INVESTMENT IN COLLABORATIVE E-COMMERCE PLATFORM BASED ON OPTION GAME. Received November 2008; accepted January 2009

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1 ICIC Express Letters ICIC International c 2009 ISSN X Volume 3, Number 1, March 2009 pp INVESTMENT IN COLLABORATIVE E-COMMERCE PLATFORM BASED ON OPTION GAME Yunfu Huo 1,2, Jing Wang 1 and Deli Yang 1 1 School of Management Dalian University of Technology Dalian , P. R. China 2 Institute of e-commerce and Logistics Dalian University Dalian , P. R. China josephhuo@sina.com Received November 2008; accepted January 2009 Abstract. Many companies that seek to jointly build a Collaborative e-commerce Platform (CECP) with their supply chain partners face a challenge to estimate the investment value while the attitude toward the participation is full of uncertainty. This research provides an option game valuation approach that clarifies the investment uncertainties by analyzing the expected revenue, cost, and time to the market for the au pair and cooperative partners, and the relation between the partners in CECP is au pair and cooperative other than traditional IS. This paper analyzed how investment and effort level of partners impact investment occasion based on real-option and principal-agent theory, which found that the success of CECP is lied on the cooperation between supply chain partners, although, there are some problems like ride free and adverse selection in the process. The research attempted to find what bring the puzzle and how to solve it. Keywords: Collaborative e-commerce platform, IT investment, Principal-agent theory, Real-option 1. Introduction. In global economy, cooperation is more and more important between the supply chain partners [1]. IT provides a better condition for it, thus supply chain partners are joining forces to create Collaborative e-commerce Platform (CECP) to meet the needs of each other in a particular market. However, many CECP have less success to attract members than they expect, because companies share their product and marketing information through the CECP can be very risky. The risks involved in the participation make partners attitude full of uncertainties, especially in the initial stage of system development. Since the traditional MIS (such as ERP, SCM, CRM) are often initiated by supply chain leaders who have already built deep relationships with their upstream and downstream companies. The leader-follower relation may force or impact supply chain partners participate in the systems building. So the puzzle of investment of these systems is a problem of opportunity choice. But CECP is different from traditional MIS as Figure 1. CECP will solve the problems of effectively interaction between different partners, and don t request they have the leader-follower relation. Thus other than the opportunity choice, there is a problem of ride free. So the methods to traditional IT payoff research will not be enough, and a more promising evaluation approach with the concern of reciprocal partner participation uncertainties should be built. 2. Literature Review. Traditional IT payoff research focuses on well-known financial measures, such as the return on investment (ROI), net present value (NPV), the internal rate of return (IRR), and the payback period. These methods may be suitable to measure 85

2 86 Y. F. HUO J. WANG AND D. L. YANG Figure 1. Relations of CECP between ERP, SCM and CRM in supply chain the value of simple and intra-organizational IT applications. However they are not as wellsuited for systems that across business boundaries, where uncertainty and risks is added to the situation as the investment payoffs are no longer depend only on internal contingencies but also on the decisions of supply chain partners [2]. So some researchers suggested the use of Real Option models to deal with the uncertainties of IT investments [3]. Kumar madeanotetocomparethedifference between Black-Scholes model and Margrabe model in the treatment of the cost of the second-stage project [4]. Zhu introduced Geske compound option model to treat IT investment projects as a sequence of growth options [5,6]. The most current development is from Benaroch and Kauffman [3]. They applied binomial option pricing model and Black-Scholes models to evaluate IT investment, with a real case study on the Yankee-24 electronic banking network. Although there is a growing research to apply real option approach to IT investment, mostly focus on IT investment of leader-follower, and few research put it into reciprocal partner context [7]. So we think real-option game approach provides a better approach to identify the uncertainties involved in CECP investment. 3. Framework and Basic Assumptions. We suppose that the cooperative enterprises A and B will decide to develop the CECP together. If the CECP can play an important role, the expected income will be the sharable income V t, It Subjects to the following the geometric Brownian motion process [8]: dv t = μv t dt + σv t dz (1) where, μ is the expected rate of the return, σ is the instantaneous standard deviation, supposing they are all constants. dz is a standard Wiener process incremental. (1) means that A and B will always be concerned about the changes of the variable V t and consider the benefits and costs of their own to choose the right investment opportunity. Under the cooperation conditions, the vestment costs of the A and B include fixed costs and efforts costs. Fixed costs can be verifiable and quantifiable and clearly agreed in the contract. Efforts costs are hidden costs. It is a function of the level of effort, and it grows rapidly with the efforts level increase. To study conveniently, supposing the fixed costs of A and B are the C A and C B,theefforts costs are 0.5aE 2 A and 0.5bE 2 B,inthis,a and b are the costs coefficient. E A and E B are the level of the efforts. The proceeds of the two costs are V S and V C,thesharableproceedsisthefollowingformula. ( Vt = V S + V C (2) V C = ζeb α E1 α A where, ζ is the output coefficient, α istherelativeimportanceforb in the cooperation. Therefore, A must invest more separately when B is not involved, CECP will succeed. Supposing after investing fixed costs (C A + θc B ), V S will be realized. θ is cost-saving coefficient. Based on the both inputs of the fixed costs, if the two sides further input the efforts costs, in addition to the V S, they will get extra revenue V C.ButifB doesn t input the efforts cost, it will share the V C by ride free.

