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Schedulers, Potentials and Weak Potentials in Weakly Acyclic Games

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  • Igal Milchtaich

    ()
    (Bar-Ilan University)

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    Abstract

    In a number of large, important families of finite games, not only do pure-strategy Nash equilibria always exist but they are also reachable from any initial strategy profile by some sequence of myopic single-player moves to a better or best-response strategy. This weak acyclicity property is shared, for example, by all perfect-information extensive-form games, which are generally not acyclic since even sequences of best-improvement steps may cycle. Weak acyclicity is equivalent to the existence of weak potential, which unlike a potential increases along some rather than every sequence as above, as well as to the existence of an acyclic scheduler, which guarantees convergence to equilibrium by disallowing certain (improvement) moves. A number of sufficient conditions for acyclicity and weak acyclicity are known.

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    Bibliographic Info

    Paper provided by Department of Economics, Bar-Ilan University in its series Working Papers with number 2013-03.

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    Length: 8 pages
    Date of creation: Mar 2013
    Date of revision:
    Handle: RePEc:biu:wpaper:2013-03

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