Countermeasures of Financial Internal Supervision Institutions of Administrative Institutions Based on the Double Game

. The state audit in the new era focuses on strengthening the restriction and supervision of public power, and it will inevitably require strengthening the audit and supervision of administrative institutions, which leads to the discussion of the efficiency of the internal supervision institutions in administrative institutions. In order to effectively control the finance internal supervision risk, a moral hazard monitoring model with a two-tier game mechanism is proposed. In the model, it establishes an upper-level game and a lower-level game analysis framework for the "lazy" and "Free-riding" behaviors in moral hazard. Combining the equilibrium conditions to explain the game results, and put forward the overall risk monitoring countermeasures for the two behaviors.


Introduction
As an important part of the supervision system, the national audit in the new era must strengthen the restriction and supervision of public power, that is, focus on realizing the full audit coverage of administrative institutions (hereinafter referred to as "units"). In this context, it is more and more important to improve the unit's internal control mechanism and implement the unit's financial internal supervision and management. Therefore, how to ensure the efficient operation of the financial internal supervision organization of the unit is a problem worthy of in-depth discussion [1][2][3] . Under the condition of asymmetric information, the internal financial supervision organization of the unit may not act in full accordance with the wishes of external audit (National Audit), and there is the possibility of "moral hazard", which is manifested in the specific behavior of "laziness [4] " or "free ride [5] ". Therefore, strengthening the guidance of external audit supervision and effectively reducing the probability of moral hazard [6] is an effective measure to improve the operation efficiency of the internal financial supervision organization of the unit.
Based on game theory and principal-agent theory, this paper establishes a moral hazard monitoring model with two-tier game mechanism [7][8][9][10] . Under the constraints of external audit, this paper discusses the countermeasures to establish the financial intern10l supervision mechanism of administrative institutions and scientifically avoid the moral hazard of internal supervision.

2.Upper level game of "laziness" between external audit department and internal supervision organization 2.1 Description of basic assumptions
(1) Establish the basic framework of the upper game, and define the two sides of the Bureau as the external audit department and the internal supervision organization respectively. The game is a repeated game under asymmetric information. The national audit department is the principal and the internal supervision organization is the agent.
(2) The audit department performs an audit task on a unit. The internal supervision organization of the unit carries out daily financial supervision with effort level u . u U  , U represents all optional action combinations of the supervision organization. The value range of u is 0 u l   ,  is the exogenous random variable affecting daily financial supervision, and the value range of  is  .
(3) The audit department judges the performance of the supervision organization by observing the audit results. ( , ) x u  . The financial supervision of the supervision organization improves the efficiency of the use of financial funds, and the total value created is ( , ) v u  . It is assumed that ( , ) v u  is a strictly increasing concave function of u .
(4) v is determined according to the observed performance ( , ) explanation, it is assumed to be 1. In the process of supervision, the audit department rewards and punishes the internal supervision institutions according to the observed value ( , ) x u  . Generally, effort level u and performance x should be in direct proportion, that is, the harder the internal oversight body works, the easier it is to be observed to perform its duties. Here, it is assumed that: , so Q is an unbiased estimate of x .
(6) The audit department supervises the "lazy" behavior of the supervision organization, and sets the payment function given to the supervision organization as In the formula, D is the fixed expenditure cost of the audit department for the audit supervision of the supervision organization, and n is the sharing and transformation coefficient of the total value x obtained by the supervision organization after performing its duties. It can be understood as the savings of supervision resources caused by the internal supervision organization playing the role of financial supervision and forming an efficient and standardized virtuous circle system of financial management, which is obviously 0 1 n   .  reflects the remuneration paid to the supervision organization according to the supervision signal.
(7) In the game process, it is assumed that the audit department is risk neutral and the internal supervision organization is risk averse. The risk cost of the person in the bureau is Where, w is the actual acquired value of the players, and at this time   is the risk aversion of the players.

