Abstract In this paper we propose a basic fixed-point theorem for correspondences inspired by Tarski’s intersection point theorem. This result furnishes an efficient tool to prove the existence of pure strategy Nash equilibria two player games with possibly discontinuous payoffs functions defined on compact real intervals.

Based on Nakajima’s Classification Theorem [N] we describe the precise form of the binomial equations which determine toric locally complete intersection (“l.c.i”) singularities.

We obtain a number of consequences of the theorem on the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the derived subgroup of the group, as well as an analogue of Lie’s theorem for (not necessarily continuous) finite-dimensional representations of connected soluble locally compact groups. In particular, we give a description of connected ...