Optimal sizes of facilities on a linear market (Q1110447)

Let n facilities be located on a bounded linear market and assume that demand for a homogeneous commodity is uniformly distributed along the market. Initially each facility has a given size which determines its attraction to the customers. Independently at each facility a profit function is maximized by selecting new facility sizes. The individual optima are then combined and the optimization procedure is repeated. In a series of tests it is shown that such a decentralized optimization procedure quickly converges to an overall equilibrium.