Establishment and analysis of "lazy" behavior supervision model
According to the marginal cost theory and principalagent theory, the agent's effort cost is positively correlated with the degree of effort, and the greater the degree of effort, the greater the increase of the required cost. Therefore, it is assumed that the financial supervision cost of the internal supervision organization The larger b is, the higher the cost of the same effort u is. Accordingly, the payment function given by the audit department to the internal supervision organization is From equation (5), the deterministic income of the internal supervision organization is According to the game theory, the Pareto optimal condition is that the marginal cost is equal to the marginal income, that is, equations (1) and 2 f bu  obtain the partial derivative of effort level u respectively 1 2 At this time, the deterministic income of the audit department is Obviously, according to hypothesis shows that the audit department wants the internal supervision organization to work harder and not "lazy", while the internal supervision organization wants the audit department to give sufficient incentives, otherwise it will lack the motivation to work hard and choose "lazy" behavior. In order to achieve Pareto optimality, a "lazy" behavior supervision model is established, and the audit department supervises the performance of the supervision organization, in the form of: In equation (9) ② Satisfy the incentive compatibility constraint (IC). Only when the effort level selected by the internal supervision organization is within the scope of feasibility set, the internal supervision organization will perform the financial supervision function according to the wishes of the audit department.
③ Audit supervision signals introduce constraints. Only when the audit department can ensure its deterministic income growth after introducing the audit supervision signal can it implement the signal supervision.
According to the partial derivative of u obtained by the constraint condition IC in equation (9), it can be seen that the maximum effort of the internal supervision organization to perform its duties is Calculate the first-order partial derivative of  of equation (11), there is Calculate the first-order partial derivative of n in equation (11), that is, the optimal * n is * 2 Substituting equation (14) into equation (13) , there is Substituting equation (15) into equation (14) , there is Substituting equation (13) into the IR condition of equation (9), it is found that the optimal fixed expenditure cost of the audit department is

game result analysis of "laziness" behavior supervision
Analyze the results of the "lazy" behavior supervision game in equations (13)  an alternative relationship. This shows that the higher the accuracy of the audit supervision signal, the more the audit department can truly detect the effort level of the internal supervision organization. Therefore, the more sufficient the basis for the audit department to accurately pay the internal supervision organization (obtain effective audit supervision opinions) according to the audit supervision signal. shows that in the process of long-term game, the more stable the state of audit supervision signal is, the higher the reliability of the conclusion of detecting whether there is "laziness" behavior of internal supervision institutions, and the audit department will rely more on audit supervision signal for payment, that is, increase the payment weight. Fourth, *  is inversely proportional to b , and D is negatively correlated with b , which indicates that when the financial supervision cost of the internal supervision organization is too high, the "lazy" behavior will probably occur. At this time, the signal fails, and the audit department is no longer willing to pay according to the audit supervision signal. If we want to ensure that the internal supervision institutions will not be "lazy", we can only improve the fixed payment cost of the audit department under the condition of constant cost conversion efficiency, that is, increase the frequency and intensity of audit supervision.

description of supplementary assumptions
(1) Establish the basic framework of the lower level game, and define the two sides of the Bureau as the national audit department and the internal supervisors of the unit respectively. The audit department is the principal and the internal supervisors are the common agents.

establishment and analysis of "free ride" behavior supervision model
In order to effectively control the "free ride" behavior of internal supervisors, the audit department shall establish the following supervision mechanism: According to the assumptions, the common expected return of m internal supervisors is According to Pareto optimal conditions: The Pareto optimal effort level is At the same time, the deterministic income of internal supervisors i is In equation (23) Remember that the optimal effort level after partial and promote the improvement of cost conversion efficiency coefficient.
(3) Establish a rating system and "black and white list" system for financial internal supervision and assessment of the unit. From the perspective of the upper game, the supervision quality assessment is the final recognition of the audit department's work evaluation of the internal supervision organization, and it is also the basis for the audit department to make actual payment based on the supervision signal. From the perspective of lower level game, in order to reduce the risk of "free riding", it is necessary to determine the penalty i h and reward 0 m under the Pareto optimal effort level of internal supervisors. Therefore, it is necessary to establish standardized and complete quality assessment business procedures and establish five grade evaluation rating systems of a, B, C, D and E. A is the best and E is the worst. For the supervision institutions rated as grade A, they shall be commended and incorporated into the "white list" of inspection exemption for the next year. For the supervision institutions rated as grade D and E, they shall be criticized, tracked their later rectification and included in the "blacklist" of inspection required for the next year. The supervision institutions listed in files B and C shall conduct sampling inspection as appropriate.
(4) Establish a flexible and adjustable reward and punishment system for internal financial supervision of the unit. This is because in the game between the upper and lower levels, the confirmation of the payment function of the audit department is based on the conclusion that the reward and punishment effect is credible. When the effect of rewards and punishments is unbelievable or the confidence level changes, the intensity and mode of rewards and punishments shall be adjusted. Generally, rational economic people are more sensitive to positive incentives, and negative incentives will bring more resistance. At this time, it is unbelievable for the audit department to increase the punishment measures. Therefore, it is suggested to focus on the way of "high reward and low punishment", which is easier to stimulate the work enthusiasm of internal supervisors.