The Game Simulation of “The Belt and Road” Economic and Trade Network Based on the Asymmetric QRE Model

: This paper introduces the asymmetric Quantal Response Equilibria (QRE) network game model to explain the inﬂuencing factors on the cooperative behavior of "The Belt and Road" countries. The ﬁndings suggest that the belief in the sensitivity to own payo ﬀ and counterparts, the reward for cooperation by neighbor nodes, the trade facilitation index, and the reduction rate of tari ﬀ s were incorporated to have a signiﬁcant impact on the Belt and Road cooperation. Our ﬁndings provide important policy references to the belt and road countries.


Introduction
Over the past five years or so, China has engaged in extensive communication and coordination with participating countries and international organizations, and reached a broad consensus on international cooperation for building "The Belt and Road" (B&R). While committed to respecting the sovereignty and security concerns of all relevant countries, B&R countries have made concerted efforts to build an all-round, multi-level, and composite infrastructure framework centered on railways, roads, shipping, aviation, pipelines, and integrated space information networks. This framework is taking shape rapidly. It has greatly reduced the transaction costs of products, capital, information, and technologies flowing between regions, and effectively promoted the orderly flow and optimal allocation of resources among different regions. The efforts invested in the initiative have liberalized and facilitated trade and investment in the participating countries and regions, lowered the costs of trade and business, and releasing growth potential, enabling the participants to engage in broader and deeper economic globalization. Exploring investment and financing models, international multilateral financial institutions and commercial banks have played an innovative role in expanding the channels of diversified financing, providing stable, transparent, and quality financial support for the Belt and Road Initiative. The B&R countries have carried out diplomatic activities and cultural exchanges of various forms in wide fields, enhancing mutual understanding and recognition and laying a solid cultural foundation for furthering the initiative [1].
These achievements show that "The Belt and Road" is an important cooperation platform to jointly build, share mutually beneficial cooperation, and link up each country's development strategy. "The Belt and Road" has become the hottest topic of global politics and economy. Its development process directly affects the nerves of global public opinion and the community of shared future for Taking the countries shown in Table 1 as the nodes of the network, various economic and trade cooperation exists between the countries, the data on trade in goods reflect the state of trade cooperation among these countries, we obtained the bilateral trade data from 2008 to 2017 of these countries from UNCTDs [39]. There are a lot of developing countries along the "The Belt and Road", and there are political conflicts in some countries, while the bilateral trade between some countries is very small. Thus, in order to fully reflect the characteristics of the trade network of "The Belt and Road" countries and to avoid generating too many independent nodes, we took the value of the average bilateral trade volume for the decade 2008-2017 along "The Belt and Road" as the basis for judgment. Therefore, 10 million U.S. dollars was taken as the benchmark. If it was exceeded, it was determined that there was a trade relationship between the two countries. The corresponding value of its adjacency matrix was assigned a value of 1, otherwise, assigned 0. We applied UCINET software to draw up the "The Belt and Road" economic and trade network, the results as shown in Figure 1: and there are political conflicts in some countries, while the bilateral trade between some countries is 117 very small. Thus, in order to fully reflect the characteristics of the trade network of "The Belt and 118 Road" countries and to avoid generating too many independent nodes, we took the value of the 119 average bilateral trade volume for the decade 2008-2017 along "The Belt and Road" as the basis for 120 judgment. Therefore, 10 million U.S. dollars was taken as the benchmark. If it was exceeded, it was 121 determined that there was a trade relationship between the two countries. The corresponding value 122 of its adjacency matrix was assigned a value of 1, otherwise, assigned 0. 123 We applied UCINET software to draw up the "The Belt and Road" economic and trade network, 124 the results as shown in Figure 1: Transforming the "Belt and Road" complex network into a 65 × 65 relational matrix. In this 127 matrix, if there is a trade volume between countries that exceeds the set trade volume, there is a closer 128 economic and trade relationship between the two countries with a network connection between the 129 nodes. The total number of 1 in a row in the matrix is the number of neighbors for that line's 130 representative country. The degree of the node country measures the number of neighbors of the 131 node country, so it means the degree of the node is the total number of neighbors, which was set as 132 . 133 We calculated the degree of the nodes K = [6, 9, 9, 31, 27, 33, 44, 2, 18, 8, 46, 14, 63, 33, 17, 54, 26, 134 19, 46, 50, 61, 46, 42, 20, 36, 27, 36, 27, 10, 4, 30, 19, 35, 50, 2, 2, 8, 17, 4, 27, 41, 27, 57, 28, 17,

Asymmetrical QRE Model 137
The participants' thinking steps and their beliefs in other participants' sensitivity affect their 138 expected payoff and strategy choice [40]. QRE further expands the concept of equilibrium on the basis 139 of Nash equilibrium [41][42][43]. The theory holds that participants pursue rationality in their beliefs, but 140 Transforming the "Belt and Road" complex network into a 65 × 65 relational matrix. In this matrix, if there is a trade volume between countries that exceeds the set trade volume, there is a closer economic and trade relationship between the two countries with a network connection between the nodes. The total number of 1 in a row in the matrix is the number of neighbors for that line's representative country. The degree of the node country measures the number of neighbors of the node country, so it means the degree of the node is the total number of neighbors, which was set as N i .

Asymmetrical QRE Model
The participants' thinking steps and their beliefs in other participants' sensitivity affect their expected payoff and strategy choice [40]. QRE further expands the concept of equilibrium on the basis of Nash equilibrium [41][42][43]. The theory holds that participants pursue rationality in their beliefs, but inevitably make mistakes in calculating the expected utility of each strategy, which is determined by human's innate limited cognitive ability [20]. Therefore, in practice, the optimal choice under Nash equilibrium does not appear as probability 1, which means complete rationality. QRE is often expressed through logit model or exponential payoff reaction function: P(s i ) indicates the probability of i, one of the game participants, adopting s i strategy. Numerator indicates that when the probability of the other game participant adopting s −i strategy is P(s −i ), the expected return of i adopting s i strategy is s −i P(s −i )U i (s i , s −i ); Denominator indicates the total Sustainability 2019, 11, 3377 5 of 17 expected return of i when taking k strategies. The sign k is the number of all possible strategies that are available for i, and s i ∈ s k . QRE incorporates the endogenous factors in human decision-making into equilibrium analysis, and develops a balanced paradigm that is not based on complete rationality by modifying the behavior of participants [44]. This makes the equilibrium analysis of economics move one step further. The asymmetric QRE model can be obtained by incorporating the asymmetric cognition that participants always think they are smarter than others into the analysis of the game equilibrium. The logit form of asymmetrical QRE is defined as follows: P(s i ) and P(s −i ) indicate the probability of game participants, i and -i, adopting s i and s −i strategy respectively. λ i and λ −i express the belief in the sensitivity of own payoff and the sensitivity of their counterparts respectively.
In the asymmetric QRE model, the probability of i, one of the participants, adopting s i strategy is related to self-sensitivity cognition and expected utility of the other participants. The expected probability of other participants adopting s −i strategy is related to participants' beliefs in the sensitivity of their reactions and the expected utility of other participants. P(s i ) and P(s −i ) form a loop nesting relationship. This model can better explain that when the participants' perception of their own sensitivity is inconsistent with that of their counterparts' reaction sensitivity, the equilibrium of the game is not the optimal solution, and the phenomenon of sub-optimal selection may occur. The asymmetric QRE model was introduced into the game model of the economic and trade network of "The Belt and Road", which can better explain the sensitivity to payoff and the effect of the difference of decision steps on the equilibrium results. The endogenous factors of participating countries were incorporated into the analysis of the network game so that the conclusion would have a stronger explanatory power.

Model Assumptions
In "The Belt and Road" economic and trade network in Figure 1, the nodes represent countries and regions, and the edges in the network represent the game relationship among the network participants. Each country is a rational economic man, pursuing profit maximization. Whether or not these countries participate in "The Belt and Road" economic and trade network depends on whether the maximum benefits can be obtained from their participation. Based on the actual situation of "The Belt and Road" economic and trade network, the following assumptions were made for the model of the network game.

