3.1.1 Data sources

The essential data for this study was taken from a questionnaire survey that was completed in April and May of 2017. The survey of tourist enterprises in the four tourist attraction areas of Erlangjian, Bird Island, Fairy Bay and Sand Island in Qinghai Lake combined random sampling and in-depth interviews. During the survey period, 418 questionnaires were distributed, of which 416 were returned. The retrieval rate was 99.5%. After samples with incomplete answer or questionable authenticity were eliminated, the final number of l valid questionnaires was 414, an effective rate of 99.5%. In order to ensure the validity of the sample size, this study took the total number of the tourist enterprises in the four Qinghai Lake tourist attraction areas as the reference and then used Scheaffer’s formula for sample size to calculate sampling size. The formula is as follows:

$n=\frac{N}{\left( N-1 \right){{\varepsilon }^{2}}}+1$ (1)

where n stands for the sampling size of tourist enterprises, N stands for the total number of the tourist enterprises in the four Qinghai Lake tourist attraction areas, and ε stands for the sampling error. According to the Scheaffer formula, the value of the sampling error is set at 0.06 and the calculation is based on the total number of the tourist enterprises in the four Qinghai Lake tourist attraction areas in the year 2016. It was determined that the minimum total sampling size for the four areas was 286. The actual survey sample size used in the study is larger than the minimum sample size, indicating that that survey findings are representative.

3.1.2 Data analysis

SPSS 20.0 was utilized for the descriptive statistical analysis and reliability analysis of the collected and disposal questionnaire data. The findings show that the reliability for the indicators of symbiotic factors of tourist enterprises with government, residents, tourists and tourist enterprises was, respectively, 0.833, 0.802, 0.887 and 0.901; and the KMO measurement and Bartlett sphericity test for the indicators of symbiotic factors of tourist enterprises with government, residents, tourists and tourist enterprises were, respectively, E-G(˃0.83), E-R(˃0.82), E-T(˃0.86), and E-E(˃0.88). Cronbach's Alpha values for tourist enterprises with government, residents, tourists and tourist enterprises were greater than 0.8. This demonstrates that the reliability of the data used for these four aspects exceeds the minimum acceptable standard of 0.6 as a whole, and has a good reliability value. The Cronbach’s Alpha values for the indicators of symbiotic factors of tourist enterprises with government, residents, tourists and tourist enterprises in this model have obviously increased, which indicates that, from the perspective of tourism enterprises, measurement indexes of symbiosis factors of each multiple tourist agent have good structural validity in these four aspects.

3.2.1 Establishment of the symbiotic index system

The symbiosis of multiple tourist agents represents a positive relationship existing in a specific model and consisting of symbiotic agents that are in a symbiotic interface integrating the ecological environment and tourism development. The ecological environment can be protected, the benefits accruing to each agent can be in equilibrium and the development of tourism can be sustainable (Baum and Szivas, 2007). In the process of the symbiosis of multiple tourist agents, the key to the formation of a harmonious, reciprocal, stable and integrative symbiotic system lies in structuring the symbiotic units that are constituted by such agents as governments, tourist enterprises, residents and tourists, accommodating and optimizing symbiotic conditions, symbiotic interfaces, and organizational and behavioral models for each symbiotic agent (Li et al., 2012). In consideration of the diverse influences agents have on tourism development and related factors that have an impact on agents, therefore, based on the principle of “trust, fairness, respect, mutual benefit, cooperation and communication”, the related factors that influence the agents’ symbiosis are analyzed and summarized as follows: Governments impact tourism development in numerous ways, including “policy formulation, preparation planning, financing, and resources conservation” (Su and Huang, 2012). Some of the ways that tourist enterprises impact tourism development include “folk-custom authenticity conversations, resources conservation, coordination and communication, fair competition, and collaborative symbiosis” (Chu, 2009). The impact of residents on tourism development consists of “sincere folkways, a sense of participation, initiative communication, ideology renewal” and so forth (Shen, 2012). The impact of tourists on tourism development includes “self-cultivation, folkway esteem, enhancement of environmental consciousness” and so forth (Bao and Sun, 2006). Based on a consideration of tourist enterprises around the lake and combined with the symbiotic relationship of correlative agents “Tourist Enterprises→Governments-Residents-Tourists-Tourist Enterprises” in a symbiotic interface, the symbiotic indicator system is structured as follows (Table 1).

