COMPETITIVE LOCATION UNDER UNCERTAINTY OF COSTS

In this paper, we study the centroid problem from competitive location theory for a linear market with uniform demand, assuming that the lea der has imperfect information about the follower's fixed and marginal costs. It is shown that the general version of this problem can be for mulated as a nonlinear programming problem and the exact solution can be obtained analytically in a special case. A simple strategy is also given for the general problem, and it is proven that this strategy has a guaranteed error bound. It is demonstrated that uncertainty of cost s might lead to market failure in the centroid problem, but this disap pears if the game is repeated and the firms learn from observing each other's moves. It is also shown that it is possible for the leader to obtain optimal expected profit at a low perceived risk, with only suff icient, and not necessarily perfect, information. These two observatio ns lead to our primary conclusion from the study that although cost un certainty is a realistic feature of most competitive location models, there are very effective ways of dealing with it.