Indeterminacy of Cournot–Walras equilibrium with incomplete markets

Abstract

This paper studies a sole proprietorship economy with imperfect competition in a transferable utility setting. While consumers behave as price takers, producers issue real assets strategically to maximize their own utility. Even when complete markets are technologically feasible, equilibria with incomplete markets are robust, and they appear in large numbers: There is a continuum of equilibria with different asset spans that can be welfare-ranked. This real indeterminacy does not vanish as the number of producers goes to infinity. Therefore, the self-interest of producers restricts economic outcomes but does not determine them.

An evolutionary finance model with short selling and endogenous asset supply

“…Remark 1. The approach to short selling that involves "replicas" of assets with the same exogenous payoffs is quite common in mathematical models considered in Financial Economics (Magill and Quinzii [44]) and Mathematical Finance (Pliska [48], Ross [50], Föllmer and Schied [29], and Zierhut [61]). However, quite often it is not explicitly spelled out, since usually there is no need in a deeper analysis of the question.…”

Generic regularity of differentiated product oligopolies

“…Thus, the properties of Cournot-Walras equilibrium are substantially different in a setting with strategic asset structure choice. This setting is studied in a companion paper, Zierhut (2020), and the interested reader is referred to the analysis therein, as well as to Carvajal et al (2012) for related result. Since those models of Cournot competition with strategic asset choice are based on quasilinear economies, the following section provides a complementary derivation of generic regularity under quasilinear utility as a corollary to Theorem 1.…”