The spillover effects on strategic interdependence neighboring countries: A game theory approach

The main aim of sustainable development is to ensure an intelligible and long-lasting balance between the economy, society, and the environment. Sustainable tourism could only be successful if the inter-relationships between all three dimensions are accepted. In the limited number of research analyses, the focus of the research is on competition between tourist countries and destinations. This study has used Game theory to analyze the competition applies time-series data in selected neighboring countries measure of a VAR-based spillover index, developed by [1] to investigate the time-varying relationship between tourism and Gross Domestic Product. Each country analyzed Vector Error Correction (VEC) and Granger analysis to explore the causal short and long-term tourism and use a sample that spans from 1997 to 2019. From the main results of Cholesky, the total spillover index is 59.0% between Russia and Mongolia which suggests a moderate interdependence among the four variables. Findings indicate that neither China nor Mongolia have a short-run influence on tourism development. China's inbound tourism is affected in the long run by Mongolia's inbound tourism but not vice versa can be explained by the fact that the number of tourists visiting Mongolia would include China in their travels.


Introduction
Tourism is one of the dynamic and fastest-growing sectors of the world economy. Tourism is the processes, activities, and outcomes arising from the relationships and the interactions among tourists, tourism suppliers, host governments, host communities, and surrounding environments that are involved in the attracting and hosting of visitors. In 2019, The World Tourism Organization (WTO) claims tourism is currently the world's largest industry with annual revenues of over USD 1.7 trillion. It also employs a number of departures that exceed 1168 and arrivals that exceed 1401 million in 2018. The world tourism data have shown that the total contribution of the Travel and Tourism sector to Gross Domestic Product was USD 8,9 trillion (10.3% of global GDP) and was 330 million jobs in 2019 [2]. Tourism creates many Asian country's economies, with international tourism receipts exceeding Asia and the Pacific international tourist arrivals by 308 million in 2017 [3]. Although Asia and the Pacific account for 348 million (25%) of international tourism arrivals, this generates 435 billion (30%) of international tourism receipts. In 2018, the world's most visited region of Europe steadily grew. Europe received 710 million (51%) of international tourism arrivals in 2018, this generated USD 570 billion (39%) of international tourism receipts [4]. In 2017, the United Nations' World Tourism Organization named the tourism sector as the world's third largest export category with USD 1.3 trillion. That year, Mongolia received about 542.000 foreign visitors, of which 469.300 were tourists. As the number of tourists in 2017 increased by 16.1 percent compared to 2016, Mongolia is considered as one of the leading countries by tourism revenue, according to UNWTO [10]. The long term development policy of Mongolia titled "Vision -2050" has 9 fundamental goals and 50 development targets and focuses on the vision of "Mongolia becoming a leader with its economic growth, social development and a country that achieved sustainable preservation of its nature, language, territorial integrity, and culture". Mongolia will (1) increase domestic travel in Mongolia and increase the number of foreign tourists to one million annually, (2) promote sustainable development of tourism, (3) develop tourism infrastructure and develop ecologically, special interest and cross-border tourism, and (4) develop eco-tourism regions and products compliant with environmental and health requirements [11]. The Mongolian government focuses on which country or continent can cooperate with tourism development strategy. Then industry follows on providing competitive products, marketing those products, and conducting pricing strategies, while the government provides infrastructure, regulates tourist arrival, and helps the industry in the promotion.
Against this background, this study's main questions are what is the best reaction for each country? and whether or not how Mongolian neighboring countries of China's GDP and Russia's GDP change influences Mongolian tourism in the long term. The paper has set up matrix tables using time series data of tourists from neighboring countries with tourism in a three countries during the 23 year period 1997-2019. In this study, the 2x2 matrices were set up for two key players: player 1 China (CHN), player 2 Mongolia (MNG) and player 1 Russia (RUS), player 2 Mongolia (MNG).

Literature Review
In 1944, Von Neumann and Morgenstern founded the field of game theory book Theory of Games and Economic Behavior. They were in search of a more effective way of solving certain kinds of economic problems to account for the presence of others who are making decisions in accordance with their own best wishes [12]. Game theory is the study of optimal behaviors and helps solve many problems in various fields of science. It is a branch of applied mathematics that is used in the social sciences especially economics. In economics and philosophy, researchers use game theory to help understanding good or proper behavior.
