On the General Existence of Pure Strategy Political Competition Equilibrium in Multi-dimensional Party-Faction Models

In this paper, we consider political competition games of two parties in multi-dimensional policy spaces, where the two parties have two factions, opportunists and militants, that intra-party bargain with each other. In such a game, we adopt the party-unanimity Nash equilibrium (PUNE) [Roemer (1998; 1999; 2001)] as an appropriate solution concept, and examine the general existence problem of this. In particular, we suppose that any faction of each party does not necessarily have dictatorial power. We then provide a general existence theorem for PUNE in this class of games. JEL Classification Numbers: C62, C72, D72, D78