3 ICIC EXPRESS LETTERS, VOL.3, NO.1, Thus, a reasonable distribution of income V S will determine the attitude of the investment cooperation between the two sides. Because the inputs can be quantified, this paper proposes to take the following pattern to the income of the fixed inputs. C B γ = (3) C A + C B γ is the share of the proceeds for B, 1 γ is the share of A. In order to avoid the ride free in the fixed inputs, because of the effortscannotbeseen,weshoulddesignan appropriate incentive mechanism. Based on the income V C of the efforts inputs, supposing The distribution of proceeds for B is sv C, the distribution of proceeds for A is (1 s)v C, s is allocation coefficient of the efforts income, 0 s 1. The cooperated development process of the CECP: All partners observe it, choose the best time for the common input. A and B signed a contract to determine the allocation coefficient γ of fixed-income V S and the allocation coefficient s of the efforts income, V B = γv S + sv C C B 0.5bE 2 B is the net income of partner B. V A =(1 γ)v S +(1 s)v C C A 0.5aE 2 A is the net income of the partner A. Under maximizing their net income conditions, each partner decides his own fixed input and efforts input. Generally, in Principal agent model, supposed A first issued the invitation of the cooperation, as it is willing to develop CECP, it can be considered as clients. Models are as follows. max V A = max {(1 γ)v S +(1 s)v C C A 0.5aE C A,E A A, 2 0} (4),r,s ( ª max VB = max γvs + sv C C B 0.5bE 2 B,V p C B,E B (5) V p 0 In addition, the income can be created only through partners participate in the investment, so we set that C A 0, C B Investment Decision Analysis. To build the cooperated development and participation of the CECP, the first step is to analyze the allocation mechanism of the cooperation income. And then to determine the conditions of the cooperation and participation according to the cooperation income and input costs. In the allocation mechanism, γ can be decided by (3) directly, but s must be decided by backstepping, after the γ and s are determined, the last is to determine the participation threshold conditions The distribution analysis of the efforts income. Given the maximum efforts income of A and B, we can get the response function of the efforts level [9]: 1/(1+α) (1 s)(1 α)ζ E A = E α/(1+α) B a (6) µ 1/(2 α) αsζ E B = E (1 α)/(2 α) A b From (6) we can know that A and B in the Nash equilibrium efforts level. µ α/2 (2 α)/2 αζ (1 α)ζ E A = s α/2 (1 s) (2 α)/2 b a (7) µ (1+α)/2 (1 α)/2 αζ (1 α)ζ E B = s (1+α)/2 (1 s) (1 α)/2 b a

