Game Theory Analysis of Bidding for A Construction Contract

Abstract

The authors are concerned with a bidding problem. There are two companies (P1 and P2) bidding for a highway construction project. In order to be more competitive, P1 considers buying a new gravel pit near the construction site. The basic cost of the pit is known to both companies. However, there is also an additional, hidden, cost (C) known only to P1. P2 is uncertain whether the hidden cost is C = 0 or C = x. P1 plans to bid for the job, but has to decide whether to buy the gravel pit. P2, not having a complete knowledge about C, thus not knowing the strategy choice of P1, has to decide if to bid for the job. In effect we have two payoff matrices, one for the additional cost C = 0, and the other one for C = x. If the probability of P2 bidding for the project can be estimated by propagating intelligence information through a Bayesian Belief Network, the best strategy for P1 can be readily determined. Otherwise, the solution calls for changing this game of incomplete information (players may or may not know some information about the other players, e.g., their "type," their strategies, payoffs) into a game of imperfect information (players are simply unaware of the actions chosen by other players). This is achieved by introducing an additional "Nature" node which for this problem determines with some probability "p" the additional cost C= 0 (thus, C = x with probability 1-p). The solution of this game turns out to depend on the probability "p". For some values of p the game is solved with pure strategies, whereas for other values the game is in equilibrium when the players randomly mix their strategies.