Simulation Analysis of Artificial Intelligence Technology Diffusion under Market Competition and Policy Incentives Based on Complex Network Evolutionary Game Models

Abstract

The relationship network between enterprises will change their adoption behavior of AI technology and this micro-decision-making mechanism will eventually decide whether AI technology can diffuse and the extent of diffusion on the macro level. However, the existing AI technology diffusion research mostly focuses on the integration of AI technology with other industries from the industrial level, ignoring the complexity of the micro-complex game process and interactions within the enterprise network on the macro technology diffusion. In this regard, this paper builds a game model of AI technology diffusion in core and non-core enterprises from the levels of market competition and policy incentives based on complex network evolutionary game theory. It does this through simulation analysis that examines the mechanism of key factors affecting the diffusion of AI technology, as well as the influence and combination effects of pertinent policies. The study shows that (1) AI technology diffuses more effectively in non-core enterprises than it does in core enterprises; (2) changes in parameters like technology cost and policy regimes have a more evident impact on core enterprises than non-core ones; (3) in market competition, increasing the network average degree, the proportion of AI technology products in the mainstream market, the opportunity cost, the cost reduction factor, or decreasing the cost of AI technology can all promote the diffusion of AI technology; (4) under policy incentives, increasing the proportion of AI technology subsidies and the influence of high-tech identification of enterprises can both promote the diffusion of AI technology.

1. Introduction

As the engine of the fourth industrial revolution, AI technology can not only significantly improve social productivity but also trigger structural changes in the economy and society [1,2,3]. Currently, nations all over the world are actively encouraging the development of AI technology and decision-making in order to take advantage of the many opportunities that come with its implementation. Additionally, China strongly supports the AI sector and views it as a strategic emerging industry. The rapid development of AI technology cannot be separated from the breakthroughs in basic research, the integration of multi-source technology, and the cross-border application of technology [4,5], the root of which lies in technological innovation. Technological innovation, as a key constituent of the national development strategy, includes not only new inventions and their first commercialization, but also the process of promotion and dissemination of new technologies among potential adopters. This process of new technologies developing and maturing over time, and ultimately achieving large-scale commercialization, is the process of diffusion of new technologies. Technology diffusion is an important means to promote industrial transformation and upgrading, economic growth, and the optimization of resource allocation [6], which is not only a technological activity but also an economic and social activity, often accompanied by the game between technologies, and new technologies gradually replace the old ones so as to occupy more market shares [7]. Success in diffusion will drive the revolutionary advancement of related industries; failure in diffusion will waste a large amount of resources invested in the preliminary research and development process, so that enterprises lose the window of opportunity to innovate and profit, and make the technology fall into the predicament of self-locking. Therefore, to promote the high-quality development of AI technology, it is indispensable to analyze the process of technology diffusion, and the smoothness or otherwise of the diffusion process directly affects the process of its marketization and industrialization.

Unlike other disruptive technologies, AI technology is not only an independent technology but also can penetrate into other industries and fields, and it can integrate and develop with other industries, so as to promote industrial upgrading and realize a wider social and economic impact. Therefore, accelerating the proliferation of AI technology is not only conducive to realizing the integrated innovation between AI technology and the real economy but also helps to promote the country to realize the transformation of old and new kinetic energy, innovate products and services, improve the production process of traditional industries, and reconstruct the business model of traditional industries [8,9]. However, at present, the proliferation of AI technology is not uniform, which is specifically manifested in the fact that AI technology shows different proliferation processes in different industrial fields and geographic spaces [3], such as notable growth in industries like manufacturing, financial services, retail e-commerce, and construction; slow growth in industries like agriculture and construction; notable growth in large cities with rich resources for science and technology innovation and a well-developed Internet industry; and slow growth in rural areas. Therefore, there is an urgent need to analyze the evolutionary process of AI technology diffusion, explore the key factors affecting technology diffusion, and improve the phenomenon of the stagnation of AI technology in slow-diffusing industries and regions in order to accelerate the diffusion process and promote the balanced diffusion of AI technology, which will in turn promote technological innovation and optimize the economic benefits.

The process of AI technology diffusion can be divided into two stages, one is the natural market competition stage without policy intervention in the pre-diffusion stage, and the other is the policy incentive stage with the introduction of policies for guidance. In the first stage, in the market competition, due to the unevenness of resources, some core enterprises with a large number of information resources for the adoption of AI technology behavior tends to affect the strategic choices of non-core enterprises, presenting a trend of small enterprises to large enterprises. This micro-decision-making mechanism between enterprises will ultimately determine whether the macro AI technology can diffuse as well as the degree of diffusion. In the second stage, on the basis of market competition, the government, as the guide and policy maker of AI technology development, introduces a series of incentive policies to promote the diffusion of AI technology, of which subsidy policy and recognition policy are two important types of policies that affect the development of AI technology [10,11,12]. In this context, this paper first analyzes the evolution process of AI technology diffusion under the state of natural competition in the market, explores the key factors affecting the diffusion of technology and its functioning mechanism, and then, based on this, introduces the policy factors to explore the influence mechanism and policy combination effect of subsidy policy and enterprise high-tech recognition policy to help the diffusion of AI technology, in order to promote the diffusion of AI technology to provide a theoretical reference and application reference. In theory, it is conducive to improving the theoretical framework of AI technology diffusion, analyzing in depth the law of technology diffusion under market competition and policy incentives and the influence mechanism of key factors. In practice, on the one hand, it is conducive to the government’s targeted introduction of relevant policies to improve the rate of AI technology diffusion in industries or regions where technology diffusion is slow; on the other hand, it is conducive to the related enterprises to cultivate their core competitiveness, increase their profits, accelerate the promotion of industrial upgrading, and realize the development of digital-intelligence integration.