4 88 Y. F. HUO J. WANG AND D. L. YANG As for form (7), based on maximum s (4), we can determine the optimal allocation of s under the Nash equilibrium. α + α 2 p α(1 α 2 )(2 α), α 6= 1/2 s = 2(2α 1) (8) 1/2, α =1/2 Partners assignment share of income is related to the relatively importance of the cooperation Cooperation development option analysis. To be the sponsor of the CECP, A should clearly know the value of it, so he will be act the system when the best opportunity comes. According to the option viewpoint, A is similar to grasp Unlimited time American option which s carries out the price is this project s income pays fixedcost,andwaited forthatthevalueistheoptiontimevalue. WhenA solely invests CECP, the Bellman equation is as follows: F S (V t )=max V t C A θc B,e rdt E[F S (V t + dv t )] ª In the formula, F S expressed A alone invests when option value r expressed discount rate. This is a most superior stop question, the stopped state is a sole investment obtains the net income V t C A θc B, The continuum is waited for that the opportunity carries on the investment. A sole investment option value and most superior investment strategy standard inferential reasoning process can be seen by Dixit and Pindyck [8], the result is: where V S ( YV β t, F S = V t C A θc B, V t <V S V t V S is the sole investment threshold value, Y and β is constant: VS = β β 1 (C A + θc B ) Y = V S (C A + θc B ) (VS )β β =0.5 μ r ³ μ σ + 2 σ r + 2 σ > 0 2 When A s option value is F C in the cooperation development, the related Bellman equation is as follows: F C (V t )=max (1 γ)v t +(1 s)v C C A 0.5aE 2 A,e rdt E[F C (V t + dv t )] ª Solute above equation, obtain A s income and investment strategy in the cooperation development: ( XV β t, V t <VC F C = (11) (1 γ)v t +(1 s)v C C A 0.5aE 2 A, V t Vt where, VC is the threshold value of the participation and cooperation development, X is a constant. VC = β 1 CA +0.5aE 2 A (1 s)ζeb α E 1 α A (β 1) 1 γ X = 1 γ (12) β V C 1 β In order to make V C > 0, it is necessary to make C A +0.5aE A 2 (1 s)ζe B α E A 1 α > 0. (9) (10)

5 ICIC EXPRESS LETTERS, VOL.3, NO.1, The analysis of decision-making for cooperating and building. There are two purposes for cooperating and building: first, gaining saving of cost; second, gaining saving of cost and making great efforts together. From (5), γv S C B V p,wecanknow the income critical value for B participating in is VB, when the original value is very small, A as the sponsor of cooperating, once he discover V t VC, he will sponsor cooperating, so there is VB V C V S. For above, we can gain decision-making for cooperating and building as follows: (1) when E A =0,E B =0,thequalification for A choosing B as co-worker is θ 1, and V P + C B C B β/(β 1) (13) TheincomecriticalvalueforB participating in: VB = V P C A /C B + V P + C A + C B (14) (2) when E A 6=0,E B 6=0,thequalification for A choosing B as co-worker is µ 1 θ aEA 2 (1 s)v C (15) C A C B and V P + C B +0.5bE 2 B sv C β µ C B + C B 2 0.5aEA (1 s)v C (16) β 1 C A TheincomecriticalvalueforB participating in VB = V P + C B +0.5bE 2 B sv C + C A + C A (V P +0.5bE 2 B sv C ) (17) C B 4.4. Cooperative exploitation occasion analyzed. Cooperative sponsor observes CECP income change in every time. If he finds opportunity, he will suggest cooperative initiatives and make investment decision. Its optimal investment opportunity is T =inf(t t V ), namely first passage time. Assuming that when V t = V (< V ), T is A s opportunity which developed alone, T C is the opportunity which only exist in the saving of cost, when A initiative the development of cooperation, T E is not only exist in the saving of cost but also have the opportunity which is the development of cooperation, is initiatived by A, when it is working hard for proceeds. The length of time which development alone shorter than development of cooperation is: Γ C = E(T T C )andγ E = E(T T E ). According to Harrison [10], when the proceeds achieves at the critical value V, the unused probability distribution function is: ln (V /V )+(μ 0.5σ 2 )t Pr [T t] =N µ V + V σ t ( 2/σ 2 )(μ 0.5σ 2 ) N (18) ln (V /V ) (μ 0.5σ 2 )t Thereinto, N(Z) is the standard normal cumulative probability distribution function, V is the initial state of the potential gains, respectively, V corresponds to (10) of VS and (12) of VC When μ 0.5σ2 > 0, V will reach the time expectations E(T )ofv, E(T ) must exist for: E(T )= ln (V /V ) (19) μ 0.5σ 2 1 Γ C = μ 0.5σ [ln(c 2 A + θc B ) ln(c A + C B )] (20) 1 Γ E = ln(ca ) ln(c μ 0.5σ 2 A +0.5aEA 2 (1 s)v C ) (21) There is a static comparative analysis between (20) and (21), the following conclusions: σ t

