58 research outputs found
An extension of Reny's theorem without quasiconcavity
In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened: roughly, we introduce a measure allowing to localize the lack of quasiconcavity; this allows to refine the analysis of equilibrium existenceNash equilibrium, existence, discontinuous games, non quasiconcave
Existence of Nash Equilibrium in Discontinuous Games
This paper offers an equilibrium existence theorem in discontinuous games. We introduce
a new notion of continuity, called quasi-weak transfer continuity that guarantees the existence
of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider
possible extensions and improvements of the main result. Our conditions are simple and
easy to verify. We present applications to show that our conditions allow for economically
meaningful payoff discontinuities
Existence of Equilibria in Discontinuous Games
This paper investigates the existence of pure strategy, dominant strategy, and mixed strategy Nash equilibria in discontinuous games. We introduce a new notion of weak continuity, called weak transfer quasi-continuity, which is weaker than most known weak notions of continuity,
including diagonal transfer continuity in Baye et al (1993) and better-reply security in Reny (1999), and holds in a large class of discontinuous games. We show that it, together with strong diagonal transfer quasiconcavity introduced in the paper, is enough to guarantee
the existence of Nash equilibria in compact and convex normal form games. We provide sufficient
conditions for weak transfer quasi-continuity by introducing notions of weak transfer
continuity, weak transfer upper continuity, and weak transfer lower continuity. Moreover, an
analogous analysis is applied to show the existence of dominant strategy and mixed strategy
Nash equilibria in discontinuous games
- …