2. Literature Review

In this paper, with reference to existing studies, technology diffusion is defined as the process by which a new technology replaces a traditional one and is widely adopted by enterprises and gradually takes over the market share. Regarding the research object of technology diffusion, it is mainly divided into three categories, the first one is energy technology, including green technology [13,14], renewable energy technology [15,16,17,18,19], new energy automobile technology [20,21,22], etc.; the second one is agricultural technology [23,24]; and the third one is disruptive technology [25,26,27,28,29]. Regarding the research methods of technology diffusion, the three main types include case analysis [30,31], regression analysis [32,33,34,35,36], and simulation modeling [37,38]. Regarding the study of technology diffusion under the state of natural competition in the market, some scholars pointed out that the competitiveness of the market, i.e., the large-scale network, is conducive to the diffusion of disruptive technologies [5], and some scholars pointed out that the green consumer premium and the proportion of green consumers are the key factors influencing the diffusion of new energy automobile technologies [22]. Regarding the study of technology diffusion under policy incentives, there are differences in the types of policies involved due to the different types of technologies; some scholars studied the impact of renewable energy quota policy on renewable energy technology diffusion [19], and some scholars studied the impact of subsidy policy on the diffusion of robotics technology [10]. Through reading the literature, it is found that most of the existing studies on technology diffusion regard AI technology as a component of disruptive technology and generally regard AI technology and other emerging technologies as disruptive technologies as a whole to be investigated as a generic technology diffusion problem, and few scholars have conducted independent research on it.

Regarding the issue of AI technology diffusion, only a few scholars have studied it, and the research methods adopted by different scholars and the focus of their research also differ. First, some scholars used regression analysis to study the diffusion of AI technology in different industrial fields, including the online learning field [39], healthcare field [40], and so on. Second, some scholars explored the diffusion of AI technology among early experiencers [41] and other issues. Third, some scholars have systematically analyzed the innovation mechanism of the integration with traditional industries in the process of AI technology diffusion through the research method of combining survey research and complex network analysis [42]. Fourth, there are also scholars who analyzed the problem of AI technology diffusion by constructing a geographical value network map of the technology diffusion of the AI science and technology industry in Beijing based on the social network analysis method [3].

Existing studies on the diffusion of AI technology are relatively scattered in terms of research themes, mainly focusing on the integration of AI technology with other industries and the diffusion of AI technology among experiencers, and they fail to examine the ways in which inter-enterprise relational networks affect the ways in which businesses adopt AI technology from the standpoint of enterprise networks. Additionally, the important factors influencing the spread of AI technology in market competition and its mechanism of operation are not examined, nor are the effects of policy combinations and their influence mechanisms from the standpoint of policy incentives. In terms of research methodology, the existing studies are mainly based on regression analysis, supplemented by complex network analysis, and few studies are based on the method of modeling simulation to study the problem of AI technology diffusion. While regression analysis is more inclined to deal with linear static data, complex network analysis pays more attention to the static characteristics of the network structure, and both research methods have certain defects in simulating dynamic nonlinear social systems. In contrast, modeling simulation has significant advantages in simulating dynamic processes, dealing with nonlinear systems, and analyzing parameter sensitivity, which is more suitable for analyzing dynamic systems. Therefore, it is necessary to analyze the evolution of the dynamic AI technology diffusion process based on the research method of modeling simulation.

Based on the above analysis, this paper will construct an AI technology diffusion model according to the complex network evolutionary game theory, analyze the key factors affecting technology diffusion and its role mechanism through the method of constructing a simulation, and use it as a basis for researching the role of government policy on the micro-decision-making mechanism of enterprises and the diffusion of AI technology. The marginal contribution of this paper is that it expands the relevant theoretical research on AI technology diffusion from the perspective of market competition and policy incentives and explores the results of the adoption behavior of AI technology by a network of firms in a social network influenced by external factors. At the same time, this paper breaks through the limitations of previous research on the impact of policy on technology diffusion itself and explores the optimal policy measures of government policy on the diffusion of AI technology with the idea of policy adjustment, with a view to expand the relevant research on the government’s promotion of AI technology development.

3. Model Construction

The AI technology diffusion model in this paper consists of three parts, including network structure, enterprise game model, and evolutionary rules. First, the BA scale-free network model is constructed to simulate the game relationship of enterprises in the market; second, the enterprise game model is constructed, the basic assumptions are put forward, and the game payoff matrix is constructed; and lastly, the strategy updating rules of the enterprise game are set.

3.1. Network Structure

We abstract the network and construct a complex network model with the interaction relationship network between enterprises as the carrier, using enterprises as nodes and connections like cooperation, competition, and coopetition between enterprises as edges. The diffusion of AI technology is reflected in the technology spreading among nodes through inter-organizational learning and competitive relationships, the enterprises learn games and strategies through the edges in the network, and their micro-decisions ultimately decide whether AI technology can diffuse and the degree of diffusion on the macro level. The real enterprise network is highly consistent with the structural characteristics of the BA scale-free network, where a small number of core enterprises have a lot of competitive and cooperative relationships with other enterprises, with a large scope of information acquisition and influence on the technological decision-making of other enterprises in the industry; while a large number of small- and medium-sized enterprises (SMEs) are in a non-core position, which have relatively few connections with other organizations, with a small scope of information acquisition and limited influence. This unbalanced connectivity structure leads to a power-law distribution of enterprise network degree, which exhibits scale-free characteristics.

