Great Power Competition, Technology Substitution and Industrial Policy Coopetition: An Analysis Based on a Two-Country Game

Abstract

As the concept of national security and the nature of strategic competition evolve, industrial policy competition has increasingly become a defining feature of great-power competition. This study constructs a welfare function based on the analysis of industrial policy returns, employing a duopoly game model to explore the dynamics of competition and cooperation in the context of great-power competition. The findings suggest that in the short run, major powers tend to adopt strategic competition strategies, leading to instability in cooperation. In the long run, the realization and maintenance of cooperation depend on incentive mechanisms and penalty constraints. Specifically, a higher proportion of strategic industries raises the threshold for cooperation, making nations more likely to sustain short-term strategic competition. Sensitivity to technological gaps, however, facilitates the realization of long-term cooperation. When retaliatory subsidy probabilities are included, the stability of long-term cooperation hinges on the enforceability of the penalty mechanism. Furthermore, an infinite-horizon game does not necessarily lead to cooperation, and a finite punishment mechanism makes cooperation even more difficult. Numerical simulations are employed to validate the stability of the model, providing theoretical support for the strategic choices of latecomer countries in global industrial competition.

1. Introduction

In recent years, industrial policy has garnered increasing attention with intense debates surrounding it. Critics contend that industrial policies may distort markets, cause resource misallocation, thereby harming trade partners’ interests [1,2]. Conversely, proponents assert that industrial policies foster technological innovation and that international cooperation in policy could yield welfare benefits for all parties involved [3]. The heated discussions in academia stem from the practical implementation of industrial policies across different countries. As the new round of technological revolution and industrial transformation deepens, the competition among major powers around key core technologies and industries continues to intensify, with each country formulating industrial policies to develop their own advanced technology sectors in order to gain international competitive advantages. Lei [4] proposes that the essence of current major power competition is the competition of industrial policies, which is mainly reflected in the contention for cutting-edge technologies and market scale. Huang and He [5] argue that if emerging industries among nations exhibit competitive or even confrontational characteristics, then the implementation of industrial policies is necessary, as they can help emerging industries gain competitive advantages.

Following the financial crisis of 2008, U.S. governments have enacted policies to preserve the nation’s advanced manufacturing and technological leadership. With the rapid development of cutting-edge technologies in China, the U.S. has experienced status anxiety and views China as a strategic competitor. Across the Obama, Trump, and Biden administrations, U.S. industrial policy has been overhauled to technologically contain China, escalating external uncertainties for the country. Consequently, China has implemented policies to foster industrial technology development. It is evident that the interaction of industrial policies between nations is increasingly becoming a primary aspect of great power competition. Evenett et al. [6] find that the application of industrial policy by major economies exhibits a Tit-for-Tat characteristic. Specifically, the implementation of industrial policy by one country can provoke retaliatory actions from others. On average, the probability that a subsidy by a major economy in a particular industry will prompt another economy to subsidize the same industry within a year is as high as 73.8%. Their research also indicates that the current application of industrial policy is concentrated among major economies, with China, the EU, and the US accounting for 48%.

Consequently, as China undergoes industrial technological transformation, it will inevitably face dynamic competition from economies such as the US and the EU. On the one hand, to ensure their absolute dominance in cutting-edge technology and hinder the application of new technologies by emerging powers, these leading countries with advanced technology continue to make their industrial policies more explicit and strategic. On the other hand, the international development environment facing China remains severe, posing challenges to the formation of China’s industrial technological advantages. How should latecomer countries effectively respond to industrial competition from established powers? How can great powers achieve from competition to cooperation? These are issues that require further attention.

Against the backdrop of great power competition, industrial policy is no longer merely a tool to address market failures and enhance technological innovation. It has increasingly become a strategic instrument in the competition among major powers, serving to protect national security and promote strategic competition. In the face of technological containment, latecomer countries can strengthen their industrial policies to regulate market mechanisms and foster innovation domestically, and to elicit policy responses from their rivals internationally [7]. Traditional research on great-power competition and industrial policy has predominantly focused on perspectives from international relations and geopolitics, with less attention given to the economic logic and welfare effects of industrial policy in a systematic framework. To address this gap and contribute to the literature in this area, this study introduces a game-theoretic framework, incorporating the strategic attributes of industrial policy into an economic model. The study explores the strategic choices and interactions of major powers in the field of industrial policy from the perspective of welfare maximization.

Based on this framework, the study seeks to answer the following core questions: How do great powers engage in strategic competition and cooperation in industrial policy? How do technological substitution rates and the proportion of strategic industries become key variables influencing the game outcomes? Specifically, this study theoretically constructs a duopoly industrial policy game model, shedding light on the optimal decision-making mechanisms of great powers in technological competition, strategic deterrence, and policy response. First, the model introduces technological substitution rates and the proportion of strategic industries into the welfare function, illustrating the trade-offs between economic benefits, security benefits, and technological disparity benefits. Second, by analyzing the equilibrium results of both one-shot and repeated games, and incorporating response mechanisms such as Tit-for-Tat and trigger strategies, the study links these to discount factors and retaliation probabilities, revealing the conditions and pathways through which industrial policy transitions from competition to cooperation under different strategies. Third, building on the theoretical model, the study conducts numerical simulations of the evolutionary trajectories of strategies under varying key parameters, providing empirical insights into the dynamics of policy interaction.

The contributions of this study are as follows. First, it integrates the logic of strategic competition from international politics with the game-theoretic methods of economics, thereby constructing an analytical framework for the geostrategic shift in industrial policy. Second, the study incorporates technological substitution rates and the proportion of strategic industries into a quantifiable welfare model, while also introducing Tit-for-Tat and trigger strategies as behavioral mechanisms. This approach provides a parameterized foundation and a dynamic micro-foundation for future empirical research. Third, through an equilibrium analysis of the industrial policy game, the study proposes pathways for latecomer countries to mitigate risks, optimize industrial structures, and alleviate external technological containment pressures via technological innovation and policy coordination in an environment of external deterrence. In the context of great-power competition, this study offers new insights into the strategic choices of major countries regarding their competitive and cooperative relations, particularly in terms of their industrial policy games. These insights have significant theoretical and policy implications for enhancing international industrial technological cooperation and promoting the security and development of national industries.

2. Literature Review

Industrial policy, as a crucial tool for promoting technological innovation and industrial development, has long been a focal point of academic attention, particularly regarding its mechanisms and returns. In the context of the new wave of technology-driven geoeconomic competition, industrial policy has evolved from being a tool for correcting market failures and fostering innovation to becoming a central instrument for nations to shape technological advantages and safeguard industrial security. Helpman and Krugman [8] argue that profit shifting is the core driver of policy competition. In imperfectly competitive markets, countries adjust industrial or trade policies that not only affect the profits of domestic firms but also directly influence the economic interests of other countries through profit transfers. This cross-national interaction makes the industrial policy game increasingly complex and an integral part of international economic competition.

Against this backdrop, scholars have explored the role of industrial policy from various perspectives. From the technological innovation perspective, research focuses on how government intervention stimulates enterprise R&D and facilitates industrial upgrading [9]. From the perspective of policy externalities and spillover effects, studies analyze how industrial policy influences other countries’ industrial structures and the global supply chain through trade channels [10,11]. From the national security and strategic competition perspective, industrial policy’s role in safeguarding critical industries and enhancing national strategic competitiveness is examined [6,12,13]. Specifically, existing literature highlights four main areas of benefit from industrial policy.

