A New Existence and Uniqueness Theorem for Continuous Games
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Seamus D Hogan
This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mappings from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobian matrix of best-response functions has positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games. In particular, we show how the same conditions used in those theorems to show uniqueness, also guarantee existence in games with unbounded strategy spaces.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Artikel in diesem Heft
- Advances Article
- Strategy-Proof Compromises
- Make-or-Buy Decisions and the Manipulability of Performance Measures
- Optimal Mechanism for Selling Two Goods
- A Property of Solutions to Linear Monopoly Problems
- Interactive Epistemology and Solution Concepts for Games with Asymmetric Information
- No-Trade in the Laboratory
- Symmetry or Dynamic Consistency?
- Contributions Article
- When Two-Part Tariffs are Not Enough: Mixing with Nonlinear Pricing
- Sellers Like Clusters
- Network Architecture and the Left-Right Spectrum
- Information, Authority, and Corporate Hierarchies
- The Benefit of Mixing Private Noise into Public Information in Beauty Contest Games
- Intertemporal Bounded Rationality as Consideration Sets with Contraction Consistency
- The Survival Assumption in Intertemporal Economies
- A New Existence and Uniqueness Theorem for Continuous Games
- Multiproduct Duopoly with Vertical Differentiation
- Topics Article
- Sequential Investments, Know-How Transmission, and Optimal Organization
- Input Production Joint Venture
- On the Existence and Social Optimality of Equilibria in a Hotelling Game with Uncertain Demand and Linear-Quadratic Costs
- Stochastic Stability in Finitely Repeated Two Player Games
- Alliance Partner Choice in Markets with Vertical and Horizontal Externalities
- Transitional Dynamics in a Tullock Contest with a General Cost Function
- Strategic Choice of Preferences: the Persona Model
- Implementation of the Core in College Admissions Problems When Colleagues Matter