In view of this, this paper takes the BA scale-free network as a carrier to analyze the game of AI technology diffusion. It is assumed that there are $N$ enterprises in the market, which are divided into core enterprises and non-core enterprises based on resource strength and network status: core enterprises occupy core positions in the network, have greater influence and resource advantages, and are incumbent enterprises that have survived in the industry for a long time; non-core enterprises are located in sparse positions in the network, with weak roots and limited resource capacity, and are emerging enterprises that have survived in the industry for a short time. Assume that the proportion of core enterprises is $r_c$ and the proportion of non-core enterprises is $r_n$.

3.2. Enterprise Game Model

3.2.1. Problem Description

AI technology diffusion refers to the process by which an enterprise decides whether or not it will adopt AI technology through competitive games and trade-offs of benefits in a complex network structure. In the process of AI technology diffusion, the technology adoption strategy of enterprise $i$ at moment $t$ is $s_i\left(t\right)$, and there are two pure strategy combinations. One is to adopt AI technology, and the other is to continue to adopt conventional technology, and the micro-decision of the enterprise ultimately decides whether AI technology can diffuse and the degree of diffusion on the macro level. At the same time, exogenous variables such as government policies also affect the enterprise’s strategy benefit, which in turn affects the process of AI technology diffusion.

3.2.2. Basic Assumptions and Parameterization

In this paper, based on the characteristics of the enterprise network and the reality of the game model construction considerations, the following basic assumptions are put forward.

Assumption 1. 

The main body of the game is the enterprise, and the scope of the enterprise game is the local network composed of itself and its neighboring enterprises. This paper only considers the cooperative game between different enterprise subjects and assumes that the number of enterprises and the network structure remain unchanged during the diffusion of AI technology, i.e., we ignore the growth of nodes and connected edges in the network. All the firms are finite rational and possess incomplete information, and all the enterprise strategies are pure strategies.

Assumption 2. 

Information is shared in a local network organized by an enterprise and its neighboring enterprises, i.e., the firm has access to the strategies and revenues of its neighboring enterprises, and the enterprise’s revenues are related to the strategies adopted by its neighboring enterprises. Enterprises make strategy choices by comparing their own expected returns and those of their neighboring enterprises.

Assumption 3. 

Suppose the enterprise sells a homogeneous product in the market and the unit price of the product is $P$. If the enterprise adopts conventional technology, the cost of producing a unit of the product is $C$, while it will incur an opportunity cost due to not choosing AI technology $I_1$. If the enterprise adopts AI technology, the cost of producing a unit of the product is $\left(1-\alpha \right)C$, where $\alpha$is the cost reduction factor after the enterprise adopts AI technology, and at the same time, it will also incur additional AI technology costs of $I_2$due to R&D investments, equipment purchases, personnel training, etc.

Assumption 4. 

Assume that the market demand in the mainstream market is $q_1$and the market demand in the non-mainstream market is $q_2$. Initially, the market where conventional technology is located is the mainstream market, and the market where AI technology is located is the non-mainstream market, and the diffusion of AI technology means that AI technology gradually occupies the mainstream market share. If AI technology completely replaces conventional technology, the market where AI technology is located is the mainstream market, and other emerging technologies will occupy the non-mainstream market in the future, repeating the above process for technological innovation. When core and non-core enterprises compete in mainstream or non-mainstream markets at the same time, due to resource differences, non-core enterprises can eventually occupy a market share of only $\frac{1}{a}$of the core enterprises, $a>1$, where coefficient $a$reflects the relative advantage of the core enterprises, and a higher value of $a$indicates that the core enterprise’s relative advantage is stronger.

Assumption 5. 

The essence of AI technology diffusion is the process of breakthrough from the non-mainstream market to the mainstream market, and as one of the disruptive technologies, AI technology diffusion follows the general path of disruptive technology diffusion, i.e., “non-mainstream market—technology accumulation—mainstream market” [43]. In this paper, it is assumed that AI technology intrudes into the mainstream market from the non-mainstream market, resulting in the proportion of the mainstream market that can produce AI technology products being at most$e$, the number of $e{q}_1$, that is, the market share of AI technology in the mainstream market is $e{q}_1$, and at this time, the market share of conventional technology in the mainstream market is $\left(1-e\right)q_1$, of which 0 $\le e\le 1$. $e$is the probability of invasion of the AI technology and the erosion ability of the integrated decision; when $e=0$, AI technology does not invade the mainstream market at all, and at this time, only conventional technology is in the mainstream market; when $e=1$, artificial intelligence technology completely invades the mainstream market, and at this time, only AI technology is in the mainstream market, and conventional technology is completely replaced by AI technology.

3.2.3. Game Modeling under Market Competition

Unlike the NW small-world network model, the nodes in the BA scale-free network model differ according to the amount of information they hold and the number of connections, and in this paper, the nodes are divided into core nodes and non-core nodes, which represent the core and non-core enterprises, i.e., the incumbent enterprises and the emerging enterprises, respectively. Therefore, this paper discusses the game between enterprises and neighboring enterprises in two cases when constructing the game model: one is the game between different types of enterprises and the other is the game between enterprises of the same type. The first stage of the diffusion of AI technology is the natural competition stage of the market without policy intervention in the pre-diffusion period. This paper introduces the parameters of market demand, product unit price, product cost, etc., and establishes the payment matrix of the game under the market competition, as shown in

Table 1. Payment matrix for the game between different types of enterprises under market competition.

