On the existence of Bayesian Cournot equilibrium

Abstract

We show that when …rms have incomplete information about the market demand and their costs, a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. In fact, we are able to construct surprisingly simple and robust examples of duopolies with these features. However, we also …nd some su¢ cient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries.More general results arise when negative prices are possible.

Bayesian Equilibrium in a Public Good Economy

“…Existence of a Bayesian equilibrium is assured by cardinal normality conditions 4 . This is in contrast to Einy et al (2010), who show that Bayesian equilibrium in a Cournot oligopoly may not exist when prices are non‐negative.…”

On the Existence of Nash Equilibrium in Bayesian Games

“…In Einy et al [30] it is shown that when firms have incomplete information about market demand and cost functions, a Cournot equilibrium in pure strategies need not exist, even in simple cases with linear demand and cost functions. The existence of equilibrium in behavioral (or distributional) strategies easily follows from standard arguments if market demand and cost functions are assumed continuous, but remains an open question in the presence of discontinuities.…”

“…Then, for each n, , and, in light of (30), either (i) q 1 ≥ G 1 (t, p 1 , q 1 , q 2 ), q 2 ≥ G 2 (t, p 1 , q 1 , q 2 ), and in this case To see that Γ is uniformly payoff secure, fix i, ε > 0, and s i ∈ P i . By Assumption L, the family {D(t, ·) : t ∈ T} is equicontinuous on R + .…”

Bayesian Nash equilibrium in “linear” Cournot models with private information about costs

“…Einy et al (2010) examine conditions for existence and uniqueness of equilibria in oligopoly models with more general imperfect information structures when non-negativity of prices is taken into account.…”