Hypothesis 1:
Assuming that each node country is homogeneous, the impact of economic and trade cooperation on each country is consistent and brings the same benefits to each country. The purpose of our study was to test the influence of factors on the trend of cooperative game, so this hypothesis would not substantially change the research results.

Hypothesis 2:
In a social dilemma, the income relationship generated by strategy combination must satisfy the following four conditions: R > P. Game players prefer to cooperate together rather than betray each other. R > S. Game players prefer to cooperate together rather than unilaterally. c.
2R > T + S, the benefits of joint cooperation are greater than the collective benefits of unilateral cooperation or unilateral betrayal. d.
T > R or P > S, the players prefer to betray unilaterally rather than cooperate together or the players prefer to betray jointly rather than cooperate unilaterally.
represents the strategy set of node i. There are two strategies for node i that are optional in the game, 1 for cooperation and 0 for betrayal. Therefore, the income payoff matrix can be obtained as shown in Table 2:

Hypothesis 3:
Participants choose cooperation and non-cooperation strategies according to probability, assuming that they cooperate according to probability P(s i ) and choose non-cooperation according to probability 1 − P(s i ).

Hypothesis 4:
Each node country is affected by its neighbor nodes. The neighboring nodes have close trade relations with them, and they can affect the game gain of the node through reward and penalty. Suppose the reward of the cooperative action given by each neighbor node is w ij , and the total reward that node i gets from its neighbors is j∈NBR w ij .

Hypothesis 5:
Assuming the trade facilitation index is f, which means the degree of trade facilitation promotes economic growth, the amount of economic growth brought about by trade facilitation is f*Y(i), and Y(i) is the average value of the GDP in 2008-2017 of the node country i.

Hypothesis 6:
Assuming that the economic and trade network community gives member countries a tariff rate reduction rate of r, r ∈ [0, 1], then the tax concession obtained by a member state joining the community is r multiplied by its total trade. Q (i, j) is the average value of trade volume in 2008-2017 between node i and node j. Table 3 provides the detailed descriptions of the above variables. Table 3. Description of variables.

Variable Description Range
The belief in the sensitivity to counterparts The reward of i of the cooperative action given by the neighbor node j [0, +∞) f The trade facilitation index The GDP of the node country i \ r The tariff reduction rate The trade volume between node i and node j \

Model Analysis
Based on the above assumptions, the total utility value of the node countries at time t is as follows: Introducing the asymmetrical QRE model: Combining with the game payoff matrix in Table 2, the values in the matrix are brought into the formulas (7) and (8), and the formulas (9) and (10) are obtained: In the network, countries will adjust their behavior strategies according to the revenue situation. When the cooperation revenue of the node countries is greater than the betrayal revenue, they will adopt the cooperation strategy, otherwise they will adjust to the betrayal strategy. Using N to represent the total number of nodes, and Nc to represent the number of collaborators. The Formula (7)-(10) is brought to the Formula (4), and the Formula (11) can be obtained: The equilibrium condition for node i to select the cooperation strategy is to satisfy: the benefit of cooperation ≥the benefit of defection, as is shown in Formulas (12) and (13): It can be seen from Formula (13) that the choice of strategy made by each node country of the Belt and Road network in a certain round of game is directly related to the reward for cooperation by neighbor nodes, the trade facilitation index, the tariff rate reduction rate, the return of strategies about cooperation and defection, and the probability value of neighbor nodes choosing cooperation. In addition, the probability of neighbor nodes choosing cooperation is directly related to the asymmetry of payoff sensitivity.

Analysis of Simulation Results
Based on the above model, we analyzed the influence of various factors on "The Belt and Road" economic and trade network through Matlab simulation. The simulation process is shown in Figure 2 and the basic algorithm code is shown in Appendix A.