		Non-Core Enterprises
		AI Technology	Conventional Technology
Core enterprises	AI technology	$\frac{\mathrm{a}}{\mathrm{a}+1}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2$	$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{\left(1-\mathrm{e}\right){\mathrm{a}\mathrm{q}}_1}{\mathrm{a}+1}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2\right]-{\mathrm{I}}_2$
		$\frac{1}{\mathrm{a}+1}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2$	$\frac{\left(1-\mathrm{e}\right)\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{\mathrm{a}+1}-{\mathrm{I}}_1$
	Conventional technology	$\frac{\left(1-\mathrm{e}\right)\mathrm{a}\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{\mathrm{a}+1}-{\mathrm{I}}_1$	$\frac{\mathrm{a}\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{\mathrm{a}+1}-{\mathrm{I}}_1$
		$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{\mathrm{a}+1}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2\right]-{\mathrm{I}}_2$	$\frac{{\left(\mathrm{P}-\mathrm{C}\right)\mathrm{q}}_1}{\mathrm{a}+1}-{\mathrm{I}}_1$

and

Table 2. Payment matrix for the game between same type of enterprises under market competition.

		Enterprise 2
		AI Technology	Conventional Technology
Enterprise 1	AI technology	$\frac{1}{2}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2$	$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{\left(1-\mathrm{e}\right){\mathrm{q}}_1}{2}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2\right]-{\mathrm{I}}_2$
		$\frac{1}{2}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2$	$\frac{\left(1-\mathrm{e}\right)\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{2}-{\mathrm{I}}_1$
	Conventional technology	$\frac{\left(1-\mathrm{e}\right)\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{2}-{\mathrm{I}}_1$	$\frac{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{2}-{\mathrm{I}}_1$
		$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{2}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2\right]-{\mathrm{I}}_2$	$\frac{{\left(\mathrm{P}-\mathrm{C}\right)\mathrm{q}}_1}{2}-{\mathrm{I}}_1$

.

The Game between Different Types of Enterprises under Market Competition

This type of game takes place between core and non-core enterprises and consists of the following four possible combinations of strategies, and the game payment matrix is shown in Table 1.

(1) Both core and non-core enterprises choose conventional technology. At this time, both core and non-core enterprises have their business layout in the mainstream market, in which the market share of core enterprises is $\frac{a{q}_1}{a+1}$ and the expected return is $\frac{a\left(P-C\right)q_1}{a+1}-I_1$; the market share of non-core enterprises is $\frac{q_1}{a+1}$ and the expected return is $\frac{{\left(P-C\right)q}_1}{a+1}-I_1$.

(2) Core enterprises choose conventional technology, while non-core enterprises choose AI technology. At this time, the AI technology innovation is initiated by the non-core enterprise, and although the non-core enterprise erodes its original mainstream market share of $\frac{e{q}_1}{a+1}$ due to technological cannibalization, it obtains the full market share of the non-mainstream market, as well as the mainstream market share of $e{q}_1$. Therefore, the non-core enterprise’s expected return is $\left[P-\left(1-\alpha \right)C\right]\left[\frac{{\left(1-e\right)q}_1}{a+1}+e{q}_1+q_2\right]-I_2$; the core enterprise’s market share due to the invasion of AI technology becomes $\frac{\left(1-e\right)a{q}_1}{a+1}$, with an expected return of $\frac{\left(1-e\right)a\left(P-C\right)q_1}{a+1}-I_1$.

(3) Non-core enterprises choose conventional technology, while core enterprises choose AI technology. At this time, the AI technology innovation comes from the core enterprise. Similarly, the expected return to the core enterprise is $\left[P-\left(1-\alpha \right)C\right]\left[\frac{\left(1-e\right){aq}_1}{a+1}+e{q}_1+q_2\right]-I_2$, and the non-core enterprise’s expected return is $\frac{\left(1-e\right)\left(P-C\right)q_1}{a+1}-I_1$.

(4) Both core and non-core enterprises choose AI technology. At this time, the core enterprise obtains a market share of $\frac{a{q}_1}{a+1}$ in the mainstream market and $\frac{a{q}_2}{a+1}$ in the non-mainstream market, with an expected return of $\frac{a}{a+1}\left\{\left(P-C\right)q_1+\left[P-\left(1-\alpha \right)C\right]q_2\right\}-I_2$. The non-core enterprise obtains a market share of $\frac{q_1}{a+1}$ in the mainstream market and $\frac{q_2}{a+1}$ in the non-mainstream market, with an expected return of $\frac{1}{a+1}\left\{\left(P-C\right)q_1+\left[P-\left(1-\alpha \right)C\right]q_2\right\}-I_2$.

The Game between the Same Type of Enterprises under Market Competition

This type of game is occurring between core enterprises and core enterprises, and non-core enterprises and non-core enterprises, assuming that the same types of enterprises have the same competitive strength, so that for the above game with $a=1$, we can obtain the game payment matrix between the same types of enterprises under the market competition, as shown in Table 2.

3.2.4. Game Modeling under Policy Incentives

The second stage of AI technology diffusion is the policy incentive stage in which policies are introduced for guidance, so this paper establishes the game payment matrix under policy incentives by introducing the subsidy policy and the enterprise high-tech recognition policy on the basis of the market competition game model, as shown in

Table 3. Payment matrix for the game between different types of enterprises under policy incentives.