3.2.2 Weight of symbiotic indicators

The entropy method is used to establish the weight of symbiotic indicators in this study. The entropy method for symbiotic measurement of multiple agents is a method to confirm the weight of symbiotic indicators that uses the concept of entropy so as to avoid to some extent the defects of some subjective valuation methods. As for the symbiotic indicators, the larger the value of factor information entropy is, the greater the value of the symbiotic indicators varies, and the more powerful the impact of the functions contributed by the symbiotic indicators in the symbiotic interface (Shannon et al., 2001). The specific calculation procedures are as follows:

Construction of the symbiotic matrix for multiple agents

$S={{\{{{S}_{ij}}\}}_{m*n}}$ (2)

In the formula (2), m stands for the number of symbiotic correlative agents, and n stands for the number of symbiotic factors. This study uses the critical value method to standardize the dimension of the primary data of the indicators.

Entropy of symbiotic indicators

${{K}_{ij}}={{{S}_{ij}}}/{\sum\limits_{i=1}^{n}{{{S}_{ij}}}}\;$ (3)

${{E}_{j}}=-G\times \sum\limits_{j=1}^{n}{{{K}_{ij}}\text{ln}{{K}_{ij}}}$ (4)

In the formula (3), K_ij stands for the proportion of symbiotic indicators, S_ij stands for the standardized data, i stands for the number of questionnaire, and j stands for the number of symbiotic indicators. In the formula (4), E_j stands for the symbiotic indicators’ entropy of section j, G=1/lnn (n stands for sample size), and 0≤E_j≤1 (when K_ij=0, it is stipulated that K_ijlnK_ij=0).

Weight of symbiotic indicators

${{W}_{j}}={{{g}_{j}}}/{\sum\limits_{j=1}^{n}{{{g}_{j}}}}\;$, (${{W}_{b}}\in [0,1]$, $\sum\limits_{b=1}^{n}{{{W}_{b}}}=1$) (5)

In the formula (5), W_j stands for the symbiotic indicators’ weight of section j, ${{g}_{j}}=1-{{E}_{j}}$, and ${{g}_{j}}$stands for the diversity factor of the symbiotic indicators of section j.

3.2.3 Symbiotic correlation coefficient

Based on symbiosis theory, symbiotic factors are the significant indicators that can impact symbiotic units (agents) of tourists, and the formation of a harmoniously symbiotic interface of multiple tourist agents is the consequence of combined actions by several symbiotic factors. Therefore, grey correlation analysis is used in this study, and symbiotic relationship is estimated and the objective symbiotic correlation coefficient is obtained by means of symbiotic factors of the symbiotic agents that have been established. On basis of grey system theory, x₀(t) is intended to be the characteristic standard data array, x₀(t)={x₀(1), x₀(2), …, x₀(m)}, and t={1, 2, …, m} totally m data; x₁(t) is intended to be the correlation data array, x₁(t)={x₁(1), x₁(2), …, x₁(n)}, and t={1, 2, …, n} totally n indicators. The standard data array of symbiotic indicators of the multiple tourism agents “E→G-R-T-E” is confirmed according to Fishbein-Rosenberg model. It is generally acknowledged that the higher the correlative degree of the symbiotic factors of tourist enterprises with correlative agents is, the greater the symbiotic value is. Hence, the value of the reference sequence is set as 7. The specific calculation procedures are as follows:

$Z=\sum\limits_{i=1}^{n}{{{Q}_{i}}{{P}_{i}}}$ (6)

In the formula (6), Z stands for the scores of recognition degree; Q_i stands for the weight of the No.i symbiotic indicator based on a Likert scale; P_i stands for the coefficient of symbiotic correlation degree of the No.i symbiotic indicator; and i stands for amount of evaluation indicators.

