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Journal ArticleDOI

Embedding Games with Strategic Complements into Games with Strategic Substitutes

TL;DR: In this article, the authors revisited the problem of games with strategic substitutes (GSS) from two new perspectives, a network one and a computational one, and showed that strategic substitutability is more fundamental than strategic complementarity, in the sense that the class of GSS is much broader than GSC.
Abstract: Games with strategic substitutes (GSS) are generally more intractable than games with strategic complements (GSC). This well-known fact is revisited from two new perspectives, a network one and a computational one. From the network perspective, it is shown that every GSC, under certain mild conditions, can be embedded into a larger GSS, such that the set of the pure strategy Nash equilibria of the former is the projection of that of the latter. From the computational perspective, it is shown that the two focal equilibria of a GSC with linear best responses can be computed in polynomial time, while computing a pure strategy Nash equilibrium of a GSS with linear best responses is PPAD-hard. These results indicate that strategic substitutability is more fundamental than strategic complementarity, in the sense that the class of GSS is much broader than the class of GSC. Combined with the previous results in the literature, our paper provides a more complete picture about the relationship between GSC and GSS.
References
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Book
21 Nov 2010
TL;DR: In Social and Economic Networks as discussed by the authors, a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics, is presented.
Abstract: Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function. This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business.

3,377 citations

Book
13 Apr 1998
TL;DR: In this article, the authors introduce the concept of lattices, supermodular functions, and optimal decision models for cooperative games and non-cooperative games, and present a review of the literature.
Abstract: PrefaceCh. 1Introduction3Ch. 2Lattices, Supermodular Functions, and Related Topics7Ch. 3Optimal Decision Models94Ch. 4Noncooperative Games175Ch. 5Cooperative Games207Bibliography263Index269

1,981 citations

Book
01 Jan 1999
TL;DR: In this article, Vives applies a modern game-theoretic approach to develop a theory of oligopoly pricing, using two-stage games, the modeling of competition under asymmetric information and mechanism design theory, and the theory of repeated and dynamic games.
Abstract: The "oligopoly problem"--the question of how prices are formed when the market contains only a few competitors--is one of the more persistent problems in the history of economic thought. In this book Xavier Vives applies a modern game-theoretic approach to develop a theory of oligopoly pricing. Vives begins by relating classic contributions to the field--including those of Cournot, Bertrand, Edgeworth, Chamberlin, and Robinson--to modern game theory. In his discussion of basic game-theoretic tools and equilibrium, he pays particular attention to recent developments in the theory of supermodular games. The middle section of the book, an in-depth treatment of classic static models, provides specialized existence results, characterizations of equilibria, extensions to large markets, and an analysis of comparative statics with a view toward applied work. The final chapters examine commitment issues, entry, information transmission, and collusion using a variety of tools: two-stage games, the modeling of competition under asymmetric information and mechanism design theory, and the theory of repeated and dynamic games, including Markov perfect equilibrium and differential games.

1,581 citations

Journal ArticleDOI
Rabah Amir1
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

Posted Content
TL;DR: In this paper, the authors provide an overview and synthesis of the literatures analyzing games in which players are connected via a network structure, and discuss the impact of the structure of the network on individuals' behaviors.
Abstract: We provide an overview and synthesis of the literatures analyzing games in which players are connected via a network structure. We discuss, in particular, the impact of the structure of the network on individuals' behaviors. We focus on game theoretic modeling, but also include some discussion of analyses of peer effects, as well as applications to diffusion, employment, crime, industrial organization, and education.

324 citations