		Non-Core Enterprises
		AI Technology	Conventional Technology
Core enterprises	AI technology	$\frac{\mathrm{a}}{\mathrm{a}+1}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2+\mathrm{S}$	$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{\left(1-\mathrm{e}\right){\mathrm{a}\mathrm{q}}_1}{\mathrm{a}+1}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2+\mathsf{\theta }\right]-{\mathrm{I}}_2+\mathrm{S}$
		$\frac{1}{\mathrm{a}+1}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2+\mathrm{S}$	$\left(\mathrm{P}-\mathrm{C}\right)\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{\mathrm{a}+1}-\mathsf{\theta }\right]-{\mathrm{I}}_1$
	Conventional technology	$\left(\mathrm{P}-\mathrm{C}\right)\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{a}\mathrm{q}}_1}{\mathrm{a}+1}-\mathsf{\theta }\right]-{\mathrm{I}}_1$	$\frac{\mathrm{a}\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{\mathrm{a}+1}-{\mathrm{I}}_1$
		$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{\mathrm{a}+1}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2+\mathsf{\theta }\right]-{\mathrm{I}}_2+\mathrm{S}$	$\frac{{\left(\mathrm{P}-\mathrm{C}\right)\mathrm{q}}_1}{\mathrm{a}+1}-{\mathrm{I}}_1$

and

Table 4. Payment matrix for the game between the same types of enterprises under policy incentives.

		Enterprise 2
		AI Technology	Conventional Technology
Enterprise 1	AI technology	$\frac{1}{2}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2+\mathrm{S}$	$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{\left(1-\mathrm{e}\right){\mathrm{q}}_1}{2}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2+\mathsf{\theta }\right]-{\mathrm{I}}_2+\mathrm{S}$
		$\frac{1}{2}\left\{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1+\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]{\mathrm{q}}_2\right\}-{\mathrm{I}}_2+\mathrm{S}$	$\left(\mathrm{P}-\mathrm{C}\right)\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{2}-\mathsf{\theta }\right]-{\mathrm{I}}_1$
	Conventional technology	$\left(\mathrm{P}-\mathrm{C}\right)\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{2}-\mathsf{\theta }\right]-{\mathrm{I}}_1$	$\frac{\left(\mathrm{P}-\mathrm{C}\right){\mathrm{q}}_1}{2}-{\mathrm{I}}_1$
		$\left[\mathrm{P}-\left(1-\mathsf{\alpha }\right)\mathrm{C}\right]\left[\frac{{\left(1-\mathrm{e}\right)\mathrm{q}}_1}{2}+\mathrm{e}{\mathrm{q}}_1+{\mathrm{q}}_2+\mathsf{\theta }\right]-{\mathrm{I}}_2+\mathrm{S}$	$\frac{{\left(\mathrm{P}-\mathrm{C}\right)\mathrm{q}}_1}{2}-{\mathrm{I}}_1$

.

The Game between Different Types of Enterprises under Policy Incentives

This type of game takes place between core and non-core enterprises and consists of the following four possible combinations of strategies, and the game payment matrix is shown in Table 3.

(1) Both core and non-core enterprises choose conventional technology. Since the government does not implement punitive measures for enterprises not adopting AI technology but increases the profits of enterprises adopting AI technology through subsidies, enterprise high-tech recognition, etc., the expected returns of core and non-core enterprises at this time are the same as those in Table 1, i.e., the expected return of the core enterprise is $\frac{a\left(P-C\right)q_1}{a+1}-I_1$ and the expected return of the non-core enterprise is $\frac{{\left(P-C\right)q}_1}{a+1}-I_1$.

(2) Core enterprises choose conventional technology, while non-core enterprises choose AI technology. At this time, non-core enterprises will reduce costs and increase profits because of the government subsidy, and the government subsidy to enterprises for adopting AI technology is recorded as $S=\beta C$. Because of the enterprise high-tech recognition and increased market share, non-core enterprises will be damaged by the asymmetry of market knowledge. If the enterprise high-tech recognition has an impact of $\theta$, then the increase in enterprise market share should be reported as $\theta$. Therefore, the expected return of the non-core enterprise is $\left[P-\left(1-\alpha \right)C\right]\left[\frac{{\left(1-e\right)q}_1}{a+1}+e{q}_1+q_2+\theta \right]-I_2+S$, and that of the core enterprise is $\left(P-C\right)\left[\frac{{\left(1-e\right)aq}_1}{a+1}-\theta \right]-I_1$.

(3) Non-core enterprises choose conventional technology, while core enterprises choose AI technology. Similarly, it can be seen that the expected return of the core enterprise is $\left[P-\left(1-\alpha \right)C\right]\left[\frac{\left(1-e\right){aq}_1}{a+1}+e{q}_1+q_2+\theta \right]-I_2+S$ and the expected return of the non-core enterprise is $\left(P-C\right)\left[\frac{{\left(1-e\right)q}_1}{a+1}-\theta \right]-I_1$ at this point.

(4) Both core and non-core enterprises choose AI technology. At this point, the expected return for the core enterprise is $\frac{a}{a+1}\left\{\left(P-C\right)q_1+\left[P-\left(1-\alpha \right)C\right]q_2\right\}-I_2+S$; the expected return for the non-core enterprise is $\frac{1}{a+1}\left\{\left(P-C\right)q_1+\left[P-\left(1-\alpha \right)C\right]q_2\right\}-I_2+S$.

The Game between the Same Types of Enterprises under Policy Incentives

This type of game occurs between core enterprises and core enterprises, and non-core enterprises and non-core enterprises, assuming that the same types of enterprises have the same competitive strength, so that $a=1$ in the above game, and we can obtain the game payment matrix between the same types of enterprises under the policy incentives, as shown in Table 4.