$\begin{align}& \xi \left( {{x}_{0}}(t),{{x}_{i}}(t) \right)= \\& \ \ \ \ \frac{\underset{i}{\mathop{\min }}\,\underset{k}{\mathop{\min }}\,\left| \left( {{x}_{0}}(t)-{{x}_{i}}(t) \right) \right|+\rho \underset{i}{\mathop{\max }}\,\underset{k}{\mathop{\max }}\,\left| \left( {{x}_{0}}(t)-{{x}_{i}}(t) \right) \right|}{\left| \left( {{x}_{0}}(t)-{{x}_{i}}(t) \right) \right|+\rho \underset{i}{\mathop{\max }}\,\underset{k}{\mathop{\max }}\,\left| \left( {{x}_{0}}(t)-{{x}_{i}}(t) \right) \right|} \\\end{align}$ (7)

In the formula (7), $\underset{i}{\mathop{\min }}\,\underset{k}{\mathop{\min }}\,\left| \left( {{x}_{0}}(t)-{{x}_{i}}(t) \right) \right|$ and $\underset{i}{\mathop{\max }}\,\underset{k}{\mathop{\max }}\,\left| \left( {{x}_{0}}(t)-{{x}_{i}}(t) \right) \right|$stand for minimum value of range and maximum value of range, respectively; and$\rho $stands for resolution ratio and its evaluation is 0.5.

According to formula (7), the correlation coefficients of x₀ and x_i can be calculated as follows:

${{\theta }_{i}}=\frac{1}{n}\sum\limits_{k=1}^{n}{{{\xi }_{i}}(k)}$ (8)

In the formula (8), k=1, 2, …, n; i=1, 2, …, m. θ_i stands for the correlation coefficient of symbiotic factors; the larger θ_i is, the more outstanding the symbiotic relationship will be, and vice versa. According to the divide of symbiotic degree of the target value, when θ_i $\in$ (0, 0.30), then θ_i is the slight symbiotic correlation; when θ_i $\in$ (0.30, 0.60), then θ_i is the medium symbiotic correlation; when θ_i $\in$ (0.30, 1], then θ_i is the strong symbiotic correlation.

3.2.4 Symbiotic correlation degree

Based on symbiosis theory, symbiotic correlation degree is mainly used to represent the relationship of the units of symbiotic agents. If it is represented by the method that combines the weight of symbiotic indicators and symbiotic correlation degree, correlation degree can be expressed as follows:

${{\delta }_{j}}=\sum\limits_{i=1}^{n}{{{w}_{j}}\times {{\xi }_{i}}\left( {{x}_{0}}(t),{{x}_{i}}(t) \right)}$ (9)

In the formula (9), the larger δ is, the higher the symbiotic correlation degree of agent 1 to agent 2 in the unit of symbiotic agents will be.

In this study, the critical value method is used to standardize the primary data of the indicators and then the entropy evaluation method formulas (3), (4), and (5) are used to confirm the unit of symbiotic agents “E→G-R-T-E” in the symbiotic interface (Qinghai Lake) and the weight of symbiotic factors (Table 2). The findings represent: 1) In the unit of symbiotic agents “E→G-R-T-E”, the symbiotic impact of “E-G” is maximum with a weight value is 0.3154; next in sequence is “E-E” with a weight value is 0.2489; the symbiotic impact of “E→R-T” is comparatively minor with weight values of 0.2164 and 0.2193. 2) In the unit of symbiotic agents “E-G”, the symbiotic factor with maximum weight value is “Coordination and communication (E-G₂)” (0.2264), while the symbiotic factor with minor weight value is “Guidance and support (E-G₃) ”(0.1665). In the unit of symbiotic agents “E-R”, the symbiotic factor with maximum weight value is “Participate in operation (E-R₁)” (0.2671), while the symbiotic factor with minor weight value is “Mutually-beneficial cooperation (E-G₄)” (0.2347). In the unit of symbiotic agents “E-T”, the symbiotic factor with maximum weight value is “Polite manner (E-T₄)” (0.2521), while the symbiotic factor with minor weight value is “Living in harmony (E-T₅)” (0.1456). In the unit of symbiotic agents “E-E”, the symbiotic factor with maximum weight value is “Fair competition (E-E₁)” (0.2525), while the symbiotic factor with minor weight value is “Mutually-beneficial cooperation (E-E₂)” (0.1535).