First, the benefits of technological innovation. Industrial policy can promote innovation activities in high-tech industries through resource allocation and incentive mechanisms, thereby driving economic growth and technological progress. Schumpeter [14] emphasized in his innovation theory that technological innovation is the core driver of economic growth, and that industrial policy, as an institutional arrangement for innovation-driven development, plays a decisive role in determining a country’s position in technological competition. Recent studies further confirm that industrial policy significantly enhances national technological output and economic resilience by stimulating corporate R&D investment and promoting innovation diffusion effects [3,15].

Second, trade benefits. When industrial policy drives technological breakthroughs in key industries, it often leads to an improvement in export competitiveness. On the one hand, policy support enhances technological advantages of firms, increasing product value-added and thus boosting trade growth [2,16]. On the other hand, excessive policy intervention may distort trade [17]. Therefore, scholars emphasize the importance of balancing innovation promotion with market fairness to maximize the external benefits of industrial policy [18].

Third, the spillover effects of national security and strategic industries. The technological development of strategic industries plays a crucial role in maintaining national security and enhancing international competitiveness. Industries with dual-use applications not only promote economic growth but also strengthen defense capabilities [16]. Moreover, industrial policy increasingly incorporates economic security and national security considerations, with technological breakthroughs in key areas contributing to the strengthening of military power and potentially reshaping the balance of global military forces in the future [19,20].

Fourth, the benefits of technological gap. As the speed of global technological diffusion accelerates, the technological gap between countries has become a critical variable in determining their strategic competition. Tucker [21] noted that when the power and technological gap between two countries is large, their competitive relationship tends to be relatively mild. However, as the gap narrows, the intensity of competition increases significantly. For the latecomer, achieving breakthroughs in key technological areas can help expand their development space and international influence. From this perspective, leading powers, when formulating industrial policies, often balance technological catch-up with strategic defense, aiming to maximize the gains from technological convergence. The U.S. National Security Strategy also explicitly stated that “technology is the core of geopolitical competition”, and technological innovation capabilities have become a key factor in shaping great-power competition [22]. As a variable of national power, technology not only drives economic growth and industrial upgrading, but also serves as the foundation for international negotiations and institutional competition [19].

Grossman and Helpman [23] analyze how countries, in a non-cooperative equilibrium, use tariffs and subsidies to maximize their political and economic welfare. Their research shows that such strategies typically lead to overprotection, resembling a “prisoner’s dilemma” scenario, where each country’s protectionist policies seem beneficial in the short term, but result in global welfare loss from a broader perspective. Therefore, while countries seek to enhance competitiveness and secure market share through industrial policies, overprotection is often inevitable, particularly in the absence of effective international coordination. However, they also point out that only when the power balance of cross-national interest groups is sufficiently symmetrical, or through agreements covering all sectors, can deep liberalization agreements be achieved. This would ease competitive pressures, enabling countries to adopt industrial policies within a more cooperative framework and reach long-term agreements beneficial to the global economy. This theory provides strong support for understanding industrial policy in international games and offers significant insights for this study.

Currently, research on industrial policy under great-power competition tends to focus more on the fields of international relations and international politics [16,21]. On the one hand, studies in international relations provide a theoretical foundation for understanding the strategic competition logic between nations and the geopolitical motivations behind contemporary industrial policies. On the other hand, relying solely on an international relations perspective, without economic analytical tools, makes it difficult to clearly uncover the behavioral mechanisms behind government decisions and interactions in industrial policy. Therefore, an interdisciplinary approach is urgently needed to analyze strategies in industrial policy during great-power competition. By combining game theory from economics with power theory from international relations, this study aims to capture the dynamic logic of government policy interactions within the context of strategic competition. For the latecomer, effectively responding to strategic competition from other great powers requires strengthening industrial policies that foster domestic innovation and enhance external competitiveness. For technologically advanced incumbent powers, maximizing welfare involves controlling retaliatory actions and actively promoting cooperation among great powers.

Existing studies have mainly explored the mechanisms of industrial policy in four key areas: firstly, emphasizing the role of industrial policy in fostering innovation, focusing on how government intervention stimulates R&D and industrial upgrading. Secondly, discussing the external spillover effects of industrial policy, investigating how policies influence foreign industrial structures through trade. Thirdly, highlighting the security and strategic competition aspects of industrial policy, emphasizing its role in geopolitical competition, supply chain resilience, and national strategic competitiveness. And fourthly, examining the technological gap perspective, exploring how differences in technological accumulation, innovation capacity, and knowledge diffusion across countries influence policy responses, particularly how latecomer countries use industrial policy to catch up technologically. However, these studies generally adopt a single perspective and have yet to form a unified theoretical framework that integrates the four core dimensions—innovation, spillover, security, and technological gap—into a coherent model. As a result, they are unable to systematically explain the multiple mechanisms of industrial policy in great-power competition. To address this gap, this study constructs a duopoly industrial policy model within a game-theoretic framework, incorporating technological substitution rates, strategic industry proportions, and output into the welfare function. This model systematically characterizes the dynamic trade-offs that great powers face in balancing innovation incentives, policy spillovers, security defense, and technological gap adjustment. The model aims to reveal the strategic interaction logic of great powers in the field of industrial policy from the perspective of welfare maximization, thereby explaining the geostrategic characteristics and the cooperative-competitive dynamics of industrial policy.

In addition, this study draws on Wu [19] regarding the structure of great-power competition. In the global practice of great-power competition, many countries find themselves caught between their primary ally, the United States, and their largest trading partner, China, amidst escalating geopolitical and technological competition. These countries are unlikely to play a balancing role between the two powers. Regarding the two-country game model, numerous studies have already applied it to issues like trade frictions and arms races. In reference to the two-country game model framework proposed by Fourçans and Warin [24] for macroeconomic policy competition, and Wang [25] for policy game analysis, this study constructs a model of industrial policy competition between two countries, using latecomer countries and technologically advanced countries as examples. Building on these frameworks, the study incorporates Tit-for-Tat and trigger strategies into the model, examining how strategic adjustments by both parties, as well as the interaction of key influencing factors, affect the transition from competition to cooperation and the stability of cooperation. The analysis uncovers the critical parameters and behavioral mechanisms that shape great powers’ strategic choices in industrial policy, highlighting the conditions under which cooperation may emerge and be sustained.

3. Problem Description and Model Setup

3.1. Problem Description

Industrial policy, as a key tool for government intervention in the economy and promoting technological innovation, has increasingly demonstrated its strategic significance in the context of great power competition. In particular, in the geopolitical and economic environment marked by deglobalization and technological blockades, industrial policy has evolved from an economic tool designed to correct market failures to a strategic instrument for safeguarding national security and shaping international competitiveness. The competitive and defensive differences exhibited by some developed countries in their industrial policy implementation have led to a shift where industrial policy is no longer merely a domestic policy choice to foster innovation but has become a critical tool for interstate strategic games. This is especially evident in the case of the U.S. technological containment of China and China’s corresponding countermeasures. This has made the geostrategic trend of industrial policy in developed countries increasingly prominent, with latecomer countries needing to actively engage in strategic maneuvers to counteract such policies.

Based on this, the study constructs a duopoly game model within the framework of welfare maximization, incorporating key variables such as technological substitution rates, strategic industry proportions, and technological gaps. The model analyzes how two types of countries evolve into cooperation and competition equilibria in both one-shot and repeated games. Furthermore, the study employs numerical simulations to examine the relative strength of anxiety effects and deterrence effects, exploring the policy stability and welfare change paths. The study aims to address three core questions. First, how does industrial policy, through technological substitution rates, influence the equilibrium outcomes of policy games in the context of great-power competition? Second, how do strategic industry proportions and sensitivity to technological gaps determine the stability of cooperation between great powers? Third, how should latecomer countries respond to strategic competition in the context of external deterrence and technological blockades?