3.3. Evolutionary Rules

In this paper, the Fermi update rule is chosen as the enterprise strategy update rule. Compared with the replication update rule and the learning optimal rule, which are deterministic update rules, the Fermi update rule comprehensively examines the influence of external noise on the evolutionary game, which better takes into account the irrational decision-making in the decision-making process of the enterprise and is more in line with the reality of the enterprise game scenario.

In each game, each enterprise randomly chooses one of its neighboring enterprises to compare its returns to determine its strategy choice in the next game. The probability that enterprise $i$ learns the strategy of its neighbor enterprise $j$ is as follows:

$$P_{\left(s_i\to s_j\right)}=\frac{1}{1+exp\left[\left(U_i-U_j\right)/k\right]}$$

where $s_i$ and $s_j$ are the strategies adopted by enterprises $i$ and $j$ in the current round, respectively, and $U_i$ and $U_j$ are the expected returns in the current game cycle for enterprises $i$ and $j$, respectively.

The above function indicates that in the process of this game, if the expected return of enterprise $i$ is lower than the expected return of enterprise $j$, it is easy for enterprise $i$ to accept the strategy of enterprise $j$. If the expected return of enterprise $i$ is higher than the expected return of enterprise $j$, enterprise $i$ will still take the strategy of enterprise $j$ with a weak probability. $k$ is the random noise in the strategy updating process, which indicates the environmental noise in the strategy learning process and represents the degree of irrationality of enterprises. When $k$ is close to 0, it indicates that the game subject has high rationality and great probability to learn the strategy of the neighbor whose return is higher than its own. When $k$ tends to infinity, it indicates that the game subject learns the neighbor’s strategy with a completely random probability and cannot make a rational choice. According to the degree of rational decision-making of enterprises in reality, this paper sets $k=0.2$.

4. Numerical Simulation Analysis

4.1. Simulation Steps and Initial Value Setting

Based on the above model setting, combined with the existing research paradigms, Matlab software 2018b is used to analyze the evolution process and results of the diffusion of AI technology. Specifically, it can be divided into the following four steps.

Step 1: Scenario generation. Since the enterprises have unequal influence in the industry and the market presents a more monopolistic character, this paper constructs an AI technology diffusion network containing $N$ nodes based on the generation rules of the BA scale-free network, and the nodes in the network represent each enterprise in the game. Randomly initialize the strategies of core and non-core enterprises, where the number of enterprises adopting AI technology strategies under the initial conditions is smaller than the number of enterprises adopting conventional technology strategies, and initialize the relevant parameters of the evolutionary game model based on the information of government policies, industry reports, etc., as shown in

Table 5. Parameter initial value setting.

Parameter	Numerical Value	Parameter	Numerical Value
number of enterprises $N$	200	average demand from enterprises in the mainstream market $q_1$	2000/N
proportion of core enterprises $r_c$	0.2	average demand from enterprises in the non-mainstream market $q_2$	500/N
proportion of non-core enterprises $r_n$	0.8	coefficient of relative advantage of core enterprises $a$	2
product unit price $P$	100	proportion of AI technology products in the mainstream market $e$	0.25
cost per unit of product produced using conventional technology $C$	40	AI technology subsidy factor $\beta$	10%
opportunity cost $I_1$	20	the influence of enterprise high-tech recognition, i.e., increase in market share of enterprises $\theta$	10%
cost of AI technology $I_2$	50	network average degree $K$	6
cost reduction factor $\alpha$	0.1	noise factor $k$	0.2

. $P$, $C$, $I_1$, and $I_2$ are ten thousand quantities.

Step 2: Conduct an evolutionary game among enterprises, calculate the expected returns of each enterprise, and make strategy adjustments according to the Fermi update rule.

Step 3: Repeat Step 2 until asymptotic stabilization and a predefined evolutionary duration $T$ is reached.

Step 4: Repeat the simulation of Step 2 and Step 3 several times and analyze the average of the results of several independent runs to reduce the error caused by the stochastic process, so as to better reflect the general trend of the proliferation of AI technology. In this paper, we refer to related research [5] and set the number of independent runs to 50.

The simulation results show that the evolution results under each parameter value basically reach a stable state when 100 cycles have evolved, so the evolution duration $T$, i.e., the number of simulation iterations, is set to 100.

4.2. Simulation Analysis under Market Competition

This section explores the diffusion of AI technology in the natural competitive state of the market when there is no policy intervention from three perspectives: network average degree, the proportion of AI technology products in the mainstream market, and the cost of AI technology.

4.2.1. The Impact of Network Average Degree on AI Technology Diffusion

The network average degree can effectively reflect the density characteristics of the diffusion network, the higher the average value of the degree, the denser the network, the more frequent the inter-firm interactions, and the wider the scope of the enterprise learning and competitive objects. In order to analyze the influence of the complex network structure of enterprise relations on the diffusion of AI technology, this study sets different network average degrees (all even) to simulate the diffusion process of AI technology, and the specific evolution process is shown in Figure 1 and Figure 2. From Figure 1 and Figure 2, it can be seen that the higher the average degree of the network, the denser the network, the more frequent the competition and cooperation between enterprises, and the more conducive it is to the diffusion of AI technology, and at the same value of $K$, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises.

4.2.2. The Impact of the Proportion of AI Technology Products in the Mainstream Market on AI Technology Diffusion

The proportion of AI technology products in the mainstream market $e$ can reflect the degree of AI technology’s intrusion into the mainstream market from the non-mainstream market, which is one of the technical characteristics and is determined by the combination of the probability of invasion and the erosion ability of AI technology, and a higher value of $e$ indicates that the degree of subversion of the mainstream market is greater, i.e., the more extensive the scope is of the replacement of conventional technology. As can be seen from Figure 3 and Figure 4, with the same value of $e$, the diffusion proportion of AI technology in non-core enterprises is higher than that of its diffusion proportion in core enterprises, and with the increase in the value of $e$, the diffusion of AI technology becomes more and more extensive. The results show that since the correlation between non-core enterprises and the original enterprise network is not as strong as that of core enterprises, in the face of the invasion of the mainstream market by the emerging technology of AI technology, non-core enterprises are more motivated than core enterprises to try out the new technology without the constraints imposed by the original technological system and so on.