This study uses the critical value method to standardize the primary data of the indicator, and the characteristic standard data array of symbiotic indicators in the unit of symbiotic agents “E→G-R-T-E” is obtained on the basis of formula (6). The correlation coefficient of the factors of symbiotic indicators in each sample is calculated by formula (7), and then formula (8) is used to calculate the average value of the correlation coefficient that has been calculated by formula (7). Finally, the symbiotic correlation coefficient (θ) of each symbiotic factor in the unit of symbiotic agents “E→G-R-T-E” is shown in Table 3.

The use of a grey correlation system and symbiosis the-ory shows that the larger the correlation coefficient θ_i, the more outstanding the symbiotic relationship is, and vice versa. On the basis of the symbiotic degree divide of target values, the medium and strong symbiotic factors of multiple tourist agents “E→G-R-T-E” in Qinghai Lake are obtained based on Table 3.

The result represents: 1) The values of symbiotic correlation coefficients of the symbiotic factor “Guidance and support” that affects the unit of symbiotic agents “E-G”, the symbiotic factor “Participate in operation” that affects the unit of symbiotic agents “E-R”, the symbiotic factors “Participation in tourism” and “Living in harmony ” that affect the unit of symbiotic agents “E-T”, and the symbiotic factors “Reaching a consensus” and “Harmonious and friendly” that affect the unit of symbiotic agents “E-E” are all greater than 0.60, and are the strong symbiotic factors of the unit of symbiotic agents “E→G-R-T-E”. These indicate that local governments have provided some political and financial support for ecosystem protection and tourism development of Qinghai Lake, and that tourist enterprises around the lake have benefited greatly. Residents around the lake can participate in the tourist business organized in the Qinghai Lake area, and the sense of communal ownership is strong. Tourists can participate enthusiastically in tourist activities organized in the Qinghai Lake area, and they often get along with each other very well. Finally, tourist enterprises around the lake emphasize conservation of the ecological environment and local culture, and they live in harmony. 2) The values of the symbiotic correlation coefficients of the remaining symbiotic factors that affect the unit of symbiotic agents “E→G-R-T-E” range from 0.55 to 0.60, and are all medium symbiotic factors. These indicate that local governments do not have strong symbiotic relationships with tourist enterprises in the areas of “Justice and equity”, “Coordination and communication”, “Mutually-beneficial cooperation” and “Supervision and administration”. Local residents do not have strong symbiotic relationships with tourist enterprises in the areas of “Cooperation and collaboration”, “Trust and communication” and “Harmony and progress”. Tourists do not have strong symbiotic relationships with tourist enterprises in the areas of “Services recognition”, “Ease of management” and “Polite manner”. Finally, the tourist enterprises do not have strong symbiotic relationships with each other in the areas of “Fair competition”, “Mutually-beneficial cooperation” and “Close contact”.

Based on formula (8), symbiotic correlation degrees δ (Table 4) of “E→G-R-T-E” are obtained: the symbiotic correlation degree δ of “E-G”(δ_E-G) is 0.5777, the symbiotic correlation degree δ of “E-R”(δ_E-R) is 0.5834, the symbiotic correlation degree δ of “E-T”(δ_E-T) is 0.5902, and the sym- biotic correlation degree δ of “E-E”(δ_E-E) is 0.5913. Therefore, the rand-size relationship of the symbiotic correlation degrees δ of “E→G-R-T-E” is δ_E-E˃δ_E-T˃δ_E-R˃δ_E-G.

5.1.1 The combination of symbiotic behavior routes of multiple tourist agents “E→G-R-T-E” of Qinghai Lake does not come up to an equilibrium state