3.2. Parameter Settings

Setting 1: Technological Substitution Rate and Output Gains Assumption. Let the proportion of a country’s cutting-edge technology in the global technological frontier be denoted as $s\in \left[\mathrm{0,1}\right]$, representing the technological substitution rate. As sincreases, it indicates that the country holds a larger share of cutting-edge technologies, thereby enhancing the marginal contribution of technological innovation to economic output. Accordingly, the output gains resulting from technological innovation are given by $S=sY$, where $Y$ is the total economic output. The higher the technological substitution rate $s$, the greater the innovation benefits from industrial policy, thereby strengthening the country’s technological leadership in international competition.

Setting 2: International Trade Gains Assumption. Let the international trade gains induced by industrial policy be given by $E=\left(a{s}^2+bs\right)Y$, where $a<0, b>0$. This function reflects that an increase in the technological substitution rate leads to higher trade gains, but after a certain point, excessive competition and intensified trade friction result in diminishing marginal returns.

Setting 3: Strategic Industry Proportion and Security Spillover Assumption. Let the proportion of strategic industries in a country’s total economic output be denoted as $\phi \in \left[\mathrm{0,1}\right]$, which reflects the importance of strategic industries in the country’s national security and industrial structure. Strategic industries exhibit significant dual-use and security spillover characteristics. Their technological advancements not only improve economic efficiency but also enhance the country’s national security capabilities. The security spillover effect of strategic industries is represented as $D=s\phi Y$. As the proportion of strategic industries increases, the government places greater emphasis on security considerations in industrial policy, resulting in a deterrence effect that enhances the stability of cooperation.

Setting 4: International Technological Gap and Strategic Anxiety Assumption. Let the technological gap between the two countries be denoted as $\Delta s=s-s^e$, where $s^e$ represents the expected technological level of the rival country. When $\Delta s>0$, the country is technologically advanced; when $\Delta s<0$, it is in a catch-up position. The technological gap determines the competitive pressure and the level of strategic anxiety between the countries. As the technological gap narrows, strategic anxiety intensifies, and countries are more likely to increase their industrial policy interventions to prevent falling behind. The welfare difference due to the technological gap is expressed as $d=(s-s^e)Y$, where $Y$ is the total economic output.

Setting 5: Policy Benefits and Welfare Function Composition Assumption. The total welfare of a country in the industrial policy game can be expressed as:

$$V=s·Y+\alpha \left(a{s}^2+bs\right)Y+\beta ·s·\phi ·Y+\gamma \left(s-s^e\right)Y$$

(1)

The components of the total welfare function are as follows: first, industrial technological innovation gains; second, net international trade gains, where $\alpha$ represents the relative weight of net trade gains in total welfare, with $\alpha >0$; third, strategic industry benefits for national security, where $\beta$ represents the relative proportion of these benefits in total welfare, with $\beta >0$; forth, technological gap gains, where $\gamma$ represents the relative weight of excess returns from the technological gap in total welfare, with $\gamma >0$.

Table 1. Variables Description.

Variables	Description
s	Technological substitution rate
$s^e$	Expected technological substitution rate
$\phi$	Proportion of strategic industries
$Y$	Total economic output
$\alpha$	International trade gains weight
$\beta$	Policy security gains weight
$\gamma$	Technological gap gains weight

is a detailed description of the model variables.

3.3. Model Construction

Based on the above assumptions, the game payoff matrix for the two countries is shown in

Table 2. Payoff Matrix of the Two-Country Game.

		Country 2
		Dove	Hawk
Country 1	Dove	$(V_1^{D/D}$, $V_2^{D/D}$)	$(V_1^{D/H}$, $V_2^{D/H}$)
	Hawk	($V_1^{H/D}$, $V_2^{H/D}$)	$(V_1^{H/H}$, $V_2^{H/H}$)

.

Furthermore, we can obtain the return values of the strategy combination, as shown in

Table 3. Payoff of the Two Countries in the Game.

Strategy	Country 1	Country 2
$(V_1^{D/D}$, $V_2^{D/D}$)	$s_1{Y}_1+{\alpha }_1\left(a_1{s_1}^2+b_1{s}_1\right)Y_1+{\beta }_1{s}_1{\phi }_1{Y}_1$	$s_2{Y}_2+{\alpha }_2\left(a_2{s_2}^2+b_2{s}_2\right)Y_2+{\beta }_2{s}_2{\phi }_2{Y}_2$
$(V_1^{D/H}$, $V_2^{D/H}$)	$s_1{Y}_1+{\alpha }_1\left(a_1{s_1}^2+b_1{s}_1\right)Y_1+{\beta }_1{s}_1{\phi }_1{Y}_1$	$s_2{Y}_2+{\alpha }_2\left(a_2{s_2}^2+b_2{s}_2\right)Y_2+{\beta }_2{s}_2{\phi }_2{Y}_2+{\gamma }_2{s}_2{Y}_2$
($V_1^{H/D}$, $V_2^{H/D}$)	$s_1{Y}_1+{\alpha }_1\left(a_1{s_1}^2+b_1{s}_1\right)Y_1+{\beta }_1{s}_1{\phi }_1{Y}_1+{\gamma }_1{s}_1{Y}_1$	$s_2{Y}_2+{\alpha }_2\left(a_2{s_2}^2+b_2{s}_2\right)Y_2+{\beta }_2{s}_2{\phi }_2{Y}_2$
$(V_1^{H/H}$, $V_2^{H/H}$)	$s_1{Y}_1+{\alpha }_1\left(a_1{s_1}^2+b_1{s}_1\right)Y_1+{\beta }_1{s}_1{\phi }_1{Y}_1+{\gamma }_1\left(s_1{-s}_1^e\right)Y_1$	$s_2{Y}_2+{\alpha }_2\left(a_2{s_2}^2+b_2{s}_2\right)Y_2+{\beta }_2{s}_2{\phi }_2{Y}_2+{\gamma }_2\left(s_2{-s}_2^e\right)Y_2$

.

4. Analysis of the Equilibrium Mechanism of Industrial Policy Game Among Major Powers

4.1. Short-Run Equilibrium Analysis of the Interaction Between Industrial Policies and Strategies

In the short term, if both players adopt a cooperative strategy, neither will mislead the other’s expectations. Each will maintain the technological substitution rate that maximizes their welfare, with no motivation to further increase their rate at the expense of the other country’s technological development. The welfare level of Country 1 is given by

$$V_1^{D/D}=s_1·Y_1+{\alpha }_1\left(a_1{s_1}^2+b_1{s}_1\right)Y_1+{\beta }_1·s_1·{\phi }_1·Y_1$$

(2)

The welfare level of Country 2 is given by

$$V_2^{D/D}=s_2·Y_2+{\alpha }_2\left(a_2{s_2}^2+b_2{s}_2\right)Y_2+{\beta }_2·s_2·{\phi }_2·Y_2$$

(3)

In the short-term equilibrium

$${ s}_1^{\mathrm{*}D/D}={\displaystyle \frac{-\left(1+{\beta }_1{\phi }_1\right)-{\alpha }_1{b}_1}{2{\alpha }_1{a}_1}}, s_2^{\mathrm{*}D/D}={\displaystyle \frac{-\left(1+{\beta }_2{\phi }_2\right)-{\alpha }_2{b}_2}{2{\alpha }_2{a}_2}}, {\mu }_i=\left(1+{\beta }_i{\phi }_i\right)$$

(4)

$$V_1^{\mathrm{*}D/D}={\displaystyle \frac{-{\left({\mu }_1+{\alpha }_1{b}_1\right)}^2}{4{\alpha }_1{a}_1}}{Y}_1, V_2^{\mathrm{*}D/D}={\displaystyle \frac{-{\left({\mu }_2+{\alpha }_2{b}_2\right)}^2}{4{\alpha }_2{a}_2}}{Y}_2$$

