Argentina and Brazil have the most powerful sub-national governments and are the most decentralized federal countries in Latin America. Being politically and administratively strong, provincial and state governments ransacked national coffers several times in recent history, contributing to profound fiscal imbalances at the central government level and large macroeconomic crises. Likewise, the resources and autonomy of sub-national units have also been assaulted by the central government. Fiscal re-centralization processes triggered large budget deficits in the provinces and, hence, shortages in the delivery of basic services. In many cases, provincial authorities could not pay for salaries or afford basic supplies, having to face protests, demonstrations, and violence. This oscillating distribution of resources has occurred despite federal rules that should, in principle, institutionalize relations and ease conflicts between the two levels of government. What determines these changes in the distribution of resources among units in these federal democracies? When are substantive changes in the distribution of resources more likely to occur? This work intends to explain under what conditions substantive shifts in the allocation of resources and functions are more likely to occur. The central argument of this work is that changes in the allocation of fiscal resources and the distribution of administrative functions are to be expected when either presidents or governors prevail in their power relations, when they are pressed by fiscal urgency, and when they have to cope with hard budget constraints. This study presents, first, a theoretical argument making use of formal modeling and game-theoretical tools. Relying on a statistical analysis, it also tests the main explanation and alternative arguments to account for changes in the distribution of resources and functions in federal democracies in a large-N study. Third, it applies the game theoretical framework to a comparative historical analysis of Argentina and Brazil since their transitions to democracy until 1999 and 2002 respectively. It finally concludes with some theoretical and comparative implications for the study of fiscal federalism and the functioning of developing federal democracies.