The Belief in the Sensitivity to Own Payoff ( ) 252
When the values of other factors remain unchanged, suppose = 0, 0.1, 0.2, 1, 10, 500 253 respectively. The simulation results are shown in Figure 3. According to the four conditions of value selection in various situations of social dilemma of hypothesis (2), we set R = 5, S = -2, T = 6, P = 3 to simplify the model. This simplification did not make substantial changes to our final test results. Considering the range of λ i , λ j , and w, we adopted a value-taking strategy from a small to a large diffusion to test their influence on the cooperative game. At the same time, considering that the setting of the initial value should reflect its influence in the game process, that is, zero value is not desirable, we set λ i = 0.2, λ j = 0.2 and w = 0.5. According to the range of f and r, we adopted the strategy of median diffusion to test the influence on the cooperative game and it was very representative of the distribution sequence. Therefore, we set the initial values f = 0.5, r = 0.5. In the initial stage of the game, all countries randomly choose cooperation or betrayal strategies, so P (0) = 0.5. Such values not only fully consider the realities of "The Belt and Road" economic and trade network, but also make the simulation results show the influence trend and degree of various factors more clearly on the cooperative network. Next, we provided the simulation results in the sub sections. cooperators obtained by the game is decreasing. It can be seen that the growing belief in the 262 sensitivity of countries to their own payments will enable more countries to choose betrayal strategies 263 in "The Belt and Road" economic and trade network, which suggests that the belief in the sensitivity 264 to own payoff is negatively correlated with the equilibrium number of collaborators in the network. 265

The Belief in the Sensitivity to Counterparts ( ) 266
When the values of other factors remain unchanged, suppose = 0, 0.2, 1, 10, 500 respectively. 267 The simulation results are shown in Figure 4. 268 As can be seen from Figure 3, suppose the values of other factors remain unchanged: when λ i = 0, the number of cooperators is stable at 45 after three rounds of the game; when λ i = 0.1, the number of cooperators is stable at 41 after two rounds of the game; When λ i = 0.2, the number of cooperators is stable at 38 after two rounds of the game. Finally, when the value is large enough, the number of cooperators is 0. The results suggest that with the value λ i increasing, the stable number of cooperators obtained by the game is decreasing. It can be seen that the growing belief in the sensitivity of countries to their own payments will enable more countries to choose betrayal strategies in "The Belt and Road" economic and trade network, which suggests that the belief in the sensitivity to own payoff is negatively correlated with the equilibrium number of collaborators in the network.

The Belief in the Sensitivity to Counterparts (λ j )
When the values of other factors remain unchanged, suppose λ j = 0, 0.2, 1, 10, 500 respectively. The simulation results are shown in Figure 4.
As can be seen from Figure 4, suppose the values of other factors remain unchanged: when λ j = 0, the number of cooperators is stable at 40 after three rounds of the game; when λ j = 0.2, the number of cooperators is stable at 38 after one round of the game; when = 1, the number of cooperators is stable at 36 after two rounds of the game. Finally, when the value is large enough, the number of cooperators is 0. With the value increasing, the stable number of cooperators obtained by the game is decreasing. It can be seen that the increasing belief in the sensitivity of countries to other countries will make more countries choose betrayal strategies in "The Belt and Road" economic and trade network, which also suggests that the belief in the sensitivity to counterparts is negatively correlated with the equilibrium number of collaborators in the network.
in "The Belt and Road" economic and trade network, which suggests that the belief in the sensitivity 264 to own payoff is negatively correlated with the equilibrium number of collaborators in the network. 265

The Belief in the Sensitivity to Counterparts ( ) 266
When the values of other factors remain unchanged, suppose = 0, 0.2, 1, 10, 500 respectively. 267 The simulation results are shown in Figure 4.

The Reward for Cooperation by Neighbor Nodes (w)
When the values of other factors remain unchanged, suppose w = 0, 0.5, 1, 2, 3, 5 respectively. The simulation results are shown in Figure 5.  decreasing. It can be seen that the increasing belief in the sensitivity of countries to other countries 276 will make more countries choose betrayal strategies in "The Belt and Road" economic and trade 277 network, which also suggests that the belief in the sensitivity to counterparts is negatively correlated 278 with the equilibrium number of collaborators in the network. 279

