Author
Rabah Amir
Other affiliations: University of Dammam, State University of New York System, Odense University ...read more
Bio: Rabah Amir is an academic researcher from University of Iowa. The author has contributed to research in topics: Cournot competition & Oligopoly. The author has an hindex of 34, co-authored 148 publications receiving 4873 citations. Previous affiliations of Rabah Amir include University of Dammam & State University of New York System.
Papers published on a yearly basis
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TL;DR: In this paper, the authors surveyed the literature on supermodular optimization and games from the perspective of potential users in economics and provided a new approach for comparative statics based only on critical assumptions, and allowed a general analysis of games with strategic complementarities.
Abstract: The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities. The results are presented in a simplified yet rigourous manner, without reference to lattice theory, for the special case of onedimensional parameter and actions sets, with the emphasis being on wide accessibility. Detailed applications are presented for well-known models of consumer behavior, monopoly pass-through, Bertrand and Cournot competition, strategic R&D, search and matching. Wherever appropriate, useful tricks for applications and comparative comments are inserted.
431 citations
TL;DR: The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics in this paper, where the authors provide a new approach for comparative statics based only on critical assumptions, and allow a general analysis of games with strategic complementarities.
Abstract: The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities. The results are presented in a simplified yet rigourous manner, without reference to lattice theory, for the special case of one-dimensional parameter and actions sets, with the emphasis being on wide accessibility. Detailed applications are presented for well-known models of consumer behavior, monopoly pass-through, Bertrand and Cournot competition, strategic R&D, search, and matching. Wherever appropriate, useful tricks for applications and comparative comments are inserted.
319 citations
TL;DR: In this article, an extensive comparison of the well-known R&D models of d'Aspremont-Jacquemin and Kamien-Muller-Zang is provided, exposing full or partial conflict in key conclusions and policy prescriptions.
290 citations
TL;DR: In this article, the Cournot oligopoly problem is considered in light of the theory of supermodular games and the authors derive the associated uniqueness result, give an extension of a classical existence result under symmetry, and provide conditions making a Cournot-like oligopoly into a log-supermodular game with natural order on the action sets.
277 citations
TL;DR: In this article, the authors provide two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to decreasing industry price and increasing or decreasing per-firm output.
Abstract: In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per-firm output). In both cases, per-firm profits are decreasing. The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions of a global nature. As a byproduct of independent interest, new insight into existence of Cournot equilibrium is developed.
255 citations
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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …
33,785 citations
Journal Article•
28,685 citations
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations