Competitive location strategies for two facilities

In this paper we present the problem of locating a facility when competition from another facility is taken into consideration. Two problems are addressed here. One is the location of a new facility that will attract the most buying power from an existing facility. The other is the location of a facility that will secure the most buying power againts the best location of competing facility to be set up in the future.     

A game of timing and visibility

We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x_i in the interval [0,1], and a player's payoff is the distance from its point x_i to the next larger point, or to 1 if x_i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games.     

Short-run fluctuations in fertility and mortality in pre-industrial Sweden

This paper describes and interprets annual Swedish data from 1750 to 1869 on weather, harvests, real wages, birth rates, and death rates using vector autogression. Impulses due to unexplained increases in wealth, whether this occurred through increased real wages, improved agricultural yields, or warmer winters, led in the short run to increased fertility and decreased infant and non-infant mortality, and hence to increased rates of population growth. Unexplained or unanticipated fluctuations in infant mortality led to replacement cycles in fertility within one to three years, although only a negligible cumulative effect on fertility persisted after five to ten years. Fluctuations in deaths among persons older than one year evoked a fertility response several years later, but this replacement response persisted after more than a decade. Although vector autoregression is not designed to account for long-term trends and their consequences, the interrelationships found here among exogenous weather shocks and fluctuations in economic conditions and demographic rates provide support for the homeostatic mechanisms hypothesized by classical economists and discussed by Malthus. The methodology of vector autoregression appears useful for studying historical series on climatic, economic and demographic variables where we do not yet have a sufficient theoretical foundation for specifying and estimating structural models.