Under the information asymmetry, we consider the impact of task importance on the income of university managers, introducing the non-linear income function of university managers. Based on the principal-agent theory, we construct a non-linear incentive optimisation model for subject librarians. We discussed how university managers allocate incentive intensity and how the subject librarians allocate the effort level to achieve the best net expected income for university administrators and subject librarians while satisfying the constraints of participation and incentive compatibility. The results show that the optimal incentive contract for subject librarians is related to task importance, ability level, risk aversion characteristics and the randomness of the external environment in university libraries. The relative incentive intensity increases with the increase of task importance, risk aversion, ability level and randomness of information retrieval tasks, and decreases with the increase of randomness of subject service tasks.
Keywords
- principal-agent
- incentive contract
- subject librarian
Information retrieval and subject service are the core tasks of subject librarians in university libraries. The information held by university administrators and subject librarians is asymmetric. One party has private information. As long as the behaviour of one party affects the interests of the other party, the relationship between the participants can be regarded as a principal-agent relationship, with private information. One party is called the ‘agent’, and the party that does not own private information is called the ‘principal’. There is an obvious information asymmetry between university administrators and subject librarians, and the degree of effort of subject librarians is not easily observed by university administrators. Due to the asymmetry of information, university administrators seek to maximise the interests of the library, where the focus is on the construction and development of the library. Subject librarians value their income, entertainment time, additional benefits and promotion of professional titles. As a result, subject librarians do not aim at maximising the interests of university administrators, but choose to maximise their own interests by hiding their actions and efforts, resulting in the ‘moral hazard‘ problem.
Principal-agent theory was established in the late 1960s and early 1970s. It is an important development of contract theory. Contract theory believes that the principal-agent relationship is a contractual relationship. The party at a disadvantage for information is the principal, and the party at an advantage for information is the agent. The principal authorises the agent to engage in activities for the benefit of the principal. The principal-agent relationship is a kind of bilateral contractual relationship. The principal and the agent are both economic persons pursuing the maximisation of their own interests, and their interests are related but their respective objective functions are different. The principal and the agent form a mutually acceptable contract through ‘bargaining’, that is, an equilibrium contract. The principal and the agent need to meet two conditions to form an equilibrium contract: One is the participation constraint, the expected utility obtained by the agent by accepting the contract should not be less than the maximum expected utility obtained by the agent without accepting the contract. The other is the incentive compatibility (IC) condition, in which the agent should ensure the maximisation of the expected profit of the principal according to the principle of maximisation of contract performance utility. After the principal and the agent form a contractual relationship, the principal grants the agent considerable discretionary power. The principal hopes that the agent chooses actions according to the principal's interests. However, it is difficult for the principal to directly observe what actions the agent chooses but only some variables, which are determined by the agent's actions and exogenous random factors. Therefore, what the principal observes is only an incomplete information of the agent's actions, which determines that the main problem faced by the principal, that is, to motivate the agent to choose actions that are beneficial to the principal based on the observed variables.
When an agent undertakes multiple tasks, there is a conflict in the agent's energy allocation towards the different tasks. When the tasks are different, the supervisor's ability to supervise is also affected, and it is becomes even more difficult to supervise some jobs. Holmstrom and Milgrom [1] pointed out that the multi-task analysis logic is roughly the same as the bilateral principal-agent theory, while being much more complicated than the bilateral principal-agent theory. When the agent is engaged in multiple tasks, the traditional principal-agent conclusions are not applicable. In view of this, Holmstrom and Milgrom [2] believed that when an agent undertakes multiple tasks, the degree of motivation for any one task depends not only on the observability of the task, but also on the observability of other tasks. In particular, when the principal wants the agent to make a certain effort towards a certain task, and the task is unobservable, the principal's incentive compensation should not be used for other tasks. Kirkegaard [3] proposed a new method for moral hazard, which proved the rationality of the first-order conditional method and played an important role in the analysis of multi-dimensional moral hazard. It proved the rationality of the first-order condition, especially in a specific environment, when the agent undertakes multiple tasks under the multi-dimensional economic behavior. Balmaceda [4] studied the optimal task allocation problem based on the risk-neutral principal-agent model, and pointed out that multiple tasks would bias the distribution of the agent's effort intensity. Compared with the traditional single task, in addition to the complementary relationship between multiple tasks, that is, when there is an alternative or independent relationship between multiple tasks, the principal wants the agent to undertake multiple tasks. In addition, multi-task principal agent is widely used in many fields. Kossi et al. [5] discussed how the scientific research environment affects the assignment of scientific researchers’ tasks. Based on the two tasks of scientific research and teaching undertaken by scientific researchers, and under the mutual substitution of scientific research and teaching, a multi-task scientific researcher incentive model was constructed. It was found that the dynamic environment has a significant impact on the scientific research output regardless of the scientific research