A game describes that set of players and set of strategies available to those players, and a specification of payoffs for each combination of strategies. Game theory attempts mathematically to behave in a strategic situation where the success of an individual's choice depends on the choices of others. Most economic applications of game theory use the concept of Nash equilibrium [13].
The game theory relies upon mathematical calculations and is used to predict an outcome based on interactions among multiple parties. The theory is reliant upon independent decision-making of individuals [14]. Game theory mainly studies decision-making behavior indirect interaction, that how the participants use the information that they have mastered to make a decision, and the equilibrium solution of this decision-making, which reflects the participants' actions and interactions between the conflict, competition, coordination, and cooperation in the game [15]. Game theory can be divided into non-cooperative games (Nash Equilibrium) and cooperative games [16]. Game theory studies the decision-making principles of many interdependent parties. Players choose from a variety of winning strategies. Winnings can be anything from money to profits to penalties. The player tries to maximize the winnings. The principle of the game theory is not to underestimate the player, but to get a real guaranteed victory with a strategy of surprise and forgetfulness.
The use of a powerful framework of game theory enables managers to systematically analyze the ties among interactions between actors in a market and develop appropriate competitive strategies. There must be a balance between simplifying a problem in a complex world to make it manageable and retaining enough complexity to make it relevant [17].
A game has two players or more, each player assumed to be rationally self-interested, seeking the highest possible benefit. The key requirements of a game theory analysis are determining: (1) the structure of the game, and (2) the payoffs. The structure of the game is the set of strategies available to each player. A strategy is a player's complete plan of action at each decision point to the end of the game. The payoffs available to each player for each strategy, given the other players' strategies, represent the benefit the player achieves at the completion of the game. The outcome of the game is determined by finding the Nash equilibrium. Nash equilibrium is the predicted strategy for each player that is the best response to the predicted strategy of all other players [18].
Researchers decided to study tourism by choosing the application of Game Theory. The mixed strategy pricing behavior package tour using summer season's data from 1982 to 1995 is investigating whether variances differ at different times during the season and thus differ systematically with the level of demand [19]. Liang and Yang [20] studied factors influencing the development of regional tourism cooperation and competition that are interrelated. Empirical study has explored the advantages and disadvantages of cooperation games and competition games, the method of cooperation-competition game is utilized. The first choice is the cooperation-competition strategy tactics that can regional tourism activities development.
The macroeconomic variables included relative prices, nominal exchange rates, and world income per capita identify in tourism demand. The results get from this journal is positive and significant between tourism demand and GDP [21]. The study identifies the factors that affect the destination choice process. Co-integration analysis and error correction models (ECMs) to estimate the long-run tourism demand and to forecast European tourism demand [22].
Recently, several studies [23,24] examined applying time-series analyses of the competition between tourist country destinations. Therefore, this research reveals the country indicators have not influenced each other in the short term but in the long term, inbound tourism of China will depend on the inbound tourism of Japan [23]. There was no Nash equilibrium of a payoff for the two countries [24]. Game theory was used in order to analyze the protection of tourist consumers' rights and interests. The study results are significant to the protection of tourist consumers' rights and interests [25].
Several tourism researchers have attempted to clarify the spillover effect on tourism. Yang and Wong [26] investigate and estimate the spillover effects in inbound and domestic tourism flows. The results confirm the existence of spillover effects in both inbound and domestic tourism flows and suggest that physical infrastructure factors, tourist attractions. Researchers employ the spillover effect stated the relationship between tourism and economic growth in selected European countries. This research investigates that the tourism-economy relationship is not stable over time for all countries in terms of both its magnitude and direction [27]. Furthermore, there are spillover effects of shocks to sentiment and mood on outbound tourism demand, although not of high magnitude at all times [28]. Couto et al. [29] also report on research an in-depth perception of the main issues about how this pandemic crisis affects the tourism expectations of residents, and consequently, how this situation will influence regional sustainable development.

Materials and Methods
This present study uses normal form games to determine the outcomes. That is, the game displays the strategies for each player and the payoffs for each combination of the players' strategies, in a matrix where the first number of international tourism represents the payoff for Player 1 given Player 2's strategy, and the second number of international tourism represents the payoff for Player 2, given Player 1's strategy.