According to symbiosis theory, symbiotic behavior routes are often viewed as direct modes that optimize the symbiotic relationship of the unit of correlative agents, and Nash equilibrium for the combination of such routes lies in the cooperation of several crucial strong symbiotic factors that exist in the unit of correlative agents. This can allow all the correlative agents to acquire the maximum symbiotic benefits (Butcher, 2011). The symbiotic agents constituted by “E→G-R-T-E” in the Qinghai Lake area produce general benefit by means of the division of labor among the agents and their cooperation. Even though the requirements of governments, tourist enterprises, residents and tourists get various degrees of satisfaction, the medium strong symbiotic factors of the unit of correlative agents cannot achieve the maximum symbiotic benefits of “E→G-R-T-E” and attain equilibrium, which to some extent affects the symbiotic relationship of correlative agents. Specifically: 1) There exists one strong symbiotic factor (E-R₁, E-G₃) in the symbiotic behavior routes of “E→G-R” which fails to produce the combination of symbiotic behavior routes of maximum symbiotic benefits of “E→G-R” in Nash equilibrium (Fig. 3, A and B). The reasons are as follows: in the process of intense tourist exploitation, the creation of “the grand beauty of Qinghai” tourism image and the orientation of the significant node of the Economic Belt & Road implemented by local governments, such as a series of preferential policies formulated by local governments to positively mobilize tourist enterprises and a segment of community residents. However, although the local governments actively lead tourist enterprises and some community residents to participate in tourism by means of vocational training, technological guidance and other methods, education levels (85.91% have senior high school or less education) and scope of knowledge are low and policy implementation may not be able attain ideal participation levels. Therefore, the symbiotic correlation degrees in the areas of “Coordination and communication”, “Mutually-beneficial cooperation”, “Supervision and administration”, “Participate in operation”, “Cooperation and collaboration”, etc. between local governments and tourist enterprises and community residents are not especially strong, and the symbiotic benefits are asymmetric. 2) Even though two strong symbiotic factors (E-E₄, E-E₅) exist in the symbiotic behavior routes of “E→E”, they fail to produce a combination of symbiotic behavior routes with maximum symbiotic benefits of “E→E” in Nash equilibrium (Fig. 3, D). The reasons are as follows: on account of the obvious seasonality of tourism in the Qinghai Lake area and the relatively short peak season, local tourist enterprises and community residents engage in illegal operations to maximize profits during the short peak tourist season. Local tourist enterprises can for the most part live harmoniously and in friendship, and arrive at a consensus with respect to conservation of the local culture conversation under the guidance of local governments; however, symbiotic correlation degrees in the areas of “Fair competition”, “Mutually-beneficial cooperation”, “Close contact”, etc. between local governments and tourist enterprises and community residents are not that strong, and the symbiotic benefits are asymmetric. In conditions where information access is asymmetric, illegal operations may allow tourist enterprises and some local residents to acquire surplus profits, with the negative social and economic impacts of these activities accruing to the Qinghai Lake area. 3) There exists one strong symbiotic factor (E-T₂) in the symbiotic behavior routes of “E→T” which fails to produce the combination of symbiotic behavior routes with maximum symbiotic benefits of “E→T” in Nash equilibrium (Fig. 3, C). The reasons are as follows: although tourists in the Qinghai Lake area can take part in tourist activities and get along very well with each other as a whole, there are numerous objective problems. These include the long loop line of the lake, dispersed scenic spots separated by long distances and underdeveloped tourism resources that influence quality and adequacy of tourism services available to tourists. These problems influence the overall quality of the tourist experience.

5.1.2 The model of symbiotic behavior routes of the multiple agents “E→G-R-T-E” in the Qinghai Lake area describes an asymmetrically reciprocal symbiosis

According to correlation coefficient θ of the symbiotic factors, the symbiotic correlation degree δ(δ_E-E˃δ_E-T˃ δ_E-R˃ δ_E-G), the combination of symbiotic behavior routes and an empirical investigation of the multiple agents “E→G-R- T-E” in the Qinghai Lake area, it can be determined that the symbiotic model of the multiple agents “E→G-R-T-E” in the Qinghai Lake area describes a symbiotic model of “scenic area-leading, community residents-boosting, governments- assisting and tourists-enjoying” (the symbiotic model of ERGT) which is also an asymmetrically positive symbiotic model. Qinghai Lake, which forms the basis for the symbiotic model of ERGT, depends on the four well- known scenic spots as Erlangjian, Bird Island, Fairy Bay and Sand Island. Because of the immense popularity of these spots, tourist enterprises bring in some community residents around the lake to participate in the tourism business, while local governments provide abundant political support and crucial assistance for the development of tourist enterprises around the lake. This allows tourists to participate in tourist activities and enjoy the unique natural landscapes and cultural customs of the Qinghai Lake area. Although the reciprocal symbiosis conditions of multiple tourist agents “E→G-R-T-E” in the Qinghai Lake are has formed, the numerous medium symbiotic factors of “E→G-R-T-E” cannot lead the unit of correlative agents to enforce the maximum symbiotic benefits in dimensional equilibrium; hence, a combination of symbiotic behavior routes in Nash equilibrium cannot be formed. This inevitably leads to the existence of “asymmetry” and “intermittency” in the reciprocal symbiosis of multiple-agents “E→G-R-T-E”, causes the short-term behavior of reciprocal symbiosis in the unit of correlative agents, and is detrimental to sustainably and harmoniously symbiotic development.