The Reward for Cooperation by Neighbor Nodes(w) 280
When the values of other factors remain unchanged, suppose w = 0, 0.5, 1, 2, 3, 5 respectively. 281 The simulation results are shown in Figure 5.  the equilibrium number of collaborators. In addition, we also notice that when the value of w 291 increased from 3 to 5, the process of obtaining the equilibrium number of collaborators decreased 292 from three rounds to one round. This further illustrates the role of neighborhood rewards in "The 293 Belt and Road" economic and trade network in promoting cooperative behavior. 294 As can be seen from Figure 5, suppose the values of other factors remain unchanged: when w = 0, the number of cooperators is stable at 36 after one round of the game; when w = 0.5, the number of cooperators is stable at 38 after one round of the game. With the value increasing, the stable number of cooperators obtained by the game is increasing. When w = 3, all countries chose cooperation strategy after three rounds of the game. This shows that the rewards for cooperation by neighbor nodes in "The Belt and Road" economic and trade network are positively correlated with the equilibrium number of collaborators. In addition, we also notice that when the value of w increased from 3 to 5, the process of obtaining the equilibrium number of collaborators decreased from three rounds to one round. This further illustrates the role of neighborhood rewards in "The Belt and Road" economic and trade network in promoting cooperative behavior.

The Trade Facilitation Index (f)
When the values of other factors remain unchanged, suppose f = 0.5, 0.2, 0.8, 0, 1 respectively. The simulation results are shown in Figure 6.

299
As can be seen from Figure 6, suppose the values of other factors remain unchanged: when 300 f = 0, the number of cooperators is stable at 29 after four rounds of the game; when f = 0.2, the 301 number of cooperators is stable at 34 after two rounds of the game; when f = 1, the number of 302 cooperators is stable at 48 after two rounds of the game. With the value increasing, the stable number 303 of cooperators obtained the game increases. This shows that the trade facilitation index is 304 positively correlated with the equilibrium number of collaborators in "The Belt and Road" economic 305 and trade network. In addition, we also note that the increase of the equilibrium number of 306 collaborators caused by the value from 0.5 to 0.8 is greater than that from 0.2 to 0.5, which indicates 307 that the influence of trade facilitation index on the equilibrium number of collaborators varies in 308 different ranges. 309

The Reduction Rate of Tariff (r) 310
When the values of other factors remain unchanged, suppose r = 0.5, 0.2, 0.8, 0.1, 1, 0 respectively. 311 The simulation results are shown in Figure 7. 312 As can be seen from Figure 6, suppose the values of other factors remain unchanged: when f = 0, the number of cooperators is stable at 29 after four rounds of the game; when f = 0.2, the number of cooperators is stable at 34 after two rounds of the game; when f = 1, the number of cooperators is stable at 48 after two rounds of the game. With the value increasing, the stable number of cooperators obtained the game increases. This shows that the trade facilitation index is positively correlated with the equilibrium number of collaborators in "The Belt and Road" economic and trade network. In addition, we also note that the increase of the equilibrium number of collaborators caused by the value from 0.5 to 0.8 is greater than that from 0.2 to 0.5, which indicates that the influence of trade facilitation index on the equilibrium number of collaborators varies in different ranges.

The Reduction Rate of Tariff (r)
When the values of other factors remain unchanged, suppose r = 0.5, 0.2, 0.8, 0.1, 1, 0 respectively. The simulation results are shown in Figure 7.
As can be seen from Figure 7, suppose the values of other factors remain unchanged, when r = 0, the number of cooperators is stable at 11 after two rounds of the game; when r = 0.5, the number of cooperators is stable at 38 after one round of the game; when r = 1, the number of cooperators is stable at 55 after two rounds of the game. With the value increasing, the stable number of cooperators obtained by the game increases. This shows that the reduction rate of tariffs is positively correlated with the equilibrium number of collaborators in "The Belt and Road" economic and trade network. Sustainability 2018, 10, x FOR PEER REVIEW 13 of 21 313 Figure 7. Simulation of the influence of the tariff rate reduction rate.

