Application of Least Square Approximation Algorithm in the Game Analysis and Data Prediction of the Core Competence Signal of Civil Engineering Employment

The least square approximation algorithm is often used to predict the data based on historical experience. In this paper, the method is applied to the research of “game analysis and data prediction of the core competence signal of civil engineering employment”, which theoretically verifies the existence of “weak sequence” rational equilibrium in civil engineering employment by means of mathematical reasoning. In addition, the method is applied to the prediction of civil engineering major in one university in Heilongjiang Province from 2010 to 2019 as an example, and the empirical data of employment prove the real existence of the game signal. Finally, according to the method, the research predicts the related data of employment in 2020.


Introduction
National medium and long-term educational reform and development project summary (2010-2020) pointed out that ordinary colleges and universities should "focus on cultivating high-quality talents and top-notch innovative personnel with persistent faith, excellent moral character, rich knowledge, and strong ability", "support students to participate in scientific research, and strengthen practice teaching links", and "enhance education of employment and enterprising and employment guidance service". Accordingly, colleges and universities in Heilongjiang Province "is gradually transforming and upgrading talent cultivation concept by taking students as the main body and teachers as the leading, and putting efforts on fostering students' social responsibility, spirit of innovation and practical ability". Meanwhile, more attention is given to scientific research projects, an important indicator and main content to measure students' scientific research innovation level.
It is safe to say that students' participation in scientific research projects not only "adapts to objective needs of both the country and social development", but also "abide by the rules of higher education and talent growth". The development of this activity helps "deepen education and teaching reform, innovate education teaching methods, explore various cultivation methods, form a situation that a wealth of talents and top-notch innovative personnel coming out in succession", "cultivate students' scientific innovative level, tamp their major foundation, exercise their practical ability", and "strengthen students' employment competence, enhance their employment quality". In this paper, a game theory model "between students' scientific innovative level and employment ability" is built, and empirical analysis is undertaken by using the data of scientific research projects and employment rate of students in civil engineering of one university in Heilongjiang Province in the past three years, with the expectation that it will bring some guidance effect on the real work [1][2][3] .
2 Establishment of the game model

Hypothesis of the model
(1)Client hypothesis: Firstly, two graduates with employment competence of H and L respectively, and L H  , and both meet "rational-economic person hypothesis", namely, they will actively choose the company who gives them the highest salary as their employer. Secondly, under the circumstances of market economy, two employers also meet "rational-economic person hypothesis", namely, they would like to hire the graduate with higher employment competence by giving the same lowest salary.
(2)Strategy hypothesis: First, scientific innovation level that the graduates formed in the school is e ; second, two employers give salary 1 w and 2 w after seeing e ; finally, each graduate chooses one salary (i.e. one employer). (

Establishment of the model
It is easy to know that this game theory has a weak sequential equilibrium when analyzing this mentioned hypothesized model through incomplete-information type game theory. Because graduates with employment competence H will enhance his professional innovation level by taking part in various kinds of scientific research activities when he was in university to improve his future employment competitiveness, so as to possess the ability of getting high salary [5][6] .
(1)Graduate's strategy: The graduate of Type H is equipped with , then the graduates of both types all choose employer giving higher salary. If two employers give the same salary, namely 2 1 w w = , then the graduates will choose the first company.
(2) Company's strategy: All companies believe that if a graduate choose * e , then he is Type H , the employer needs to pay him corresponding salary of H ; otherwise, a graduate chooses e , then he is Type L , and the employer needs to pay him corresponding salary of L .
The following Figure 1 is an "unfolding game theory model of imitating graduates who provide the two employers with their employment competence signal after receiving scientific innovative cultivation and training in university".

Analysis on game model
Based on the mentioned hypothesis and model establishment, we are going to solve this game theory's "weak sequential" rational equilibrium result.