4.2.3. The Impact of the Cost of AI Technology on AI Technology Diffusion

The cost of AI technology belongs to one of the cost characteristics, which directly affects the profitability of the enterprise’s products, and is a fundamental element that influences the choice of the enterprise’s strategy. The cost of AI technology consists of three parts: one part is the opportunity cost due to not choosing AI technology $I_1$; one part is due to the additional AI technology cost generated by R&D investment, equipment purchase, personnel training, etc., $I_2$; and one part is that the enterprise reduces the cost per unit of product due to the adoption of AI technology, and the corresponding cost reduction factor is represented by $\alpha$. As can be seen from Figure 5 and Figure 6, for $I_1$, under the same value of $I_1$, the diffusion of AI technology in non-core enterprises is better than its diffusion in core enterprises, with higher values of $I_1$, i.e., the higher the opportunity cost, the higher the proportion of diffusion of AI technology, and there is little difference between the impact of changes in the value of $I_1$ on core and non-core enterprises. As can be seen from Figure 7 and Figure 8, for $I_2$, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises for the same value of $I_2$. A decrease in the value of $I_2$, i.e., a decrease in the additional cost of adopting AI technology, leads to a higher diffusion proportion of AI technology, and the effect of the change in the value of $I_2$ is more significant for core enterprises. From Figure 9 and Figure 10, it can be seen that for $\alpha$, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises under the same value of $\alpha$. The value of $\alpha$ rises, i.e., the cost of adopting AI technology per unit of product decreases, with the higher diffusion proportion of AI technology, and the change in the value of $\alpha$ has a more significant impact on core enterprises. The results show that core enterprises are more affected when technology costs change because their value networks are more complete compared to non-core enterprises.

4.3. Simulation Analysis under Policy Incentives

Based on the simulation analysis of the above basic model under market competition, this section introduces relevant policy factors to construct a policy incentive model and explores its impact on the diffusion of AI technology from the three aspects of subsidies for AI technology, high-tech recognition of enterprises, and the combination of the two.

4.3.1. The Impact of AI Technology Subsidy on AI Technology Diffusion

AI technology subsidies play an important role in the diffusion of AI technology, on the one hand, by supporting infrastructure development, and on the other hand, by lowering the cost of entry into the AI field for companies so that more companies can participate. As can be seen from Figure 11 and Figure 12, under the same value of AI technology subsidy coefficient $\beta$, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises; the higher the value of $\beta$ is, the more favorable it is to the diffusion of AI technology; and the change in the value of $\beta$ is more significant to the core enterprises. The results show that, because the institutional norms of core enterprises are more perfect compared with non-core enterprises, core enterprises are more affected when there are changes in the policy system.

4.3.2. The Impact of Enterprise High-Tech Recognition on AI Technology Diffusion

Enterprise high-tech recognition can effectively promote the diffusion of AI technology, including the enhancement of corporate image and market competitiveness, and the enhancement of financing capabilities. As can be seen from Figure 13 and Figure 14, under the same value of influence of enterprise high-tech recognition $\theta$, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises; the higher the value of $\theta$, the more favorable it is to the diffusion of AI technology; and the change in the value of $\theta$ has a more significant impact on core enterprises. Similar to the AI technology subsidy, because the institutional norms of core enterprises are more perfect compared with those of non-core enterprises, when there is a change in the policy system, the core enterprises are more affected.

4.3.3. The Impact of the Policy Combination of Technology Subsidies and Enterprise High-Tech Identification on AI Technology Diffusion

This part of the study lists five policy combination cases, representing five cases of $\beta$ and $\theta$ taking high values at the same time, low values at the same time, $\beta$ taking high values while $\theta$ takes low values, $\theta$ taking high values while $\beta$ takes low values, and $\beta$ and $\theta$ taking intermediate values at the same time. From Figure 15 and Figure 16, it can be seen that under the same value of $\beta$ and $\theta$, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises, and the impact of the change in the value of $\beta$ and $\theta$ on core enterprises is greater than its impact on non-core enterprises. For core enterprises, the policy combination conditions for AI technology diffusion rated from high to low are, in order, $\beta$ and $\theta$ taking the intermediate value at the same time, $\beta$ and $\theta$ taking the high value at the same time, $\theta$ taking the high value while $\beta$ takes the low value, $\beta$ and $\theta$ taking the low value at the same time, and $\beta$ taking the high value while $\theta$ takes the low value. For non-core enterprises, the policy combination conditions for the diffusion rate of AI technology from high to low are, in order, $\beta$ and $\theta$ taking high values simultaneously, $\theta$ taking high values while $\beta$ takes low values, $\beta$ and $\theta$ taking intermediate values simultaneously, $\beta$ taking high values while $\theta$ takes low values, and $\beta$ and $\theta$ taking low values simultaneously. The results show that increasing the values of $\beta$ and $\theta$ at the same time is necessary to facilitate the diffusion of AI technology in core and non-core enterprises and that increasing the value of only one of the parameters does not optimize the proportion of AI technology diffusion.