This study makes it clear that most of the tourist enterprises around the lake are operated by people who are not members of the local community. Their overall consciousness is weak and they can easily be shocked by the strong culture backgrounds of tourists. Therefore, in order to correct such attitudes, tourists enterprises around the lake often endure the “disrespect” of tourists who demonstrate attitudes of “rejection” and “unwelcome”. Based on the empirical analysis above, this study holds the view that the symbiotic benefits of multiple tourist agents “E→G-R-T-E” in the Qinghai Lake area are focused mainly on the dimensional equilibrium of the strong symbiotic factors, the combination of symbiotic behavior routes that are composed of the few strong symbiotic factors that enforce the symbiotic benefits of correlative agents. Hence, these cannot produce the combination of symbiotic behavior routes with maximum symbiotic benefits of “E→G-R-T-E” in Nash equilibrium.

If the combination of symbiotic behavior routes of the maximum symbiotic benefits in Nash equilibrium (W_E→G-R-T-E=W₅+W₁₀+W₁₆+W₂₂) can be attained by the multiple tourist agents “E→G-R-T-E” in the Qinghai Lake area (Table 5), local governments should formulate policies for preferential revenue and financial support, harmonize the contradictions between tourist enterprises and other symbiotic correlative agents, and undertake more supervisory and administrative work to develop and operate tourist enterprises. Local governments should not only promote the overall harmony of tourists enterprises with community residents around the lake and enhance the appeal of the Qinghai Lake area, but should also actively guide the demands for satisfaction of both tourist enterprises and community residents in order to encourage enthusiastic participation. Both the needs of local development and the predi-lections of tourists should be considered by governments and tourist enterprises in the Qinghai Lake area, and the fundamental demands of tourists should be regarded as the starting point for the rational design of tourism products and the provision of attentive tourism services. Tourist facilities can be completed, the original ecological environment for tourism can be protected to attract tourists to participate in local tourist activities, and consumption of tourist services, the arrival rate and return rate can all be increased. Community residents should become fully conscious and alter their attitudes towards tourists in order to encourage tourists to standardize their travel behaviors by showing a willingness to esteem and protect local culture, customs and the ecological environment.

In order to promote the smooth progress of tourism development in the Qinghai Lake area, these analyses of the symbiotic behavior model of multiple agents “E→G-R-T-E” can form a basis. Guiding mechanisms for the tourist exploitation of Qinghai Lake should be established in the areas of fair competition, mutually-beneficial cooperation, close contact, reaching a consensus, etc. by tourist enterprises. Mechanisms to boost tourist exploitation of Qinghai Lake should be established in the areas of participation in operations, cooperation and collaboration, trust and communication, harmony and progress, etc. by local community residents. Mechanisms for assisting tourist exploitation of Qinghai Lake should be established in the areas of coordination and communication, guidance and support, mutually-beneficial cooperation, supervision and administration, etc. by local governments. Mechanisms to enjoy tourist exploitation of Qinghai Lake should be established in the areas of services recognition, participation in tourism, polite manners, etc. by tourists. Together all of these form a reciprocal and harmonious symbiotic interface of the multiple tourist agents and establish the basic mechanisms for sustainable tourism development of Qinghai Lake. By means of the establishment of symbiotic mechanisms in the areas of guidance, decision-making, supervisory control and profit distribution, the participation mechanisms of multiple agents “E-G-R-T” should be further standardized. At the same time, tourist enterprises should be regarded as the dominant agents to optimize the symbiotic model of “E→G-R-T-E” through the reinforcement of integrative supply and the construction of integrative effects, and finally should promote the integrative symbiotic model of symmetrical reciprocity of E-R-G-T “driven by scenic areas, responded to by community residents, affected by local governments and tasted by tourists”.