A game model with countries and their strategies can be formulated A and B, winning function are 1 , and 2 Equation (1), as follows: Where: α -Player 1' strategy, i=1,2,…, m β j -Player 2' strategy, j=1,2,…, n When the pair of strategies (α i , β j ) is chosen, the payoff to the first player is f 1 (α i , β j ) and the payoff to the second player is f 2 (α i , β j ); 1 , 2 are called payoff functions. Matrix A is called a payoff matrix for player 1 and matrix B is called a payoff matrix for player 2 Equation (2), as foloows: The pair of strategies ( * , * ) is called an equilibrium point, if Where: (i * , j * ) is pure strategy of Nash equilibrium point.  The players involved in this game between China(CHN) and Mongolia(MNG), Russia (RUS) and Mongolia (MNG). Each country has two strategies either to enter or withhold tourism. In the case of this study, both are four possible action profiles that measured GDP. Table 2,3 shows that scheme yields the payoff matrices. Those countries are neighboring countries of Mongolia and geographically close to each other. China with Mongolia and Russia with Mongolia are involved in a bi-matrix game; this paper assumes each country shares a common goal which is to reach a sound regional international tourism growth in Central Asia. A sound tourism partnership with countries within the region is a prerequisite for ensuring sustainable market tourism in the future.
In this study, we use the spillover index by Diebold and Yilmaz [1], which is the influence between neighboring countries' tourism and their interrelationships. Spillovers allow for the assessment of the interlinkages between the variables under examination. The spillover index is based on the Vector Auto-Regressive (VAR) model developed by [30,31] the notion of variance decompositions. The idea of an index is simple and straightforward because the analysis of the index is based on the error variance, which is a general concept of the VAR model with N variables. Specify, the error variance of any variables (i) and other (j) variables that is due to shocks to (i ≠ j) for (i = 1,2, ... N) to calculate the total effect.
The total spillovers represent the average contribution of spillovers of shocks across variables to the total forecast error variance. Put it simply, total spillovers measure the average level of interdependence among the variables under examination. To simplify the notation, consider a simple VAR model with two variables and one lag Equation (3), as follows: Where: x t = (x 1t x 2t ) and are 2x2 matrix. Convert the moving average representation of the VAR model can be Equation (4) written as follows: The structural moving average representation form can be Equation (5) written as follows: Where: A(L) = Θ(L)Q t −1 ; u t = Q t ε t ; E(u t u t ′ ) = I and Q t −1 is the unique lower-triangular Cholesky factor of the covariance matrix of . Considering assumptions can be Equation (6) written as follows: The corresponding error variance and covariance matrix after one generation can be Equation (7) written as follows: Where 1 denotes the forecast error variance after one generation is a 0,11 2 + a 0,12 2 and 2 denotes the forecast error variance after one generation is a 0,21 2 + a 0, 22 2 . Thus, the variance decomposition allows us to split the forecast error variance of each variable into parts attributable to the various system shocks. That x i (i = 1,2) variable forecast error variance after one generation effect own variable's shock is own variance shares. Other variables of x j (i, j = 1,2; j ≠ i) effect cross variance shares in shock called spillover. In this case, there are two different spillovers.
First, x 1t variable's forecast error variance x 2t shock effect spillover a 0,12 2 another is 2 variable's forecast error variance 1 shock effect spillover 0, 21 2 . The total spillover is 0,21 2 + 0,21 2 . By expressing this spillover, i.e. the total forecast error variation, relative to the total forecast error variation, it can be converted into an easily The crucial improvement achieved by using the generalized VAR framework lies in the fact that we are now able to identify the directional spillovers, i.e. we can decompose the total spillover to those coming from and to each observed asset [32]. Furthermore, p lag, N variables of VAR model forecast spillover index, is computed Equation (9), as follows: The spillovers allow us to measure the level of interdependence among variables. The paper employs a time series model to establish the payoff schedule. The most importantly, their use may suggest solutions to bias problems caused by unobserved heterogeneity, which is a common problem in configuring models with cross-sectional data sets. The second reason may be that it is possible to use a data set to detect dynamics that are difficult to detect with cross-sectional data. VAR method assumed that all of the variable in the model must be the lack of autocorrelation and homoscedasticity. The lag length selection when using a minimalvalues of the Akaike and Schwarz information criteria was obtained.
This study also employs Vector Error Correction (VEC) to describe this phenomenon. Applying the Granger-causality test is the most effective and practical way to test the direction of causality [33,34]. According to Engel and Granger [35] theorem, if two variables y and x are co-integrated, then the relationship between the two can be expressed as an (Error Correction Mechanism) ECM in which the error term from the Ordinary Least Square regression, lagged once, acts as the error correction term.
