How to effectively control the cost of software development and improve the cost efficiency has always been the focus of party A. Software cost estimation process is discussed in this paper, we studied the purchasing behavior of both sides, based on the game theory to build the party A and party B the purchase price game model of the enterprise, won the party A and party B to take different strategies of Nash equilibrium, the two sides are discussed under different parameters of the strategy, the analysis result was combing inductive. It is pointed out that demonstration + price review is the best choice of party A's price control method, which can reduce the cost of audit and have a deterrent effect on party B's enterprises, so as to standardize the quotation behavior of enterprises. The analysis also points out that the control of software development cost should be balanced comprehensively, and economic benefit should not be emphasized blindly.
Software is a special product, which is the crystallization of mental work. With the rapid development of modern information technology, the requirements of equipment interconnection are becoming higher and higher. Software plays an increasingly important role in national and social economic life. The economic research on software originated from the United States, Britain and other countries, among which Boehm B. W and Putnam L.H And Banard L. Boehm put forward the Constructive Cost Model (COCOMO) in the process of studying cost calculation, and provided the workload calculated by software scale, so as to determine the empirical statistical model of cost and duration. In 2000, he published the monograph Software Cost Measurement -- COCOMOII Model Method [1]. The U.S. Department of Defense supported the publication of Software Development Cost Estimation Manual, which clearly defined the process of software cost estimation and recommended some parametric cost tools, such as COCOMOII, Price-S, SEER-SEM, SLIM, etc. [2].
Development enterprises can calculate the cost of software system according to the above methods. However, due to various reasons, development enterprises tend to over report development costs in order to obtain higher income. How to analyze the behaviors of party A and party B and their influence on software procurement, game theory provides an effective path.
Game theory is the study of decision-making and the equilibrium of decision-making when the behavior of decision-making bodies directly interacts with each other. In economics, game theory studies the decision-making problem and equilibrium problem when the decision of an economic subject is affected by the decision of other economic subjects, and the corresponding decision of the economic subject in turn affects the choice of other economic subjects [3]. Based on game theory, Baoping Liu et al. [4] established a game model between party A and party B, analyzed the drawbacks of the current military product pricing model and proposed solutions.Shihui Wu et al. [5] established a game model between party A and party B under the incentive and constraint pricing model, and drew guiding conclusions and suggestions through analysis of the model. Guojiang Hou et al. [6] conducted indepth analysis on Nash equilibrium of pricing negotiation game, expansion of model and negotiation strategy, and obtained the key factors affecting pricing negotiation. Qin Wang et al. [7] used the multi-stage game theory to construct a model and studied the business motivation and strategic behavior of enterprises participating in the open source movement. They believed that the fundamental reason for enterprises participating in the open source movement was the expectation of future benefits of this innovative model. Game theory is an important theoretical tool to study the behavior of both sides of procurement, but there are few related literatures in software procurement.
At present, party A mainly adopts two price control modes of price review + price review and price review for the purchase of single-source software. This paper establishes a game model based on these two modes for party B's enterprise to overstate/overstate costs, and makes a detailed analysis of the model [8]. Firstly, the software cost estimation process is introduced, and the possible reasons for overstatement of software cost are pointed out. Then, the game matrix of party A and party B is established to calculate the Nash equilibrium point, analyze the parameter characteristics of the Nash equilibrium point and the conditions for its establishment, and discuss the strategy selection tendency of both parties under different parameter conditions. The influence of the value of verification reduction coefficient on party A (buyer) and party B's enterprise (supplier) is studied. At the end of the paper, the results are analyzed and the suggestions for party A to control the purchase cost are given.
of party B
In the principal-agent relationship between party A and party B's enterprise, the price department of party A plays a core role in the process of software development and pricing, playing games with party B's enterprise on behalf of party A; The enterprise of party B has a large amount of information about its own development status and is in an information advantage position. According to the existing laws and regulations, party A mainly controls the software price through demonstration and evaluation [8]. Demonstration, that is, party A shall demonstrate the development cost of the project in the demonstration stage of the project establishment, estimate the development cost and profit based on the objective laws of software development and historical data on the basis of the project's realization objectives and work required. Evaluation can not only restrain the false software development cost, but also identify some unnecessary software functions and management process, and control the project work structure from the source, so as to control the development consumption.