Graduate's action
Under the assumption of rational-economic person, it is the best strategy for graduates to accept the highest salary offered by employers at the end of the game theory. Now, we are going to think about the graduate's initial action.
(1) Type H graduate: If Type H graduate follows his own strategy and formed scientific innovative level * e , then the profit he is going to get is . Therefore, to get equilibrium, we (2) Type L graduate: If Type L graduate follows his own strategy and formed scientific innovation level 0 , then the profit he is going to receive is L ; if his formed scientific innovation level is * e , then employer will believe his employment competence is H , and then his profit is L e H * − . Therefore, to get equilibrium, we

Company's action
Under given strategy, the profit of each employing company is H H − or L L − , namely, always 0 . If employer raises his salary offer to respond to graduate's any formed scientific innovation level e , then his expected revenue will be negative, and it obviously does not conform to the assumption of rational-economic person; if employer lowers salary offer, his profit is still 0 , because his offer will not be accepted by any graduate.
In conclusion, when and only when can this game theory have "weak sequential" rational equilibrium result. Again, because we have assumed that L H  , through simple mathematical analysis, we can know that * e in this formula does exist. That is to say, to any H and L , game theory has separating equilibrium, in which graduate with high employment competence possesses higher scientific innovation level, while graduate with lower employment competence has lower or even has no scientific innovation level. This kind of level has no influence on the graduates' formation of ordinary work ability or production capacity after their entry into work, but the existence of * e means that graduates are equipped with a platform of showing their potentiality, or a chance that shed their possibility of being put in the list of employees with lower capability in the future employer-employee relationship.

Empirical study and data prediction
In order to further verify the real existence of this game theory model, this paper takes students in civil engineering of one university in Heilongjiang Province as study objects, extracts related data of "students participating in scientific research" and "employment rate of overall graduates" of this department from 2010 to 2019, out of which "high-quality employment rate" and "Fortune 500 employment rate" are taken as a cut-in dot of study, and undertakes analysis and prediction respectively towards the following data in table 1 ,table 2 and figure 2.   (1)Data in Table 1 and Table 2 indicate that from 2010 to 2019, high-quality employment rate of students in civil engineering of one university in Heilongjiang Province, whether the employment rate of graduates in scientific research or that of overall graduates, this index has been increasing year by year on the whole; percentage and growth scale of "high-quality employment rate of students participating in scientific research" are much higher than current corresponding indexes. Data contrast is shown in Figure 2.

Data contrast and analysis
(2)When analyzing graduates' "Fortune 500 employment rate", we find out that this index from 2013 to 2017 decreased compared with that in the previous year. Exterior elements that influence employment caused the slide of this index include the downturn of domestic real estate market, the shrunk of construction engineering market, the slowdown of infrastructure investment, etc. However, "Fortune 500 employment rate" of students taking part in scientific research of those years still kept strong growth. Data contrast is shown in Figure 2.

Data prediction
used to predict two data of "overall high-quality employment rate" and "high-quality employment rate of students participating in scientific research" of students in civil engineering major of one university in Heilongjiang Province in 2020. Details are as followed in Table 3 and Table 4. That is to say, the predicting data of high-quality employment rate of graduates participating in scientific researches in 2020 is 68.74%. That is to say, the predicting data of overall graduates' high-quality employment rate in 2020 is 47.18%.

Conclusion
Firstly, based on the least square approximation algorithm and historical empirical data, taking the civil engineering major of this university as an example, the predicting data of high-quality employment rate of graduates participating in scientific researches and overall graduates' high-quality employment rate in 2020 are 68.74% and 47.18% respectively. Secondly, the condition for math algorithm's establishment is that the proportion of graduates participating in scientific research shows a weak linear growth trend year by year on the whole. Thirdly, only when the "high quality employment rate of graduates participating in scientific research" in the previous years reaches the value listed in the table, can the forecast value of "overall high quality employment rate of graduates" in this year be calculated.That is to say, "weak sequential" rational equilibrium exists between these two items. Fourthly, this prediction algorithm is only a theoretical one. Real employment and formation of related data are still influenced by various kinds of interior and exterior elements.