Gross domestic product is the market value of total production of goods and services in a country. Data on GDPs was obtained from the World Bank's World Development Indicators covers the period 1997-2019. The tourism demand is measured by the tourism receipt China and Mongolia (Russia and Mongolia) in year t. Data collected from the World Tourism Organization (UNWTO).

Results
The descriptive statistics on tourism from China, Russia, and Mongolia results are shown in Table 4. The mean values simply tell the average value for each of the variables. The standard deviation implies the deviation from the sample mean with respect to each of the variables. The Skewness value shows that all variables mirror a normal distribution. The Kurtosis values mirror normal skewness and platykurtic because clearly lower than the value of 3 which implies the thickness of flatness of the distribution of a series. The Jarque-Bera statistic measures the difference of the skewness and kurtosis of the series and test is that the distribution is normal. Constant+trend -5.8759 *** -5.7823 *** -6.7385 *** -5.0002 *** -5.2070 *** -9.7779 *** Notes: * , ** , *** reject null hypothesis significance at 1%, 5%, and 10% levels respectively. Source: Results obtained by the authors. Table 4 also shows the results of the ADF unit root test. The variables tested are the logarithm of variables under the period 1997 to 2019. The ADF test for unit root in the first difference shows that the series some are non-stationary both in intercept and trend. Taking the second difference of the series and testing these with and without intercept and trend makes the series stationary. These results indicate that both of series exhibits unit root processes. In Table 5, there is an overview of the results of the spillover analysis between international tourism and GDP for neighboring countries China and Mongolia (Russia and Mongolia) left in this research. We used the spillover results Dyindex 5 package Davaajargal [36] of E-views 10 Add-ins. For each country, there are the contributions for the forecast error time series, the table cell ij represents the percentage of shock in variable j in the forecast error variance in sector i. The contributions to the forecast error variance of time series, in the table of column j total of the non-diagonal variable of own variable j represents the total contribution to others. The total spillover index of each sector from the other sectors is shown in the last column of the table.
From the main results of Cholesky, the total spillover index is 46.7% between China and Mongolia which suggests a moderate interdependence among the four variables. The international tourism explains 28.0% Chinese tourism, 50.9% Mongolian GDP, and 17.5% of Mongolian tourism at the ten-day horizon. The most influential contribution to others variables is China's GDP 96.4 % and China's tourism 60.5%. The impact of the Mongolian economy is 9.9% compared to other sectors is small.
The results from Table 5, in the case between Russia and Mongolia, show that the value obtained for the total spillover index is 59.0%. For these countries, the international tourism explains 19.0% of Russian tourism, 50.3% Mongolian GDP, and 6.7% of Mongolian tourism at the ten-day horizon.  The Vector Error Correction Model in order to depict the long-run and short-run dynamic interactions, as can be seen in Table 6, 7. The presence of cointegration between variables suggests a long term relationship among the variables under consideration. The long run relationship between GDP and Tourist receipt for one cointegrating vector for the between China and Mongolia (Russia and Mongolia) in the period 1997-2019 is displayed (standard errors are displayed in parenthesis). Table A1 indicates that there was a long run impact of Chinese tourism on Mongolian tourism also Mongolian tourism on Chinese tourism (C(1)= -0.375, P=0.02 ) and (C(1)= -0.73, P=0.06). Result shows that short run impact between two countries, a Wald test was conducted with two null hypotheses. As a result shows that, the Chi square for both of the above equations were not significant so the null hypothesis were accepted; there is no short term impact of China on Mongolia and vice versa. Table A2 indicates that there was a long run impact of Russian tourism on Mongolian tourism also Mongolian tourism on Russian tourism (C(1)=-0.939, P=0.000 ) and (C(1)=-0.216, P=0.418). Result shows that short run impact between two countries, a Wald test was conducted with two null hypotheses. As a result shows that, the Chi square for both of the above equations were not significant so the null hypothesis were accepted; there is also no short term impact of Russia on Mongolia and vice versa.  -1.58). If Mongolia decides to enter, it will yield several payoffs given China's actions. Mongolia will yield a GDP increase of (3.11) will get the highest payoffs for tourism if China decides to enter inbound tourism. China's strategy to create GDP through tourism will give her several payoffs given other countries' actions. China will take (0.32) from its GDP increase of $1 percent in tourism if Mongolia decides to enter the same thing. Therefore, the first quadrant (3.11/0.32) is the unique Nash equilibrium in pure strategies because it is the place where both players receive the highest payoff. If Mongolia enters, China should withhold (0.32 >-0.42) and if Mongolia withholds, China should enter (-0.63 > -1.13). Therefore, the best response for Mongolia is to do the opposite to China's action. China withholds, that is China restrains tourism to Mongolia as its dominant strategy, no matter what Mongolia's strategies are. There exists no Nash equilibrium in mixed strategies. Table 9 payoff matrix shows that if Russia enters, Mongolia should withhold (43.53 > -6.56) and if Mongolia enters, Russia should withhold (0.02 > -0.15). If Mongolia decides to enter, it will yield several payoffs given Russian's actions. Mongolia will yield a GDP increase of (43.53) will get the highest payoffs for tourism if Russia decides to enter inbound tourism. Russia's strategy to create GDP through tourism will give her several payoffs given other countries' actions. Russia will take (0.02) from its GDP increase of $1 percent in tourism if Mongolia decides to enter the same thing. Therefore, the first quadrant (43.53/0.02) is the unique Nash equilibrium in pure strategies because it is the place where both players receive the highest payoff. The fourth quadrant -1.67 /-0.59 is a dominant strategy for Russia because no matter what Mongolia enters or withholds, Russia always gets a higher payoff.

Discussion and Conclusions
Game theory is applied in many fields, including business, finance, economics, political science, and psychology. Understanding game theory strategies both the popular ones and some of the relatively lesser-known stratagems is important to enhance one's reasoning and decision-making skills in a complex world. The most important economic feature of activities related to the tourism sector is that contributes are a generation of income, employment, and foreign exchange earnings.
In this respect, tourism is one of the fastest-growing industries and a driving force for so many developed and developing economies. Poor countries or regions in decay could be developed through the tourism sector easily. These countries have several common characteristics, it is reasonable to believe that there would be some strategic interdependence in promoting the development of tourism between China and Mongolia (Russia and Mongolia). As a decision-making tool in conflict situations, the game theory approach is suggested for planning and adopting an optimal strategy. This study has shown that there is Nash equilibrium in this competition between China and Mongolia (Russia and Mongolia).
In terms of economy, tourism development is considered a game in which there is a winner and a loser. In order to win the game, the players should forecast the response of the competitors in the long term strategies. The problem is that any move made by one party in a competitive situation will cause subsequent moves in others and each of those moves will cause further moves. A strategy that might appear successful best upon current figurations of competitor actions may turn out to have different consequences once competitor actions and reactions have taken place. In terms of tourists, the more competitive tourism developments are the better choices become. Game theory is a measure of tourist evaluation and will allow us to determine which nature development direction tourism will take, nature versus nurture. Sustainable tourism will educate consumers on how to protect eco-friendly travel and protecting the environment.
In brief, the study provides evidence that there are spillover effects on income and tourist receipt in neighboring countries' international tourism. The total spillover index between China and Mongolia is (46.7%), between Russia and Mongolia (50.9%). The contributions of this study are to apply Game theory to measure both long-term and short-term benefits to analyze the tourism economy. The results of this study indicated between Russia and Mongolia have short-term, but between China and Mongolia have not; both have in the long term. First, the finding that China's inbound tourism is affected in the long run by Mongolia's inbound tourism but not vice versa can be explained by the fact that the number of tourists visiting Mongolia would include China in their travels. The simulation game in this study also indicates that China and Mongolia's strategies are interdependent to each other. With the absence of China tourism, Mongolia's GDP was decreased from 3.11 to -0.88. With the absence of Mongolian tourism, China's GDP was decreased from 0.32 to -0.42.
The visa is the result of a joint initiative of the Heads of State of the relevant partner countries to increase regional tourism and provide opportunities for tourists to explore the diversity of East Africa [37]. The Regional Tourism Organization of Southern Africa (RETOSA) is a permanent body of Southern African Development that promoted Univisa. This organization is responsible for the development of tourism in 14 southern African countries [38].
In order to perform an analysis comprising a sample of China, Mongolia, and Russia, data provided by the World Bank and the World Tourism Organization were used. The limit of this study is its assumption that there would be no change in the surrounding reality of international tourism patterns; there would be no wars, political conflicts, terrorist attacks affect tourism, flight accidents, economic crisis, natural and man-made disaster, etc. Additionally, we can classify the countries into sub-groups by geographic or economic reasons and make specific estimations. Future research suggestion is the elaboration of a methodological approach including compatible samples which could allow the use of other variables in the analysis.