(5)

If one player adopts a competitive strategy and the other adopts a cooperative strategy, one country will interfere with the other’s expectations.

$$s_1^{\mathrm{*}H/D}={\displaystyle \frac{-{\mu }_1-{\alpha }_1{b}_1-{\gamma }_1}{2{\alpha }_1{a}_1}}, s_1^e=0$$

(6)

$$s_2^{\mathrm{*}H/D}={\displaystyle \frac{-{\mu }_2-{\alpha }_2{b}_2}{2{\alpha }_2{a}_2}}, s_2^{\mathrm{*}\mathrm{e}H/D}={\displaystyle \frac{-{\mu }_2-{\alpha }_2{b}_2-{\gamma }_2}{2{\alpha }_2{a}_2}}$$

(7)

$$V_1^{\mathrm{*}H/D}={\displaystyle \frac{-{\left({\mu }_1+{\alpha }_1{b}_1+{\gamma }_1\right)}^2}{4{\alpha }_1{a}_1}}{Y}_1, V_2^{\mathrm{*}H/D}={\displaystyle \frac{2{\gamma }_2^2-{\left({\mu }_2+{\alpha }_2{b}_2\right)}^2}{4{\alpha }_2{a}_2}}{Y}_2$$

(8)

If both countries adopt competitive strategies and reach an extreme scenario, where they adjust their technological substitution rates in a confrontational manner, continuously limiting the other country’s technological development, resulting in a technological gap of zero, then ${s_1=s}_1^e\ne 0$ and ${s_2=s}_2^e\ne 0$.

$$s_1^{\mathrm{*}H/H}={\displaystyle \frac{-{\mu }_1-{\alpha }_1{b}_1-{\gamma }_1}{2{\alpha }_1{a}_1}}, { s}_2^{\mathrm{*}H/H}={\displaystyle \frac{-{\mu }_2-{\alpha }_2{b}_2-{\gamma }_2}{2{\alpha }_2{a}_2}}$$

(9)

$$V_1^{\mathrm{*}H/H}={\displaystyle \frac{{\gamma }_1^2-{\left({\mu }_1+{\alpha }_1{b}_1\right)}^2}{4{\alpha }_1{a}_1}}{Y}_1, { V}_2^{\mathrm{*}H/H}={\displaystyle \frac{{\gamma }_2^2-{\left({\mu }_2+{\alpha }_2{b}_2\right)}^2}{4{\alpha }_2{a}_2}}{Y}_2$$

(10)

Furthermore, we can obtain the payoff of two countries, as shown in

Table 4. Payoff Matrix of the Game.

		Country 2
		Dove	Hawk
Country 1	Dove	$V_1^{*D/D}={\displaystyle \frac{-{({\mu }_1+{\alpha }_1{b}_1)}^2}{4{\alpha }_1{a}_1}}{Y}_1$	$V_1^{*D/H}={\displaystyle \frac{2{\gamma }_1^2-{({\mu }_1+{\alpha }_1{b}_1)}^2}{4{\alpha }_1{a}_1}}{Y}_1$
		$V_2^{*D/D}={\displaystyle \frac{-{({\mu }_2+{\alpha }_2{b}_2)}^2}{4{\alpha }_2{a}_2}}{Y}_2$	$V_2^{*D/H}={\displaystyle \frac{-{({\mu }_2+{\alpha }_2{b}_2+{\gamma }_2)}^2}{4{\alpha }_2{a}_2}}{Y}_2$
	Hawk	$V_1^{*H/D}={\displaystyle \frac{-{({\mu }_1+{\alpha }_1{b}_1+{\gamma }_1)}^2}{4{\alpha }_1{a}_1}}{Y}_1$	$V_1^{*H/H}={\displaystyle \frac{{\gamma }_1^2-{({\mu }_1+{\alpha }_1{b}_1)}^2}{4{\alpha }_1{a}_1}}{Y}_1$
		$V_2^{*H/D}={\displaystyle \frac{2{\gamma }_2^2-{({\mu }_2+{\alpha }_2{b}_2)}^2}{4{\alpha }_2{a}_2}}{Y}_2$	$V_2^{*H/H}={\displaystyle \frac{{\gamma }_2^2-{({\mu }_2+{\alpha }_2{b}_2)}^2}{4{\alpha }_2{a}_2}}{Y}_2$

.

Proposition 1.

In the short term, the game has a unique equilibrium solution (Hawk, Hawk), which results in a Pareto suboptimal outcome, and the two countries cannot achieve cooperation.

Proof. 

For Country 1, given that Country 2 adopts a cooperative strategy, we have $V_1^{\mathrm{*}H/D}>V_1^{\mathrm{*}D/D}$. And when Country 2 chooses a competitive strategy, Country 1’s welfare is still higher when it adopts a competitive strategy compared to cooperation, $V_1^{\mathrm{*}H/H}>V_1^{\mathrm{*}D/H}$. Therefore, regardless of Country 2’s strategy, Country 1 always benefits more from a competitive strategy, and the welfare level is always higher than that of cooperation. Similarly, the same holds for Country 2. In the model of short-term, finite-stage games, both countries’ dominant strategy is competition, resulting in a unique equilibrium solution, namely (Hawk, Hawk). However, $V_1^{*D/D}>V_1^{\mathrm{*}H/H}$ and $V_2^{*D/D}>V_2^{*H/H}$, meaning that the welfare level of (Dove, Dove) is higher than (Hawk, Hawk), indicating the presence of a prisoner’s dilemma. Therefore, in a one-shot game, the two countries cannot achieve a Pareto optimal outcome, and cooperation is not feasible. □

4.2. Long-Term Equilibrium and Stability Path of Industrial Policy Interaction

The Pareto optimal welfare level in the (Dove, Dove) scenario is chosen as the benchmark. The welfare levels resulting from one player intentionally distorting the other country’s expectations are then compared to this benchmark. The welfare levels in the (Dove, Dove) case are $V_1^{\mathrm{*}D/D}$ and $V_2^{\mathrm{*}D/D}$, with welfare losses for both players set to zero at this benchmark.

If Country 1 adopts a competitive strategy while Country 2 adopts a cooperative strategy, the additional welfare gain for Country 1 is

$${EV}_1^{H/D}={\displaystyle \frac{-2\left({\mu }_1+{\alpha }_1{b}_1\right){\gamma }_1-{\gamma }_1^2}{4{\alpha }_1{a}_1}}{Y}_1$$

(11)

The welfare loss for Country 2 is

$${VL}_2^{H/D}=-{\displaystyle \frac{{\gamma }_2^2}{{2\alpha }_2{a}_2}}{Y}_2$$

(12)

If Country 1 adopts a cooperative strategy while Country 2 adopts a competitive strategy, the additional welfare loss for Country 1 is

$${VL}_1^{D/H}=-{\displaystyle \frac{{\gamma }_1^2}{{2\alpha }_1{a}_1}}{Y}_1$$

(13)

The additional welfare gain for Country 2 is

$${EV}_2^{D/H}={\displaystyle \frac{-2\left({\mu }_2+{\alpha }_2{b}_2\right){\gamma }_2-{\gamma }_2^2}{4{\alpha }_2{a}_2}}{Y}_2$$

(14)

If both countries adopt competitive strategies, the additional welfare loss for Country 1 is

$${VL}_1^{H/H}={\displaystyle \frac{{-\gamma }_1^2}{4{\alpha }_1{a}_1}}{Y}_1$$

(15)

The welfare changes for both countries, using (Dove, Dove) as the benchmark, are shown in

Table 5. Welfare increase (losses) for both parties based on the (Dove, Dove) benchmark.

		Country 2
		Dove	Hawk
Country 1	Dove	$V_1^{*D/D}$, Welfare losses = 0	$V_1^{*D/H}$, ${VL}_1^{D/H}=-{\displaystyle \frac{{\gamma }_1^2}{{2\alpha }_1{a}_1}}{Y}_1$
		$V_2^{*D/D}$, Welfare losses = 0	$V_2^{*D/H}$, ${EV}_2^{D/H}={\displaystyle \frac{-2\left({\mu }_2+{\alpha }_2{b}_2\right){\gamma }_2-{\gamma }_2^2}{4{\alpha }_2{a}_2}}{Y}_2$
	Hawk	$V_1^{*H/D}$, ${EV}_1^{H/D}={\displaystyle \frac{-2\left({\mu }_1+{\alpha }_1{b}_1\right){\gamma }_1-{\gamma }_1^2}{4{\alpha }_1{a}_1}}{Y}_1$	$V_1^{*H/H}$, ${VL}_1^{H/H}={\displaystyle \frac{{-\gamma }_1^2}{4{\alpha }_1{a}_1}}{Y}_1$
		$V_2^{*H/D}$, ${VL}_2^{H/D}=-{\displaystyle \frac{{\gamma }_2^2}{{2\alpha }_2{a}_2}}{Y}_2$	$V_2^{*H/H}$, ${VL}_2^{H/H}={\displaystyle \frac{{-\gamma }_2^2}{4{\alpha }_2{a}_2}}{Y}_2$

.

Proposition 2.

In the case of a long-term repeated game, when $\delta \ge {\delta }^{\mathrm{*}}$, both countries can achieve a cooperative equilibrium through strategic constraints.

Proof. 

In practice, the interaction of industrial policies between countries exhibits a “Tit-for-Tat” characteristic [6]. If either party deviates from cooperation, the other party will replicate the opponent’s strategy in the next period. □

Assume that both players start in the (Dove, Dove) state and use the same discount factor $\delta$ to discount future period payoffs. For Country 1, if it consistently chooses (Dove, Dove) in the infinitely repeated game, its additional welfare gain is zero.

If Country 1 deviates from cooperation and switches to competition, following the Tit-for-Tat strategy, an infinite sequence of outcomes such as (Hawk, Dove), (Dove, Hawk), (Hawk, Dove), and so on will occur. As a result, the net present value of the additional welfare gain for Country 1 is

$$E_1={EV}_1^{H/D}-\delta {VL}_1^{D/H}+{\delta }^2{EV}_1^{H/D}-{{\delta }^{3}VL}_1^{D/H}+\dots$$

(16)

The conditions for the sustainability of long-term cooperation are

$${\displaystyle \frac{{EV}_1^{H/D}}{1-{\delta }^2}}-{\displaystyle \frac{\delta {VL}_1^{D/H}}{1-{\delta }^2}}\le 0$$

(17)

We have

$$\delta \ge {\displaystyle \frac{{\mu }_1+{\alpha }_1{b}_1}{{\gamma }_1}}+{\displaystyle \frac{1}{2}}$$

(18)

where $2({\mu }_1+{\alpha }_1{b}_1)\ge {\gamma }_1$, ${\mu }_1=\left(1+{\beta }_1{\phi }_1\right)$.

The result is also symmetric for Country 2. Therefore, the minimum discount factor required for the stability of long-term cooperation can be expressed as

$${\delta }^{\mathrm{*}}={\displaystyle \frac{\left(1+\beta \phi \right)+\alpha b}{\gamma }}+{\displaystyle \frac{1}{2}}$$

(19)

where $2(1+\beta \phi +\alpha b)\ge \gamma$.

The discount factor $\delta$ can be understood as the level of patience of the game participants. A patient country, which considers the long-term benefits of cooperation and is more inclined to maximize future gains, will have a higher discount factor. When the government is sufficiently “patient” ($\delta \ge {\delta }^{\mathrm{*}}$), the long-term benefits of cooperation will outweigh the immediate gains from short-term competition, motivating both parties to sustain cooperation.

4.2.1. Analysis of the Equilibrium Mechanism Based on the Tit-for-Tat Strategy

When one country implements high-intensity industrial subsidies or technology restrictions in the previous period, the other country will retaliate or impose compensatory countermeasures with equal intensity in the following period. Under this mechanism, the maintenance of cooperation depends on two institutional forces. First, the strategic tension effect ($\phi$), which is the security spillover effect determined by the proportion of strategic industries; second, the self-restraint effect ($\gamma$), which refers to the policy effect triggered by a country’s sensitivity to changes in the technological gap.

Proposition 3.

The proportion of strategic industries ($\phi$) has a strategic tension effect. As $\phi$ increases, the technological game between countries becomes more sensitive and more likely to escalate into a security threat, thus raising the threshold ${\delta }^{\mathrm{*}}$for maintaining cooperation.

Proof. 

The partial derivative of the parameter $\phi$ is given by

$${\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial \phi }}={\displaystyle \frac{\beta }{\gamma }}>0$$

(20)

$${\displaystyle \frac{\partial V^{\mathrm{*}}}{\partial \phi }}=\beta sY>0$$

(21)

As $\phi$ increases, ${\delta }^{\mathrm{*}}$ also rises, indicating that long-term cooperation can only be sustained when $\delta$ is sufficiently high, thus narrowing the range for cooperation. However, an increase in the proportion of strategic industries also strengthens a country’s industrial security resilience, helping to create a deterrence effect externally. □

Proposition 4.

The sensitivity to the technological gap ($\gamma$) has a self-restraint effect. As $\gamma$ increases, a country becomes more inclined to maintain cooperation.

$${\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial \gamma }}=-{\displaystyle \frac{\beta \phi }{{\gamma }^2}}<0$$

(22)

As $\gamma$ increases, ${\delta }^{\mathrm{*}}$ decreases, indicating that a higher $\gamma$ raises the cost of competition, thereby encouraging countries to be more restrained and more willing to maintain cooperation.

4.2.2. Analysis of the Equilibrium Mechanism Based on the Trigger Strategy

In the context of long-term repeated games, when $\delta$ is sufficiently high, countries place greater emphasis on long-term institutional benefits, allowing cooperation to stabilize. However, when $\delta$ is lower, countries prioritize immediate gains, making them more likely to engage in retaliatory competition. Nonetheless, in practice, such retaliatory behavior is not inevitably triggered. Therefore, this section introduces the probability of retaliatory competition and examines its impact on the cooperation threshold.

Proposition 5.

Under a trigger strategy with a retaliatory subsidy probability $\rho \in \left[\mathrm{0,1}\right]$, and given the discount factor $\delta$, the minimum retaliatory probability required for sustained cooperation is ${\rho }^{\mathrm{*}}\left(\delta \right)$. Cooperation will be maintained as long as $\rho \ge {\rho }^{\mathrm{*}}\left(\delta \right)$.

Proposition 6.

Under a trigger strategy with a retaliatory subsidy probability $\rho \in \left[\mathrm{0,1}\right]$ and a punishment duration of $T$ periods, cooperation becomes more difficult to maintain.

Proof. 

