A New Existence and Uniqueness Theorem for Continuous Games
AbstractThis paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mapping 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 R-to-R mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobean matrix of best-response functions be have positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games.
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Bibliographic InfoPaper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/59.
Length: 28 pages
Date of creation: 01 Oct 2010
Date of revision:
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Existence; Uniqueness; Continuous Games; Contraction Mapping Theorem;
Other versions of this item:
- Hogan Seamus D, 2011. "A New Existence and Uniqueness Theorem for Continuous Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-28, August.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
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