314
As can be seen from Figure 7, suppose the values of other factors remain unchanged, when 315 r = 0, the number of cooperators is stable at 11 after two rounds of the game; when r = 0.5, the 316 number of cooperators is stable at 38 after one round of the game; when r = 1, the number of 317 cooperators is stable at 55 after two rounds of the game. With the value increasing, the stable number 318 of cooperators obtained by the game increases. This shows that the reduction rate of tariffs is 319 positively correlated with the equilibrium number of collaborators in "The Belt and Road" economic 320 and trade network. 321

Discussion 323
Our paper makes significant contributions to both theory and practice. From the theoretical 324 perspective, our paper maybe the first one to apply the asymmetric Quantal Response Equilibria 325 (QRE) network game model to the belt and road initiative. We explored the influencing factors of the 326 belief in the sensitivity to own payoff and counterparts, the reward for cooperation by neighbor 327 nodes, the trade facilitation index, and the reduction rate of tariffs. 328 Practically, some new phenomena were discovered. The first is that changes in subjective factors 329 do not necessarily change the strategic choices of all countries in the trade network. Therefore, in the 330 recent issue of the Sino-US trade conflicts, China's optimal strategy is to follow the objective laws of 331 international economy and continue to promote economic and trade cooperation of the Belt and 332 Road. The second is that different trade links already existing in reality have different effects on the 333 choice of cooperation strategies. For countries with close trade links in reality, betrayal will result in 334 greater loss of benefits. Therefore, in "The Belt and Road" trade network, cooperative behavior is a 335 virtuous promotion strategy cycle. The third is that there is always a collaborator in the trade 336 network, no matter how the objective condition variable changes, so cooperation is an endogenous 337 strategy. In addition, the simulation results verify some common sense conclusions，such as the 338 degree of trade facilitation and tariff reduction, which can promote trade cooperation. 339 According to research conclusions, the strategy of promoting the development of "The Belt and 340 Road" economic and trade network includes the following. First, countries should maintain the 341 flexibility of cooperation strategies. Countries with a different value of belief in sensitivity should be 342

Discussion
Our paper makes significant contributions to both theory and practice. From the theoretical perspective, our paper maybe the first one to apply the asymmetric Quantal Response Equilibria (QRE) network game model to the belt and road initiative. We explored the influencing factors of the belief in the sensitivity to own payoff and counterparts, the reward for cooperation by neighbor nodes, the trade facilitation index, and the reduction rate of tariffs.
Practically, some new phenomena were discovered. The first is that changes in subjective factors do not necessarily change the strategic choices of all countries in the trade network. Therefore, in the recent issue of the Sino-US trade conflicts, China's optimal strategy is to follow the objective laws of international economy and continue to promote economic and trade cooperation of the Belt and Road. The second is that different trade links already existing in reality have different effects on the choice of cooperation strategies. For countries with close trade links in reality, betrayal will result in greater loss of benefits. Therefore, in "The Belt and Road" trade network, cooperative behavior is a virtuous promotion strategy cycle. The third is that there is always a collaborator in the trade network, no matter how the objective condition variable changes, so cooperation is an endogenous strategy. In addition, the simulation results verify some common sense conclusions, such as the degree of trade facilitation and tariff reduction, which can promote trade cooperation.
According to research conclusions, the strategy of promoting the development of "The Belt and Road" economic and trade network includes the following. First, countries should maintain the flexibility of cooperation strategies. Countries with a different value of belief in sensitivity should be treated separately. They should moderately reduce the value of belief in sensitivity to other countries, which will promote other countries in the network to adopt cooperation strategies with a higher probability. Second, joint countries should increase preferential policies for economic and trade cooperation of the countries of "The Belt and Road", and the equilibrium number of collaborators in the network will increase, which will bring them more benefits. Third, the countries in the network should take full account of their own national conditions and the influence of different factors on the equilibrium number of collaborators, and adopt the best combination of strategies to achieve higher cooperation returns at lower input costs.