If a country deviates in a single period, it gains a one-time deviation payoff ${EV}_1^{H/D}$. However, once a deviation occurs, starting from the next period, the other country will trigger a subsidy for that product or industry with probability $\rho \in \left[\mathrm{0,1}\right]$. If triggered, during the punishment phase, the deviating country will receive ${VL}_1^{H/H}$ in each period. □

(1)

The case of a permanent punishment ($\mathit{T}\to \mathrm{\infty }$)

If a deviation occurs at $t=0$, the expected discounted loss for the deviating party is,

$$\rho \sum _{t=1}^T{\delta }^T·{VL}_1^{H/H}$$

(23)

Therefore, the no-deviation constraint is

$${EV}_1^{H/D}\le \rho \sum _{t=1}^T{\delta }^T·{VL}_1^{H/H}$$

(24)

Further simplification yields

$${\displaystyle \frac{-2\left({\mu }_1+{\alpha }_1{b}_1\right){\gamma }_1-{\gamma }_1^2}{4{\alpha }_1{a}_1}}{Y}_1\le \rho \sum _{t=1}^T{\delta }^T·{\displaystyle \frac{{-\gamma }_1^2{Y}_1^2}{4{\alpha }_1{a}_1}}={\displaystyle \frac{-{\gamma }_1^2{Y}_1^2}{4{\alpha }_1{a}_1}}·{\displaystyle \frac{\delta \left(1-{\delta }^T\right)}{1-\delta }}$$

(25)

Note $G_1={EV}_1^{H/D}$, $P_1={VL}_1^{H/H}$.

As $T\to \mathrm{\infty }$, we have

$$G_1\le {\rho P}_1{\displaystyle \frac{\delta }{1-\delta }}$$

(26)

Then,

$$\delta \ge {\displaystyle \frac{G_1}{G_1+{\rho P}_1}}={\delta }^{\mathrm{*}}\left(\rho \right)$$

(27)

The partial derivative of ${\delta }^{\mathrm{*}}\left(\rho \right)$ with respect to $\rho$ is

$${\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial \rho }}<0,{\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial P_1}}<0,{\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial G_1}}>0$$

(28)

Further, we have

$${\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial \phi }}>0,{\displaystyle \frac{\partial {\delta }^{\mathrm{*}}}{\partial \gamma }}<0$$

(29)

That is, as the proportion of strategic industries ($\phi$) increases, the threshold for cooperation between countries becomes higher; as the sensitivity to technological gap ($\gamma$) increases, cooperation becomes easier to sustain, which is consistent with Propositions 3 and 4.

$${\rho }^{\mathrm{*}}\left(\delta \right)={\displaystyle \frac{G_1}{P_1}}·{\displaystyle \frac{1-\delta }{\delta }}$$

(30)

Cooperation can be sustained as long as $\rho >{\rho }^{\mathrm{*}}\left(\delta \right)$.

(2)

The case of finite punishment (punishment for $\mathit{T}$ periods only)

If the punishment lasts for $T$ periods, the no-deviation constraint is,

$$G_1\le {\rho P}_1{\displaystyle \frac{\delta \left(1-{\delta }^T\right)}{1-\delta }}$$

(31)

Multiplying both sides of Equation (28) by $1-\delta$ and simplifying, we obtain

$$\rho P{\delta }^{T+1}-\left(G_1+{\rho P}_1\right)\delta +G_1=0$$

(32)

Let the unique root of the equation in the interval $\left(\mathrm{0,1}\right)$ be denoted as ${\delta }^{T^{\mathrm{*}}}$. The condition for sustaining cooperation is

$$\delta {\ge \delta }^{\mathrm{*}}\left(T\right)$$

(33)

Here, ${\delta }^{T^{\mathrm{*}}}\in ({\delta }^{\mathrm{*}}\left(\rho \right),1)$, and ${\displaystyle \frac{G_1}{G_1+{\rho P}_1}}={\delta }^{\mathrm{*}}\left(\rho \right)$ represents the threshold for permanent punishment. Therefore, compared to indefinite punishment, finite punishment makes cooperation more difficult to sustain.

If ${\rho P}_{1}T\le G_1$, Therefore, for any $\delta$, and thus cooperation cannot be sustained.

Specifically, when $T=1$, ${\delta }^{\mathrm{*}}(1)=\mathrm{m}\mathrm{i}\mathrm{n}\{1,{\displaystyle \frac{G_1}{\rho P_1}}\}$. If $\rho P_1\le G_1$, then a single-period punishment is insufficient to constrain deviation.

If ${\rho P}_{1}T>G_1$, Equation (29) has a unique root ${\delta }^{T^{\mathrm{*}}}$.

4.3. Numerical Simulation Analysis

4.3.1. Parameter Initialization Settings

To perform numerical simulations and model analysis, this study initializes the parameters based on the theoretical framework, referencing existing literature. The data used are sourced from WIPO, World Bank, IMF, CEPII-BACI, SIPRI, and computed and organized accordingly.

The technological substitution rate ($s$) represents the proportion of a country’s frontier technologies. In this study, the centrality of the country’s key and emerging technologies network is used as a proxy indicator. For example, the values for the United States and China are 0.87 and 0.77, respectively.

The expected technological substitution rate ($s^e$) is the anticipated substitution rate for the opponent’s country. This study assumes $s^e=s-0.1$.

The proportion of strategic industries ($\phi$) is represented by the share of high-tech products in total manufacturing exports. For the United States and China, the values are 0.21 and 0.31, respectively.

Economic output ($Y$) is normalized to 1 for the sake of simplicity in the analysis.

The international trade benefit weight ($\alpha$) is represented by a country’s trade network centrality. The policy security benefit weight ($\beta$) is represented by the proportion of military spending in total economic output. The technological gap benefit weight ($\gamma$) is represented by the similarity in key and emerging technology niches between countries. To simplify the calculations, these three parameters are standardized and then multiplied by 100. For the United States, $\alpha =56$, $\beta =2$, and $\gamma =42$; for China, $\alpha =55$, $\beta =1$, and $\gamma =44$.

In the welfare function, the parameters $a$ and $b$ for international trade are assumed to be such that the turning point for technological substitution is 1, meaning that excessive technological competition does not lead to welfare loss. To simplify the calculation, we set $a=-0.1$ and $b=0.2$.

The discount factor ($\delta$) has a baseline value of 0.6, with a range of $\left[\mathrm{0,1}\right]$.

The retaliatory subsidy probability ($\rho$) is represented by the probability that a country subsidizes a product or industry, causing the other country to subsidize the same product or industry within one year. The baseline value is 0.74.

Table 6. Parameter Simulation Assignments.

Parameter	$\mathit{s}\_\mathit{u}\mathit{s}$	$\mathit{s}\_\mathit{c}\mathit{n}$	$\mathit{\phi }\_\mathit{u}\mathit{s}$	$\mathit{\phi }\_\mathit{c}\mathit{n}$	$\mathit{Y}$	$\mathit{\alpha }\_\mathit{u}\mathit{s}$	$\mathit{\alpha }\_\mathit{c}\mathit{n}$	$\mathit{\beta }\_\mathit{u}\mathit{s}$	$\mathit{\beta }\_\mathit{c}\mathit{n}$	$\mathit{\gamma }\_\mathit{u}\mathit{s}$	$\mathit{\gamma }\_\mathit{c}\mathit{n}$	a	b
Value	0.87	0.77	0.21	0.31	1	56	55	2	1	42	44	−0.1	0.2

shows the values for these parameters.

4.3.2. Numerical Simulation and Sensitivity Analysis

Figure 1 illustrates the equilibrium of the short-term game between two countries under different technological substitution rates. As shown in Figure 1, regardless of the technological positions of the countries, the equilibrium of the short-term game remains (Hawk, Hawk), donates as HH in Figure 1. This indicates that, in the short term, both countries tend to adopt competitive strategies. Despite the variation in the technological substitution rate, both countries prioritize their short-term interests, remaining in a competitive state and unable to cooperate. Figure 1 demonstrates that, in the short term, the technological substitution rate does not effectively promote the possibility of cooperation but rather intensifies competitive behaviors between the two countries.

