Existence and Efficiency of Nash Equilibria under Deterministic Voting

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 (multi-dimensional policy space). In this context, we derive two 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. Furthermore, we show that efficiency requires appropriate political institutions (maximum taxation constraint). These results are interesting, because they show that i) partial commitment is an important element of the efficient solution of this problem, ii) to the best of our knowledge, this is the only game with multi-dimensional policy space, where an equilibrium exists, it is efficient and political rents are zero.