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A Game Theory: Are the payoff functions πi continuous?

  1. May 16, 2017 #1
    1. How do I show that the payoff function πi isn´t continuous? Why do best replies not always exist?
      Skärmavbild 2017-05-16 kl. 21.57.54.png Skärmavbild 2017-05-16 kl. 21.58.15.png
     
  2. jcsd
  3. May 16, 2017 #2

    mfb

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    In the same way you show that a function is not continuous for (nearly) every other function. Find a point where it is not continuous and prove that the function does not satisfy the condition for continuity there.

    Is this a homework problem?
     
  4. May 16, 2017 #3
    Okey, but what if the interval was extremely large. Is there a way to find the non continuous part in a smart algorithmic way?
    It´s a old exam without answers. Really need a explanation here. Thanks.
     
  5. May 16, 2017 #4

    mfb

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    If you have a piecewise definition, the borders between the pieces are always obvious places to check.
    The pieces itself can be discontinuous as well, but if they are simple polynomials like here you know they are continuous.
     
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