Figure 2 illustrates the changes in the cooperation thresholds between the United States and China under different proportions of strategic industries. As shown in Figure 2, as the proportion of strategic industries increases, the cooperation thresholds (${\delta }^{\mathrm{*}}$) for both the United States and China also rise. This indicates that the United States tends to maintain a competitive stance in the game and requires higher incentives to sustain cooperation. For China, as the proportion of strategic industries increases, the cooperation threshold also rises, but it remains lower than that of the United States.

Figure 3 shows the trend of changes in the cooperation thresholds between the United States and China under different levels of technological gap sensitivity. As shown in Figure 3, as the sensitivity to the technological gap increases, the cooperation threshold for both countries tends to decrease. When the technological gap sensitivity is high, countries are more likely to feel the pressure of technological catching up, which increases the likelihood of cooperation and makes them more inclined to collaborate. This also suggests that when formulating industrial policies, it is essential to consider the dynamic changes in technological gap sensitivity and actively seek cooperative mechanisms to promote mutual interests.

Figure 4 illustrates the impact of technological gap sensitivity on cooperation thresholds under different proportions of strategic industries, using the United States as an example. As shown in Figure 4, on one hand, with a fixed level of technological gap sensitivity, an increase in the proportion of strategic industries makes it more difficult for the country to develop a cooperative mindset, thus confirming Proposition 5. On the other hand, with a fixed proportion of strategic industries, as technological gap sensitivity increases, the country becomes more likely to cooperate with others, thus confirming Proposition 6.

Figure 5 illustrates the impact of the intensity of retaliatory subsidy probability on cooperation thresholds, based on simulations using data from the United States. As shown in Figure 5, as the probability of retaliatory subsidies increases, countries are more likely to cooperate. This suggests that retaliatory subsidy probability functions as a credible threat, lowering the threshold for the discount factor required to sustain cooperation. In the context of great power competition, retaliatory subsidies are not just an economic tool but also a strategic move in the game, reducing the likelihood of other countries deviating from cooperation. Therefore, by setting up reasonable subsidy mechanisms, countries can promote industrial cooperation and reduce external competitive pressures.

Figure 6 shows the impact of punishment duration on cooperation thresholds, with simulations using data from the United States. As illustrated in Figure 6, as the punishment duration increases, the minimum discount factor required to sustain cooperation reaches 0.762, which is significantly higher than the threshold for retaliatory subsidies. This indicates that the deterrent effect of finite punishments is weaker than that of retaliatory subsidy probabilities, making cooperation harder to achieve and maintain. Furthermore, when the punishment duration $T<4$, the cooperation threshold equals 1, indicating that punishments lasting fewer than 4 periods are insufficient to constrain deviations, leading countries to choose a strategy of strategic competition.

5. Further Analysis and Research on Limitations

5.1. Practically Analysis of Industrial Policy Game Theory

Proposition 1 indicates that, in the short term, industrial policy games between major powers cannot achieve a cooperative equilibrium. In practice, this short-term non-cooperative equilibrium reflects the early stage of the geopolitical strategization of industrial policies. Leading countries, in an effort to prevent potential threats and maintain relative advantages, tend to adopt aggressive intervention strategies, leading to a dual reinforcement of policy anxiety and security defense. When the proportion of strategic industries is too large or the sensitivity to technological gaps is high, the strategic competition characteristic of this equilibrium becomes more pronounced, manifesting as a continuous rise in policies and a persistent decline in cooperation willingness. Therefore, although short-term equilibrium is stable, it is essentially a non-cooperative stable state. Only by transitioning to a long-term dynamic game can countries break out of this equilibrium trap and shift toward cooperative policy coordination.

Moreover, the result of this short-term game is that, while each country achieves welfare maximization individually, the total welfare at the collective level is lower than in the cooperative equilibrium. This non-cooperative equilibrium not only leads to a decline in resource allocation efficiency and an accumulation of policy costs, but it may also create negative spillover effects through global supply chains and technology innovation networks. Given the interdependence and coupling relationships between major economies in key industries and technology sectors, the resource misallocation triggered by policy games will propagate through global production networks, weakening the stability of the global division of labor. At the same time, measures such as competitive subsidies and export controls will trigger chain reactions in the multilateral trade system, amplifying systemic fluctuations and welfare losses.

The game between major powers is not a one-off event but rather consists of multiple repeated games. In short-term, finite games, the relationship between two countries often does not establish a stable cooperative relationship, usually resorting to mutual constraints through retaliation, sanctions, and similar actions. However, in a longer-term, infinite game, the chances for establishing a cooperative mechanism increase. By imposing credible threats for any deviation and using strategies such as Tit-for-Tat and Trigger strategies, cooperation between the two countries can be sustained under certain conditions in an indefinite game.

Proposition 2 suggests that strategic behavior between nations is often not a one-time decision, and the sustainability of long-term cooperation depends on two mechanisms. The first is the incentive mechanism, where future cooperation benefits outweigh the immediate gains from short-term deviations. The second is the punishment constraint mechanism, where any deviation from cooperation results in cumulative retaliatory losses in the future. In practice, this mechanism reflects the differences in strategic patience between countries and its impact on cooperation. When formulating industrial policies, countries must often balance immediate strategic competition with long-term cooperation. If the policy objectives primarily address strategic competition, countries’ “impatience” tends to lead to competitive and retaliatory measures, such as high subsidies and technology blockades, which are non-cooperative behaviors. This is particularly evident in critical technology fields, such as semiconductors, where the U.S. and Europe tend to adopt competitive strategies in response to China’s rise, raising the threshold for long-term cooperation. As the critical value of ${\delta }^{\mathrm{*}}$ rises, the strategic patience and future expectations required to sustain cooperation also increase. This means that cooperation equilibrium can only be sustained when countries maintain rational expectations about future cooperation benefits and establish institutional commitment mechanisms.

Proposition 3 states that as the proportion of strategic industries increases, the technological game between countries becomes more security-driven, raising the cooperation threshold. In reality, this phenomenon reflects the growing trend of the security and geopolitical dimension of industrial policies. As the share of strategic sectors, such as semiconductors and artificial intelligence, increases in a country’s economy, industrial policy gradually shifts from a tool for promoting innovation and efficiency to a strategic means of safeguarding industrial security and reducing external dependencies. Leading countries are also more likely to adopt retaliatory subsidies and export controls to reinforce the confrontational nature of their policies, which undermines the stability of cooperation. Each adjustment to their industrial policies could potentially represent a threat or containment action. In the game model, this is reflected by an increase in the discount factor ${\delta }^{\mathrm{*}}$ as the proportion of strategic industries ($\phi$) rises. This means that, in structures with a higher share of strategic industries, countries must demonstrate stronger patience and strategic foresight to maintain cooperation. If there is a trust deficit and insufficient long-term benefit expectations, cooperation equilibrium will be replaced by strategic competition.

Proposition 4 suggests that the higher a country’s sensitivity to the technological gap, the more likely it is to achieve cooperation in the long term. This mechanism is also evident in real-world international industrial competition. Although, in the short term, when technologically advanced countries realize that latecomer nations are accelerating their technological catch-up, the sensitivity to the technological gap rises, leading to technological anxiety. As a result, countries strengthen strategic competition through increased export controls, technology blockades, and similar measures. However, this anxiety also fosters long-term institutional cooperation. An increased sensitivity to the technological gap corresponds to greater attention to future benefits, which, although intensifying strategic competition, will ultimately make countries aware of the costs of total confrontation. As a result, they will shift toward limited cooperation mechanisms, such as standard coordination and rule-based governance.