6 90 Y. F. HUO J. WANG AND D. L. YANG (1) Γ C / θ > 0, 2 Γ C / θ 2 < 0, namely, Γ C will non-linear increase along with the Γ increasing for θ, and the increased speed will slower rate, lim C =0. θ θ (2) Γ E / a >0, Γ E / b <0, namely, Γ E will to decreases along with the increase of the cost factor of effort for A and B. 5. Numerical Analysis. Now, through the numerical method we have more analysis of cost savings and gains on the CECP efforts to develop and operate the impact of the timing. Assuming a supply chain enterprises A found that the market value about invest and develop the CECP, that is determined by the same supply chain jointly with partners B. Common basic parameters, r =0.06, μ =0.05, σ =0.3, V p =10,C B =5,C A =15,ζ =1. Choose both cases that α =0.35, 0.75, analysis of cost savings and income to the cooperative development and operation of the timing of the CECP. Figure 2 through various cost-savingfactortocomparethedevelopment of co-operation and development uncooperative, and In such circumstances, to know the changes in the timing of the investment; Figure 3 compares the efforts of different cost factors and the relative importance, and In such circumstances, to know the timing of investment that Γ E = E(T T E ) how changes, (b = 10), dotted line is when the cost factor of B to change what about Γ E = E(T T E ), (a =10). Figure 2. Investment occasion based on Cost saving coefficient Figure 3. Investment occasion based on effort coefficient and importance

7 ICIC EXPRESS LETTERS, VOL.3, NO.1, Conclusions. Available from the above analysis than results the following conclusions: (1) The development and operation of the CECP needs the supply chain partners invest and efforts, it is obvious network effect. (2) However, to the development of the CECP fixed investment, the future will be based on a fixed proportion of input to divide the corresponding income, so the sponsors hope that the fixed input fewer, the need of fixed investment partners which is lesser that the process will be faster. This also reflects the first advantage of the CECP investments, but it will also lead to investment partners were not enthusiastic, and will also affect the cooperation. (3) In the process of working hard together to build the CECP, higher the efforts of cost factor, the effective efforts will be less significantly, with the sponsors of the root causes of those efforts will be low-cost partnerships, so the sponsors will choose the lowcost partnerships. At the same time, partners, that sharing of the efforts gains only rely on the their respective efforts in the relative importance, has nothing with the level of effort, with the cost factor increasing too high cost of efforts will decline the positive efforts and the level of efforts, then leading the net income efforts decline. This reflects the development and cooperation of CECP likely to be a dilemma, that is, cooperation between each side are not stronger than their selves, finally formed one results similarly to adverse selection, which should arouse the concern of all participants. REFERENCES [1] S.H.Chan,J.W.KensigerandA.J.Keown, Do strategic alliance create value? Journal of Financial Economics, vol.46, no.2, pp , [2] J. Gebauer and P. Buxmann, Assessing the value of interorganizational systems to support business transactions, International Journal of Electronic Commerce, [3] M. Benaroch and R. Kauffman, Justifying electronic banking network expansion using real options analysis, MIS Quarterly, vol.24, pp , [4] R. Kumar, A note on project risk and option values of investments in information technologies, Journal of Management Information Systems, vol.13, pp , [5] K. Zhu, Evaluating information technology investment: Cash flows or growth options, Workshop on Information Systems and Economics, [6] R. Geske, The valuation of compound options, Journal of Financial Economics, vol.7, pp.63-81, [7] H. Chang and M. J. Shaw, Evaluating the impact of supplier participation on investment strategies of buyer-based B2B E-commerce systems using game-based option valuation analysis, Proc. of American Conference of Information Systems, [8] A.K.DixitandR.S.Pindyck,Investment under Uncertainty, Princeton, NJ: Princeton University, Press, [9] D.FudenbergandJ.Tirole,Game Theory, Massachusetts Institute of Technology, [10] J. M. Harrison, Brownian Motion and Stochastic Floe Systems, New York: John Wiley & Sons, Inc., [11] M. Benaroch and R. Kauffman, Justifying electronic banking network expansion using real options analysis, MIS Quarterly, vol.24, pp , [12] L. D. Zhao, L. B. Qu and M. Liu, Disruption coordination of closed-loop supply chain network (I): Models and theorems, International Journal of Innovative Computing, Information and Control, vol.4, no.11, pp , 2008.