Due to the superiority of the enterprise in cost information and the lack of strong punishment measures from party A, the enterprise always tends to falsely report the cost in order to maximize the benefits. This section studies the quotation mode of party B's enterprise. It is assumed that party A can choose two strategies, namely, false or actual cost reporting.
A Nash equilibrium is a situation in which each player cannot improve his situation as long as the others do not change their strategy. Nash proved that Nash equilibrium exists on the premise that each participant has only a limited number of strategies to choose from and mixed strategies are allowed. Its definition is as follows:
Assuming that there are n players involved in the game, if in a certain situation no player can act alone to increase the returns (that is, in order to maximize their own interests, no single party is willing to change its strategy), then the strategy combination is called Nash equilibrium.
All player strategies constitute a Strategy Profile. Nash equilibrium is essentially a non-cooperative game state.
Assuming that the actual cost of software system development of party B's enterprise is C0, the standard income of the enterprise is C0(1+α), where α is the cost profit margin of party B's enterprise. At this time, party A gain of R, to carry out the appraisal can produce consumption, for C(p), p for the master degree of software development, information of party A, which is held by party A the information such as the software realization function, technical requirements, and party B enterprises or social software system efficiency, the average person month rate, etc., might as well assume that C(p) is a continuous function of p, 0≤p≤1，C’(p)>0, and C(0)=0. In addition, the software development cost C0 declared by party B's enterprise will produce consumption, which is recorded as x0. If the price is falsely stated, the declared consumption is x1, and x1≥x0.
The strategic combination and corresponding benefits of party A and party B are as follows:
(
(
(
(
The above analysis is shown in the benefit matrix in Table 1.
Assume that the probability of party B's enterprise falsely reporting costs is r, 1≥r≥0, and the probability of party A verifying the true costs by means of price evaluation is s, 1≥s≥0.
(
U1(1, r) = r[R − C( p) − (1− p)X ] + (1− r)[R − C( p)]
U2 (0, r) = r[R − X ] + (1− r)R r* = C( p) = pX
When the probability of party B's enterprise falsely reporting costs is less than r*, The optimal choice of party A is not to carry out the evaluation; when the probability is greater than r*, the optimal choice is to carry out the evaluation; When the probability of party B's enterprise falsely reporting costs is equal to r*, party A randomly chooses to implement or not to implement the evaluation.
(
U3(s,1) = s[C0(1+α ) + (1− p)X − x1] + (1− s)[C0 (1+α ) + X − x1]
(
When there is no difference between the software cost falsely reported by party B's enterprise and the actual software cost reported by party B, party A can obtain the optimal solution of price evaluation. If U3=U4, we can get: s* = X − x1 + x0 = 1 [1− pX p
When the probability of price evaluation by party A is less than s*, the optimal choice of party B's enterprise is to falsely report the cost; when the probability of price evaluation by party A is greater than s*, party B's enterprise chooses to report the actual cost; When the probability of price evaluation of party A is equal to s*, party B's enterprise randomly selects false or actual cost.
According to Equations (
C( p) ，1 [1− pC0(1+α )(x1 x0 −1) p
x0 ]） C0(1+α )
According to (9), this Nash equilibrium is related to cost C0 of party B's enterprise, cost profit margin α, party A's price examination consumption C(p), and enterprise declaration consumption x0.
If β=C0(1+α)/x0 is the declared comprehensive rate, that is, the consumption rate of party B's declared software development income, and Δ=x1−x0 is party B's falsely reported input, then r* = C( p)
pβΔ ∂r* = C′( p) p − C( p) ∂p p2 X r* is inversely proportional to the reported comprehensive rate and false report input of party B's enterprise, that is, the higher the software development cost of party B's false report, the lower the probability of false report. It will be found later that party A has a higher degree of software information and the higher the false report amount, the higher the probability of false report being detected, which will reduce the probability of false report by party B.