Proposition 5 suggests that in strategies involving retaliatory subsidy probabilities, the stability of cooperation depends on the enforceability and credibility of the punishment mechanism. As the probability of retaliatory actions increases, a country is more likely to face immediate retaliation or equivalent countermeasures after deviating from cooperation, significantly raising the costs of short-term deviation. Consequently, the threshold for maintaining cooperation lowers, meaning cooperation can be sustained at a lower level of patience. In practical terms, Proposition 5 reflects a cooperative mechanism effect, where institutionalized, predictable retaliatory probabilities strengthen cooperation incentives, thereby ensuring the stability of long-term equilibrium. However, in systems lacking a clear retaliation mechanism or sufficient institutional enforcement, countries often underestimate the long-term costs of deviation from cooperation. This leads to short-sighted competition, where cooperative equilibrium is replaced by short-term strategic actions, making cooperation more fragile.

Proposition 6 suggests that when the retaliation mechanism is of finite duration, the stability of the cooperative equilibrium is constrained by the length of the punishment period. The implementation of a finite punishment period implies that the “retaliation” is limited, and its deterrent effect is weaker than that of permanent punishment. Therefore, greater patience, higher retaliation probability, larger single-period penalties, or longer punishment durations are needed to sustain stable cooperation. This proposition highlights the crucial role of punishment continuity in cooperation. If the duration of retaliation is limited, its deterrent effect weakens significantly, which may lead some countries to revert to competitive policies after the punishment period. Propositions 5 and 6 together suggest that the stability of industrial policy games between countries depends not only on their patience but also on the enforceability and continuity of institutional punishment mechanisms. Proposition 5 shows that the higher the institutional enforcement of retaliatory actions, the more stable the cooperation; Proposition 6 indicates that the stronger the punishment continuity, the more effective the deterrence. The former emphasizes whether retaliation will occur, enhancing cooperation willingness, while the latter emphasizes how long retaliation lasts, strengthening deterrence to prevent short-term deviations. These findings provide a theoretical basis for the dynamic balance between cooperation and competition in real-world international practice and offer an analytical framework for institutional design and policy evaluation.

5.2. Research Limitations

Overall, this study focuses on two types of countries—technologically advanced and catching-up nations—and constructs a theoretical industrial policy game framework. From the perspective of welfare maximization, it reveals the strategic behavior of major powers in technological competition and policy interactions. However, due to model limitations and the focus of the research, this study has certain constraints.

Although the two-country game model developed in this study effectively characterizes the strategic interaction mechanisms between the two types of countries in the field of industrial policy, it still has some limitations. The current global industrial policy competition and coordination landscape has become increasingly multipolar, and in practice, industrial policy games are not confined to competition and coordination between two countries but are more likely to manifest as a multilateral strategic interaction system. The main reason for using a two-country game model in this study is that technologically advanced countries have significant competitive and spillover effects on catching-up countries in areas such as technological innovation and industrial security. The relationship between these two countries also forms the core of global industrial policy competition. Therefore, the duopoly game framework helps maintain the interpretability of the model while revealing the fundamental mechanisms of industrial policy competition. However, this simplified setup means that the model cannot fully capture the policy responses and strategic linkages of other major economies such as the European Union, Japan, and South Korea. It does not comprehensively reflect the multipolar nature of the global industrial policy competition, thus limiting the model’s comprehensiveness to some extent. Future research could expand upon the theoretical framework presented in this study by developing a multilateral game model, incorporating the heterogeneity of additional participants to more comprehensively capture the complex evolution of global industrial policy games. This would also contribute to a deeper understanding of global industrial policy coordination mechanisms and policy spillover effects within a multipolar competition landscape.

The core goal of this study is to establish a theoretical analytical framework that reveals the strategic behavior of major powers in the field of industrial policy and the mechanisms of strategic interaction, but the model itself holds potential for numerical simulation and parameterization validation. Based on this, the study also attempts limited numerical simulations to validate the logical consistency and dynamic stability of the model. However, the numerical simulation part serves as an auxiliary verification of the theoretical model, visually demonstrating the impact of key parameter changes on the evolution of equilibrium strategies. Since the model is essentially normative and explanatory, numerical simulation is not the main focus of this study. However, its results further confirm the rationality and applicability of the theoretical derivations. Future research can further expand upon the theoretical framework in this study by setting specific values for key parameters and conducting larger-scale and more detailed numerical simulations on the dynamic evolution paths of different strategy combinations. This will help further test the stability and sensitivity of the model and contribute to extending the theoretical analysis into a quantitative policy analysis model.

6. Conclusions

Industry, as an important support for promoting economic structural transformation and development, is key to achieving high-quality economic growth for countries, and it is also an important aspect of maintaining national security and obtaining international competitive advantages. With the acceleration of a new round of technological revolution and industrial transformation, strategic competition among major powers mainly revolves around industrial policies targeting key core technology areas. Faced with a severe and complex international competitive environment, how to effectively respond to competition from developed economies? How can major powers accomplish from competition to cooperation? These have become urgent priorities for promoting China’s development and security. Based on a systematic review of relevant literature, this study explores the game process between major powers in terms of industrial policies following the logic below. First, considering the benefits of industrial policy, a welfare function for two countries is constructed, which serves as the basis for the theoretical analysis of this study. Second, building on previous research, this study uses a two-country game model to deeply analyze the equilibrium outcomes of single-shot and repeated games from the perspective of maximizing industrial policy welfare. Finally, under the condition of infinite repeated games, different outcomes for both parties under Tit-for-Tat and trigger strategies are discussed. Based on this, this study draws the following main conclusions.

In the short term, countries are more likely to fall into strategic competition, while the stability of long-term cooperation depends on the countries’ decision-making tendencies when balancing long-term benefits with short-term interests. An increase in the proportion of strategic industries and a rise in technological gap sensitivity will intensify the technological game and competition between countries, leading to fiercer strategic competition. This competition not only increases tensions between countries, reducing the sustainability of cooperation, but may also transmit through global production networks, further weakening the stability of global supply chains and the potential for international cooperation. At the same time, higher retaliatory subsidy probabilities reduce the intensity of short-term strategic competition, aiding the maintenance of cooperation equilibrium. When the punishment period is finite, its deterrent effect is weaker than that of permanent punishment. The stability of cooperation equilibrium is therefore constrained by the duration of punishment, and a longer punishment period is required to sustain stable cooperation. In the context of major power technological competition, stable cooperation requires not only a reasonable strategic industry structure but also the establishment of appropriate countermeasure probabilities, punishment durations, and effective policy mechanisms to promote long-term cooperation. The findings of this study not only complement the existing conclusions of infinite-horizon games but also provide valuable policy insights for policymakers.

Based on the above research, this study offers the following policy recommendations: Currently, strategic competition between major powers is intensifying. To address competition from other major powers, countries must maintain strategic focus in long-term games while ensuring sufficient preparation. First, as competition increasingly centers around strategic industries, China should strongly support key technology R&D, enhance independent innovation capabilities, reduce dependence on external technologies, and strengthen industrial security. At the same time, long-term cooperation incentive mechanisms should be established, and the penalty mechanisms within cooperation frameworks should be reinforced to improve the stability of cooperation. Second, while an increase in the proportion of strategic industries enhances national industrial security resilience, it also raises the cooperation threshold. Therefore, countries should adjust the proportion of strategic industries according to industrial development needs and avoid excessive strategization. Additionally, enhancing international cooperation through global supply chain partnerships can strengthen supply chain resilience. Third, increasing technological gap sensitivity fosters long-term cooperation by adjusting strategic directions based on changes in technological gaps, while maintaining flexibility in the evolving global competitive environment. Furthermore, to address external technology blockades and strategic containment, coordination between domestic and international industrial policies should be enhanced, and communication with other countries should be strengthened to avoid trade frictions and short-term disruptions caused by technological barriers. Fourth, in the face of increasingly fierce technological competition, setting appropriate subsidy policies and countermeasures can help guide international competitors’ actions and ensure the stability of long-term cooperation.