History versus expectations in economic geography reconsidered

This paper cooiders aclass of adjustment dynamics with forward-looking migrants in anew economic $g\infty graphy $ model \‘ala Krugman (1991a). Specifically, we employ the equilibrium $dynam\ddagger cs $ due to Krugman (1991b) $\bm{t}d $ Fukao and Benabou (1993), where migration incurs moving costs which depend on the size of the current migration flow, so that migrants care about the future migration behavior of the economy. Our main goal is to $identi\theta $ astate that is absorbing (i.e., if the initial state is in aneighborhood of this state, then any equilibrium path converges to it) and globally accessible (i.e., for any initial state, there exists an equilibrium path that converges to this state) when the degree of hiction is small (i.e., the migration cost $\bm{t}d/or $ the rate of time preferenoe is snall). We show that such astate generically exists (which is unique by definition) and is characterized as aunique maximizer of apotential function of the static model. The proof strategy for our result follows that of Hofbauer $\bm{t}d $ Sorger (1999), who study stability under adifferent class of perfect foresight dynaInics, due to Matsui and Matsuyama (1995), in potential games. We first show that equilibrium paths in ou