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Schedulers, Potentials and Weak Potentials in Weakly Acyclic Games


  • Igal Milchtaich

    () (Bar-Ilan University)


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.

Suggested Citation

  • Igal Milchtaich, 2013. "Schedulers, Potentials and Weak Potentials in Weakly Acyclic Games," Working Papers 2013-03, Bar-Ilan University, Department of Economics.
  • Handle: RePEc:biu:wpaper:2013-03

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