Tax competition in a Bertrand model

We show that in Bertrand models pure-strategy equilibria exist only under extraordinarily restrictive assumptions. We analyze tax competition between two countries for foreign investment. In the symmetric case of equal gross profits of the firms, zero-taxation is the unique equilibrium in pure strategies. If gross profits differ between countries only -equilibria can exist. However, if the tax rate applies to foreign investment as well as to domestic sources no equilibria exist in pure strategies. The same holds true if countries compete for firms that differ in gross profit opportunities, unless extremely unrealistic conditions are met.