Stephane Le Roux - Infinite sequential Nash equilibrium

lmcs:1190 - Logical Methods in Computer Science, May 22, 2013, Volume 9, Issue 2 - https://doi.org/10.2168/LMCS-9(2:3)2013
Infinite sequential Nash equilibriumArticle

Authors: Stephane Le Roux

    In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn. Two existing results are relevant here: first, all finite such games have a Nash equilibrium (w.r.t. some given preferences) iff all the given preferences are acyclic; second, all infinite such games have a Nash equilibrium, if they involve two agents who compete for victory and if the actual plays making a given agent win (and the opponent lose) form a quasi-Borel set. This article generalises these two results via a single result. More generally, under the axiomatic of Zermelo-Fraenkel plus the axiom of dependent choice (ZF+DC), it proves a transfer theorem for infinite sequential games: if all two-agent win-lose games that are built using a well-behaved class of sets have a Nash equilibrium, then all multi-agent multi-outcome games that are built using the same well-behaved class of sets have a Nash equilibrium, provided that the inverse relations of the agents' preferences are strictly well-founded.


    Volume: Volume 9, Issue 2
    Published on: May 22, 2013
    Imported on: June 13, 2011
    Keywords: Mathematics - Logic,F.4

    10 Documents citing this article

    Consultation statistics

    This page has been seen 1722 times.
    This article's PDF has been downloaded 807 times.