We take the partial derivative of r* star with p If p≠0, d[C’(p)p-C(p)]/dp=C(p)p.
1) If the C’’(p)<0, because front assumption C’(p)>0, C(0)=0, C’(p)p-C(p)<0 (p > 0), r* is the reduction function of p.
2) If the C’’(p) > 0, because front assumption C’(p)>0, C(0)=0, C’(p)p-C(p)>0, (p > 0), r* is
increasing function of p.
(
C(p) Cur曲ve线2 2 C’’(p)<0
曲C线ur1ve 1CC’’’(’p()p>)>00 0 1 p
Curve 1 and curve 2 in Figure 1 correspond to C’’(p)>0 and C’’(p)<0 respectively. Curve 1 shows that with the increase of party A's mastery of information, when p approaches 1, the evaluation cost rises rapidly and has an infinite trend of increase. Curve 2 indicates that C(p) is also meaningful when p>1, and there is an upper limit. Theoretically, both of these scenarios are possible, but in general, 0≤p≤1 makes sense, and curve 1 is more consistent with the hypothesis.
If C’’(p)<0, then with the increase of party A's information mastery, The probability of party B identifying the false statement increases and party B's willingness to false statement decreases. The implied condition is that There is an upper limit for party A's consumption of price review, and party A can try to improve its information mastery.
If C’’(p)>0, party B's willingness to falsely report will increase with the increase of party A's information mastery. The increase of implied information in this leads to a sharp rise in the cost of party A's evaluation, which reduces the willingness of party A to evaluate, so that the probability of false reporting by party B increases.
From (
It is easy to know from (
C( p) x0
C0(1+α )(x1 x0 −1) ≤ 1− C0(1+α ) ≤ p
According to the analysis of C’’(p) in Figure 1, the cost of evaluation should not be too high. On the other hand, according to the actual project experience, the application cost should be far less than the software development income.
It is easy to know from Formula (
Finally, the influence of x0 and x1 is discussed.
1) Under normal circumstances, the application of r&d price according to existing software price
regulations will always produce certain consumption x0. The partial derivative of equation (
C( p) x1 pC0 (1+α ) (x1 − x0 )2 > 0 （11）
That is, r* is an increasing function of x0. The greater the declared investment of party B, the greater the probability of false report. party B shall make up for the loss caused by the declaration.
From (
2) In extreme cases, if x0 is small, it will be approximately 0 (such situation is reported according to
other price regulations), and then (
(
(
(
(
(
(
If the software enterprise overstate the cost, the main method is to overstate the software function, such as adding unnecessary function modules, overstate the number of lines of code, etc. The evaluation can identify unnecessary software functions according to party A's purchase requirements, but it requires the support of relevant expert teams and large investment in training professionals. The prophase investment is large and the demonstration cost is high. If the project cost is small, the price review should be more cost-effective.
The above suggestions are put forward according to the analysis results and problems encountered in the process of software development price demonstration, which is feasible but relatively broad. It is suggested that Party A and Party B should further study to find a software pricing method that meets the interests of both parties.
At present, party A mainly adopts two methods to control software development costs: price review and no price review, but there is no theoretical explanation on which method is more advantageous. This paper first analyzes the process of software development cost estimation, points out the false software development cost and then analyzes the influence of party A's software purchase price control mode on party A and party B by using game model. A game model is established to obtain the Nash equilibrium when party A and party B adopt different strategies. The analysis results indicate that whether party B's enterprises falsely report or actually report costs, demonstration + price review can play a good role in reducing audit costs and producing a deterrent effect on party B's enterprises. The price control mode to be selected is directly related to its reduction capacity. party A shall make a comprehensive balance based on market conditions and technological development and other factors, instead of blindly pursuing economic benefits. In general, the purchase price control mode of party demonstration + price review is the best choice for party A and can achieve the best results.