrease with the increase of $n$. If $n$ is large enough, $a_H^{*}$ will be negative. Therefore, the enterprise can get a higher contract price by improving the quality. When the value of $n$ is large enough, the high-type enterprises are willing to innovate even with negative fixed payments. The government will increase the incentive intensity and fixed payments to encourage the low-type enterprise to improve the quality of technological innovation when the value of $n$ is relatively low. However, with the increasing value of $n$, the incentive intensity will decrease accordingly. At this time, the quality-benefit coefficient of the enterprise has been able to provide the enterprise enough incentive.

The increase of $n$ has a positive effect on government benefits, the profits of high-type enterprises, and information rent. The increase of $n$ also indicates that the technology is worth purchasing at a higher price, that is, the technology is more valuable, so the increase of $n$ has a positive effect on both government and enterprise profits.

6. Conclusions and Discussion

6.1. Conclusions

In public technology innovation procurement, to encourage enterprises to sustainably improve the quality of technological innovation and solve the problem of asymmetry information faced by the government, our paper constructed the technological innovation quality-incentive model in public procurement. The model was designed to screen and motivate enterprises to improve the quality of technological innovation under single- or dual-asymmetric information. By solving the incentive model, we determined the optimal incentive contract under different cases. We analyzed and compared the optimal effort degree and contract-incentive coefficient corresponding to different technological types. We focus on the analysis of the relevant characteristics of quality-incentive contracts and further validate the impact of the proportion of enterprise technological type, technological innovation uncertainty, and the quality-benefit coefficient on contract parameters and expected profits of both parties through numerical simulation.

Through the above research, the main conclusions of this paper are as follows:

(1)

The incentive contract under dual-asymmetry information can reduce the influence of asymmetry information on government procurement through information screening and encourage enterprises of different technological types to improve their efforts. Information screening contracts encourage enterprises to truthfully report their technical information types and reduce the risk of adverse selection, thereby increasing the efficiency of public technology innovation and achieving sustainable incentives for innovation quality.

(2)

Under dual-asymmetry information, high-type enterprises can not only obtain retained earnings, but also obtain additional information rents. To prevent high-type enterprises from taking advantage of information advantages to seek rent, the government needs to pay extra information rent. When high-type enterprises occupy a relatively small share of the market, the high information rent may drown the expected benefits of the government.

(3)

The design of the parameters in the contract is influenced by the ex-ante estimate of the proportion of enterprises’ technology types in the market. The government benefit is closely related to the proportion of enterprise technological type in the market. The expected benefits of the government first increase and then decrease with the change in the market share of high-type enterprises.

(4)

The uncertainty of technological innovation will reduce the degree of enterprise effort and affect the contract design. With the increase of uncertainty degree of technological innovation, the degree of effort and incentive intensity of both types of enterprises will be weakened. If the uncertainty of technological innovation is within the government’s affordability, the contract menu will facilitate the achievement of sustainable innovation incentives, and both the government and enterprises can benefit from the innovation projects.

(5)

The quality-benefit coefficient of government and enterprise is positively correlated with the profits of all parties. However, their influence on the incentive intensity is different. The increase of the government quality-benefit coefficient can improve the incentive intensity of enterprises. Especially for high-type enterprises, the quality-benefit coefficient of the government plays a positive role in increasing their profits. Only when the quality-benefit coefficient of the enterprises is relatively low can the incentive intensity of the enterprises be improved.

In summary, through information screening contracts, the government can guide enterprises to truthfully reflect the true type of technology and make reasonable choices to achieve sustainable improvement in innovation quality and more benefits for both parties.

6.2. Management and Policy Recommendations

According to the conclusions of this paper, we put forward the following suggestions:

(1)

The government can solve the problem of information asymmetry in public technology innovation procurement by designing a quality-incentive contract to maximize government benefits, so as to encourage enterprises to improve the quality of innovation.

(2)

The uncertainty of technological innovation will hinder enterprises from making efforts to improve quality. The government can reduce the risks of enterprises by formulating relevant policies to better stimulate innovation.

(3)

The government needs to strengthen the efficiency of transforming the quality of technological innovation into public benefits and improve the practical value of innovation results.

(4)

To obtain more benefits and information rents in public procurement, enterprises need to improve their core technology and enhance market competitiveness.

6.3. Limitations and Future Research

Our model needs to be further studied. First of all, the model assumes that the technological quality type variables are discrete, divided into high-type and low-type. In reality, the technological quality type variables are often continuous. Secondly, the quality and cost functions in the model are set to fixed forms. If they can be extended to general forms, the results would be more convincing. Finally, this paper only considers the procurement supply chain formed by the government and a single enterprise. In practice, the form of R&D competition is often introduced in government procurement to carry out technological innovation, which is worthy of further research.