A contraction principle for finite global games

Laurent Mathevet

    Research output: Contribution to journalArticle

    Abstract

    I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction principle. Furthermore, the contraction-mapping approach provides an intuition for why uniqueness arises: complementarities in games generate multiplicity of equilibria, but the global-games structure dampens complementarities so that only one equilibrium exists.

    Original languageEnglish (US)
    Pages (from-to)539-563
    Number of pages25
    JournalEconomic Theory
    Volume42
    Issue number3
    DOIs
    StatePublished - Dec 2009

    Fingerprint

    Uniqueness
    Contraction
    Global games
    Complementarity
    Best response
    Contraction mapping
    Multiplicity
    Intuition

    Keywords

    • Contraction mapping
    • Equilibrium uniqueness
    • Global games
    • Strategic complementarities
    • Supermodular games

    ASJC Scopus subject areas

    • Economics and Econometrics

    Cite this

    A contraction principle for finite global games. / Mathevet, Laurent.

    In: Economic Theory, Vol. 42, No. 3, 12.2009, p. 539-563.

    Research output: Contribution to journalArticle

    Mathevet, Laurent. / A contraction principle for finite global games. In: Economic Theory. 2009 ; Vol. 42, No. 3. pp. 539-563.
    @article{106b377b55d54c1d9361c70a8d09f12d,
    title = "A contraction principle for finite global games",
    abstract = "I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction principle. Furthermore, the contraction-mapping approach provides an intuition for why uniqueness arises: complementarities in games generate multiplicity of equilibria, but the global-games structure dampens complementarities so that only one equilibrium exists.",
    keywords = "Contraction mapping, Equilibrium uniqueness, Global games, Strategic complementarities, Supermodular games",
    author = "Laurent Mathevet",
    year = "2009",
    month = "12",
    doi = "10.1007/s00199-008-0411-3",
    language = "English (US)",
    volume = "42",
    pages = "539--563",
    journal = "Economic Theory",
    issn = "0938-2259",
    publisher = "Springer New York",
    number = "3",

    }

    TY - JOUR

    T1 - A contraction principle for finite global games

    AU - Mathevet, Laurent

    PY - 2009/12

    Y1 - 2009/12

    N2 - I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction principle. Furthermore, the contraction-mapping approach provides an intuition for why uniqueness arises: complementarities in games generate multiplicity of equilibria, but the global-games structure dampens complementarities so that only one equilibrium exists.

    AB - I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction principle. Furthermore, the contraction-mapping approach provides an intuition for why uniqueness arises: complementarities in games generate multiplicity of equilibria, but the global-games structure dampens complementarities so that only one equilibrium exists.

    KW - Contraction mapping

    KW - Equilibrium uniqueness

    KW - Global games

    KW - Strategic complementarities

    KW - Supermodular games

    UR - http://www.scopus.com/inward/record.url?scp=72449189673&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=72449189673&partnerID=8YFLogxK

    U2 - 10.1007/s00199-008-0411-3

    DO - 10.1007/s00199-008-0411-3

    M3 - Article

    VL - 42

    SP - 539

    EP - 563

    JO - Economic Theory

    JF - Economic Theory

    SN - 0938-2259

    IS - 3

    ER -