Existence and Efficiency of Nash Equilibria under Deterministic Voting

Abstract

This paper considers an economy with a public good where a decision must be made both about the level of the public good and the taxation imposed on each citizen (multidimensional policy space). In this context, we derive two interesting results: i) we show that a Nash equilibrium exists under deterministic voting, ii) we show that political competition is a necessary but not sufficient condition for the elimination of political rents (efficiency). In our political game a Nash equilibrium (under deterministic voting) exists because politicians commit to the level of the public good but not to the level of taxation. However, because of the lack of commitment to the taxation level, politicians are able to overtax citizens, provide an inefficiently low level of the public good and extract rents, even under political competition. Therefore, efficiency requires appropriate political institutions (maximum taxation constraint).