This paper is motivated by the current debate concerning the possibility to extend the EU Directive on Savings Income Taxation. With the help of a two-country multiasset game-theoretic model, we assess how this measure could reshape the system of cross-border taxation. Then we analyze the consequences of its limited scope of application. For these purposes, we study the functioning of four taxation systems: a pure source-based system of withholding taxation; the model implied by the OECD Convention on Income and Capital; the scheme of coordinated withholding taxation negotiated by Austria, Belgium, and Luxembourg as a transitory measure before their full adoption of the Directive; and the residence-based regime finally adopted in 2003 which characterizes the EU Directive on Savings Income Taxation. Through analytical comparison we show that (i) the OECD system gives countries strong incentives to undertake non-collaborative policies; (ii) a system of coordinated withholding taxation cannot be adopted as a general rule in a structure like the EU where, in tax matters, decisions have to be taken at unanimity;(iii) the EU Directive offers an innovative design for the game, but its limited field of application encourages countries to issue financial products escaping the Directive; (iv) the extension of the scope of the EU Directive would permit to achieve a non-distorting scheme of international taxation allowing countries to tax individuals on their European-wide income.