# A Real Option Pricing Decision of Construction Project under Group Bidding Environment
###### Abstract  
The bidding price is one of the important factors for construction enterprises in winning a bid. In the context of public bidding in the construction industry, in the process of group competition, how to estimate the individual bids to calculate their maximum value and the best price to improve the winning probability has become an important issue. In this research, based on the real option theory, the concept of group bidding environment is introduced to establish a real option price decision-making model for construction projects. The function of the model covers two external competitive environments: independent and coupled. Finally, through model inspection and parameter sensitivity analysis, the model is discussed in depth, and suggestions for model application are obtained. The research results show that the rule of the model results has optimization characteristics, and the numerical solution is consistent with the analytical solution, which has a certain price guidance role. In the independent bidding environment, their optimal bidding price is inversely proportional to the volatility level and the option period, and it is directly proportional to the estimated costs but has no obvious relationship with the number of competitors. Moreover, the average sensitivity of the optimal bidding price to the estimated costs, the volatility level and the option period are 35.06%, 9.77% and 7.70%, respectively; the optimal mark-up ratio is 1.078. In the coupled bidding environment, the concentration of competitors' prices and the optimal price will increase significantly, by about 2.37%, and the corresponding winning probability and weighted option value will increase by about 9.36% and 28.03%, respectively. The research results can provide price optimization for bidding activities with real option characteristics and improve the price winning rate, but the selection of price mode and parameter setting need to be set by enterprises according to industry characteristics and actual conditions. construction projects; group bidding environments; real option value; optimal bidding price; sensitivity analysis Article  
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the average price-winning method has been widely used. This kind of method takes the arithmetic average of all prices as the evaluation standard price, assuming that the winner is the closest to the average price. [PERSON] used the Monte Carlo simulation to establish the model of average price winning bid [3], and [PERSON] explored the equilibrium results of average price auction and its impact on market allocation efficiency through empirical research [4; 5]. At present, we can roughly divide the models related to bidding price decision approaches into four main fields: (1) statistical, (2) operations research, (3) bidding psychology and (4) multi-objective decision models. Models are also gradually developing in an integrated way. Statistical models determine the optimal price by protecting the bidding behavior of each competitor. [PERSON] proposed the first bidding model in construction engineering, Friedman's Model, which calculates the joint probability by calculating the winning rate between the bidder and each independent competitor, and then obtains the optimal bidding price [6]. [PERSON] and [PERSON] proposed a stochastic programming model to maximize expected profit, reducing the estimated costs error and improving the expected average profit by analyzing historical data [7; 8]. [PERSON] derived the optimal conditions by assuming a single competitor and uniformly distributed estimation errors [9]. In recent years, theories such as decision tree [10], entropy metric [11] and Monte Carlo simulation [12] have also been applied to build a decision-making model for bidding price. The game theory model is the most widely used operational research model in the bidding field. It is a decision-making problem when the behavior of decision subjects interacts with each other, which is often used to study the distribution decision-making problem involving multiple interests.