ability of the researchers. Capponi and Frei [6] constructed a dynamic multi-task principal-agent model combined with the two tasks of the agent's effort and accident prevention, and designed the optimal incentive contract, the optimal degree of effort, and the behaviour of safety protection measures under the information symmetry. Under the multi-task principal-agent model, Li and Hendrikse [7] studied the influence of the member size and heterogeneity on CEO incentive factors. Fitoussi and Gurbaxani [8] considered the moral hazard problem of IT multi-task business outsourcing, and believed that the establishment of multiple incentive index system can effectively reduce the opportunistic behaviour of service providers. Dai [9] used the mean square utility to build a multi-task business outsourcing incentive model, and pointed out that the incentive intensity is related to the risk aversion of the contracting company and the main parameters of the specific task. The correlation between the motivation intensity and the main variables depends on the degree of relevance between the tasks. From an owner's perspective, Zhang [10] introduced the same ability, that is, fairness preference and reputation of the contractor, respectively, and constructed the multi-task contractor incentive model in three situations, respectively giving the contractor's second-best salary incentive contract. When both state-owned enterprise executives and government authorities are in a fair preference, Yan [11] gave the optimal salary incentive mechanism for state-owned enterprise executives, and pointed out that when the tasks are complementary or replaceable, the fairness preference of both parties will promote the return of the optimal salary of state-owned enterprise executives to fair salary through direct and indirect influence channels. Based on the economic and public welfare tasks undertaken by doctors, Guo and Gu [12] built an independent incentive model for medical staff who were between tasks. He pointed out that under the fixed salary system, doctors chose to undertake tasks with a lower marginal effort cost, and under the sharing system and rent system, doctors chose to undertake economic tasks with higher quantification, higher marginal output and higher marginal effort.
In summary, scholars have improved the traditional principal-agent theory by adding new factors and variables, applying it to all areas of life. But the model assumptions are mainly based on linear returns. This paper considers the impact of task importance on the income of university managers, introduces a non-linear performance income function, and constructs a multi-task incentive optimisation model for subject librarians. Through the model solution, the optimal salary incentive contract is designed and the incentive characteristics are analysed.
The basic multi-task principal-agent is assumed as follows:
In order to analyse the problem conveniently, the following assumptions are made for the basic model.
The income of university administrators is
The expected income of subject librarian is as follows:
Subject librarians have typical characteristics of absolute risk aversion. Furthermore, the deterministic equivalent income of subject librarians is expressed as:
Under the information
And, under asymmetric information, the IC constraint is expressed as:
Therefore, under asymmetric information, after introducing task importance, the incentive optimisation model for the subject librarians is as follows:
IR and IC are the two main constraints that university managers must face to obtain the maximum expected utility. IR indicates that the effectiveness of the salary contract designed by university administrators for subject librarians must be greater than or equal to the maximum opportunity income obtained by subject librarians who refuse the contract. IC indicates that when university administrators are unable to detect subject librarians, subject librarians always choose the best effort to maximise their expected utility.
Considering the task importance, when the information is asymmetric, the university managers can not fully observe the effort level of the subject librarians in information retrieval and subject service. In order to achieve the optimal equivalent income of their own certainty, the subject librarians will not choose the optimal effort level. Therefore, the optimal incentive optimisation model is as follows:
Managers will not pay more income for subject librarians. In the best case, participation constraints are equal, that is
Taking the first order condition for the excitation constraint condition IC, the following results are obtained:
And then
After substituting the objective function and simplifying:
Find the first order condition for
After reorganizing:
And then
So
Furthermore,
Finally, the best effort levels of subject librarians in the two tasks can be obtained as follows:
Let Since
Therefore, Since
Therefore, when
Since
So, when Since
So, when
Under asymmetric information, this paper considers the impact of task importance on the income of university managers. The non-linear income function and specific task ability of university managers are introduced, the non-linear incentive optimisation model of subject librarians is constructed, the optimal incentive contract is designed through model solution, and the characteristics of relative incentive intensity are analysed. Results show that the optimal incentive contract of subject librarians is related to the task importance, the ability level of subject librarians and the degree of risk aversion, and the randomness of the external environment of the university library. The relative incentive intensity increases with the increase of task importance, risk aversion, ability level and information retrieval task randomness, and decreases with the increase of randomness of the subject service task.
Finally, there are many factors influencing motivation intensity, such as overconfidence level, supervision level, reputation, etc. We don’t consider these factors here, and subsequent research can consider the impact of these factors on the intensity of incentives.
Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Nonlinear Differential Equations in the Teaching Model of Educational Informatisation The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe80Si10Nb6B2Cu2 Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x p m −x +δ )s +ax p m +bx overF p 2m Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Research on identifying psychological health problems of college students by logistic regression model based on data mining Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation A mathematical model of PCNN for image fusion with non-sampled contourlet transform Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology