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2 results

  • Monotone Case for an Extended Process

  • Part of
  • Małgorzata Kuchta, Michał Morayne
  • Journal:
    Advances in Applied Probability / Volume 46 / Issue 4 / December 2014
    Published online by Cambridge University Press:
    22 February 2016, pp. 1106-1125
    Print publication:
    December 2014
    • Article
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  • We consider a nonnegative discrete time and bounded horizon process X for which 0 is an absorbing state and extend it by a random variable that is independent of X. We find a sufficient condition for the resulting process to satisfy, after a canonical time rescaling, the hypothesis of the monotone case theorem. If X describes a secretary type search on a poset with one maximal element or if we consider X with no extension then this condition assumes an especially simple log-concavity type form.

  • On a discrete-time non-zero-sum Dynkin problem with monotonicity

  • Yoshio Ohtsubo
  • Journal:
    Journal of Applied Probability / Volume 28 / Issue 2 / June 1991
    Published online by Cambridge University Press:
    14 July 2016, pp. 466-472
    Print publication:
    June 1991

  • We consider a monotone case of the non-zero-sum stopping game with discrete time parameter which is called the Dynkin problem. Marner (1987) has investigated a stopping game with general monotone reward structures, but his monotonicity is too strong to apply our problem. We establish that there exists an explicit equilibrium point in our monotone case. We also give a simple example applicable to a duopolistic exit game.