Keywords: bargaining, joint venture, game theory, fuzzy logic, pricing, model.

As the modern construction market and environment encounters drastic changes, a single company alone can no longer manage a complex project and satisfy a project owner's needs. Joint venture (JV) companies, formed to integrate various expertise, becomes a necessity to obtain competitive advantages to ensure survival in the fiercely competitive market [1]. While two profit-oriented companies intend to form a JV for a particular project, it is relatively easy to divide the work scope into each party's specialties, yet to reach an agreement on the sharing of the rewards is always a challenge.

Lai [2] pointed out that bargaining is induced when a conflict lies between participating parties, and communications and compromises are required to reach an agreement. Raiffa [3] proposed the concept of "zone of agreement", which can be figured out by deducting the lowest, acceptable price of each party from the total amount. As each party strives for their maximum price, which is also acceptable to the other party, in the "zone", bargaining is usually carried out through numerous repetitions of offer-and-counteroffer until an agreement is reached, or the bargaining is given up.

The collaborations between JV parties are usually on short-term, project-to-project basis and the time allowed for bargaining is strictly limited. Thus, how to evaluate a bargaining situation and offer an acceptable price to both parties in a timely manner is critical for the success of a JV project. However, current practices are still lack a systematic tool or model for supporting a company's pricing decisions. This research aims to fill that gap.

Previous research has pointed out that the outcome of a bargaining procedure is highly influenced by the stakes of the bargainers and the bargainer's level of dependence on the outcomes of bargining [4]. Accordingly, this research focused on the variable, demand for the project, which is used to represent a company's level of dependence on the profit from a JV project. A sequential bargaining model is developed based on game theory, which is used to estimate acceptable prices in accordance with each party's cost and demand for the project. Furthermore, since the company's demand for the project always features a certain degree of uncertainty, fuzzy logic is used to deal with it. The results of sensitivity analysis indicate that JV parties' rewards are highly associated with their demand for the project; a party, which has a relatively high demand for the project, will render relatively high profits to its partner.

The proposed sequential bargaining model is useful for JV parties to determine a best price based on each party's cost and the estimated degree of demand for the JV project can thus facilitate the bargaining. Many researchers theoretically focused on the unique equilibrium price by assuming that the information for pricing is perfect. However, since there is no perfect information situation in a real bargaining case, companies inevitably continuously collect information, evaluate the bargaining situation, and repetitively make pricing decisions in the bargaining process. Instead of finding a unique equilibrium price, the research focuses on developing a method, which can be used to assess the bargaining situation and select a pricing strategy in a scientific and rational manner. An example is presented in this paper to demonstrate the applications of the proposed model.

1

S.R. Norwood and N.R. Mansfield, "Joint venture issues concerning European and Asian construction markets of the 1990's", International Journal of Project Management, vol. 17, no. 2, pp.89-93, 1999. doi:10.1016/S0263-7863(98)00016-7

2

H. Lai, A Theoretical Basis for Negotiation Support Systems, unpublished doctoral dissertation, University of Purdue, 1989.

3

H. Raiffa, The Art and Science of Negotiation, Mass: the Belknap press of Harvard University press, 1982.

4

S.B. Bacharach and E.J. Lawler, Bargaining Power, Tactics and Outcome, San Francisco: Jossey-Bass, 1981.

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