5. Conclusions and Insights

5.1. Conclusions

Based on the complex network evolution game theory, this paper constructs a game model of AI technology diffusion from the two levels of market competition and policy incentives, sets the initial value based on the information of government policies, industry reports, etc., and researches the influencing factors of AI technology diffusion and the role of policies through the method of simulation analysis. Firstly, the key factors affecting the diffusion of AI technology in market competition and their role mechanisms are explored from the perspectives of enterprise network characteristics, technology characteristics, and cost characteristics, and then, based on this, policy factors are introduced to explore the influence mechanism and policy effects of subsidy policy and enterprise high-tech recognition policy to help the diffusion of AI technology, and the evolution law of the diffusion of AI technology in the enterprise network is analyzed in depth. The research results show the following:

(1) The diffusion patterns of AI technology in core and non-core enterprises are different. The simulation results show that when the conditions of the technology cost and policy system are the same, the diffusion effect of AI technology in non-core enterprises is better than its diffusion effect in core enterprises. This reflects that compared with core enterprises, the correlation between non-core enterprises and the original enterprise network is relatively weak, therefore, in the face of AI technology, an emerging technology invading the mainstream market, non-core enterprises are more motivated than core enterprises to try the new technology without the constraints of the original technological system and other constraints. This positive adoption attitude of non-core enterprises towards AI technology is also a reminder to core enterprises to be wary of the technology lock-in effect, and that only by making efforts to innovate can they seize the window of opportunity in technological and industrial change.

(2) Compared with non-core enterprises, core enterprises are more obviously affected by changes in parameters such as technology costs and the policy system. Since the value network and institutional norms of core enterprises are more perfect compared to non-core enterprises, core enterprises are more affected when parameters such as the technology cost and policy system change.

(3) In the market competition, the diffusion of AI technology can be promoted from three aspects: enterprise network, technology, and cost. The simulation results show that with the increase in the network average degree, the proportion of AI technology products in the mainstream market, the opportunity cost, and the cost reduction factor can all promote the diffusion of AI technology to a certain extent, and similarly, the reduction in the cost of AI technology can also promote the diffusion of AI technology to a certain extent.

(4) Under policy incentives, both the proportion of the AI technology subsidy and the increase in the influence of enterprise high-tech recognition can promote AI technology diffusion to a certain extent. When the two act synergistically, only a simultaneous increase in the value of both can be conducive to the diffusion of AI technology in core and non-core enterprises, and only increasing the value of one of the parameters does not optimize the proportion of AI technology diffusion.

5.2. Management Insights

In order to accelerate the diffusion process of AI technology in industries and geographies where diffusion is slow, the findings of this paper have the following three management insights:

(1) The government should formulate practical innovation and development policies based on full consideration of the network characteristics of specific industries or geographic regions, make targeted changes to the network characteristics, technology characteristics, and cost characteristics of enterprises, and introduce relevant subsidy policies for AI technology as well as high-tech recognition policies for enterprises, in order to promote the diffusion of AI technologies and ultimately realize the balanced diffusion of AI technologies in various industries and regions. For example, the government can appropriately relax the market access restrictions of relevant industries or regions and improve the average degree of the enterprise network by strengthening the competition and cooperation among enterprises, so as to promote the diffusion of AI technology; the government can guide enterprises to increase the investment in the R&D of AI technology through the introduction of the policy of AI development planning and promote the diffusion of AI technology by increasing the proportion of AI technology products in mainstream market.

(2) Core enterprises’ attitude of avoidance and resistance to AI technology and the constraints of established systems have hindered the diffusion of AI technology in core enterprises. In the future, core enterprises should actively promote forward-looking innovation, actively explore the far-reaching impact of AI technology on enterprise development, and increase the possibility of AI technology being adopted by core enterprises, such as accelerating the construction of a perfect industrial ecosystem, actively promoting the application of AI technology throughout the entire industrial chain, and forming a benign ecological cycle, which will in turn promote the diffusion of AI technology. At the same time, core enterprises should also take measures to weaken the constraints of the existing technology system, institutional norms, value networks, etc., to avoid falling into the predicament of technology lock-in. For example, they should adopt a more flexible enterprise organizational structure, look for more flexible business partners and supply chain relationships, and build a more flexible value network.

(3) Because of their flexibility and innovativeness, non-core enterprises’ technology diffusion effect is better than that of core enterprises. In the development process, non-core enterprises should continue to take measures to maintain this flexibility and innovativeness to promote AI technology diffusion. For example, they should establish a rapid decision-making mechanism to respond quickly to market changes and the emergence of new technologies, reduce layers, and improve decision-making efficiency to ensure the rapid promotion of the diffusion of new technologies; actively participate in industry cooperation to accelerate the research and development and promotion of technologies, and to share resources and experience; and establish an open innovation platform to encourage both internal and external innovations, which will help to attract external innovators and partners, and to promote the diffusion of AI technology.

5.3. Limitations and Future Research Directions

This paper reveals the evolution law of the enterprise network in the social network on the adoption behavior of AI technology, which provides a scientific theoretical reference for promoting the diffusion of AI technology. However, there are also the following shortcomings: (1) This paper assumes that the number of enterprises and the network structure remain unchanged during the diffusion of AI technology; in fact, there is a bidirectional feedback relationship between the enterprise network and the diffusion of the technology, and in the future, we can pay attention to the evolution process of the diffusion of AI technology under the dynamic coupling of the two. (2) This paper constructs the game payment matrix based on market price and selects subsidy policy and recognition policy as the main policy influencing factors, and in the future, we can consider integrating a variety of policy factors to construct a more comprehensive game payment matrix.