Conclusions
"The Belt and Road" has been a hot topic in the field of politics and economics in recent years. Previous studies on cooperation mostly used qualitative reasoning [10] and quantitative test methods [19], but research results of the complex network game are few. The complex network analysis method incorporates many national subjects into an overall research framework, which is conducive to a better study of the impact of a country's strategic changes on all other countries within the framework. At the same time, it also ignores the influence of asymmetric cognition on "The Belt and Road" economic and trade cooperation in the national decision-making process. Previous studies have examined the impact of objective factors such as tariffs and cultural distance [19] on trade cooperation, but it cannot be ignored that asymmetric subjective decision-making between countries also plays an important role in the process of the cooperative game.
Therefore, based on the construction of "The Belt and Road" economic and trade network, this paper introduced the asymmetric QRE model to set up a complex network game model of "The Belt and Road" economic and trade cooperation. According to the simulation results of the game model, the following conclusions were drawn: (1) The sensitivity of own payoff and the sensitivity of his counterparts has little influence on the stable number of cooperators in "The Belt and Road" economic and trade network within a limited range of value. This may be the role played by the increasingly rational and mature decision-making process in various countries. At the same time, it means that subjective factors only have an impact on cooperation between countries under some specific conditions. Therefore, when considering promoting the development of an overall trade network, countries should not put subjective factors at the top of their worries. (2) The rewards of neighbor have a significant impact on the cooperation of "The Belt and Road".
Because the neighboring countries in the network are the countries that have close trade relations with each other in reality, this shows that the change of a country's cooperation strategy will first affect those countries which have close trade ties with it. Therefore, countries should first actively communicate with existing trading partners and pursue a higher-level cooperation on the basis of maintaining the existing stable trade relations. At the same time, this also means that the trade network structure has a great influence on the cooperation of "The Belt and Road". Therefore, countries should also strive to improve their position in the trade network in order to obtain more opportunities for trade cooperation. (3) The level of trade facilitation measures other than the neighbor's rewards is beneficial to the cooperative behavior of "The Belt and Road". The extensive construction of infrastructure such as roads, railways and the Internet will greatly enhance the level of trade facilitation of the entire network, and will further promote the emergence and development of trade cooperation among countries in the network. Therefore, countries along "The Belt and Road" must attach importance to infrastructure construction and attract more cooperation by improving their trade facilitation level, thereby improving their trade status and promoting trade prosperity. (4) Tariff relief has a significant effect on the cooperative behavior in "The Belt and Road" network.
As a traditional trade protection measure, high-level tariffs have become the most frequently adopted trade protection policy in today's anti-globalization tide. However, it has been proved that only low-level tariff and trade liberalization can promote the emergence of trade cooperation between countries, thereby promoting the development and prosperity of the world's economies. Compared with measures of trade protection with high tariffs, countries should maintain an open and inclusive attitude and actively carry out trade cooperation and exchanges with other countries in order to achieve healthy and sustainable development of their trade. (5) The cooperative behavior in "The Belt and Road" network is the result of the combined effects of many factors. We set a reasonable initial value in the statistical sense, so we obtained a more obvious trend of simulation results. However, in reality, the effect of cooperation will be affected by many other factors, but the trend of the impact of the factors we tested on the results was determined. (6) Our research has some limitations. First, although the influence of the asymmetry of cognition on the equilibrium of the network game was taken into account, the assumption that countries are homogeneous and rational is still too idealistic, which is different from the reality of the countries of "The Belt and Road". Second, the study assumes that the trade network structure is static, but the real trade network is dynamic, and changes in the network structure will influence policy choices. In a future study, we will relax the assumptions, take into account the size of the countries, the social and cultural differences, and other factors, while the weighted network will be used to enhance the reality of the game results. FZ1(t)=exp(lamda1*(P(t)*R+(1-P(t)) *S)); FM1(t)=exp(lamda1*(P(t)*R+(1-P(t)) *S)) +exp(lamda1*(P(t)*T+(1-P(t)) *W)); P1(t)=FZ1(t)/FM1(t); FZ2(t)=exp(lamda2*(P1(t)*R+(1-P1(t)) *S)); FM2(t)=exp(lamda2*(P1(t)*R+(1-P1(t)) *S)) +exp(lamda2*(P1(t)*T+(1-P1(t)) *W)); P(t+1) =FZ2(t)/FM2(t); for i=1: nums UC(i)=0; UD(i)=0; for j=1: nums UC(i)=C*A*C'*P1(t)*a(i,j)+C*A*D'*(1-P1(t))*a(i,j)+UC(i); UD(i)=D*A*C'*P1(t)*a(i,j)+D*A*D'*(1-P1(t))*a(i,j)+UD(i); end newUC(i)=UC(i)+w*Nlc(t,i)+f*gdp(i)+r*trade(i); Usum(i)=newUC(i)-UD(i); if Usum(i)>=0 Ent(i