In this paper we present a differential game model of two firms with different technologies producing the same good and selling in the same world market. The firm equipped with advanced technology is deciding whether to outsource parts of its production to the home country of its competitor, where wages and the level of technology are lower. Outsourcing reduces production costs but is associated with spillovers to the foreign competitor. The degree to which the foreign competitor can absorb these spillovers depends on its absorptive effort. Using numerical methods the properties of a Markov Perfect Equilibrium of this game are characterized and the implications of the variation of different key parameters are examined.