Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Game Theory Question

  1. Nov 19, 2014 #1
    Hey PF!

    Can you help me with something:

    Players alternately choose 0's or 1's. A play of this infinite game is thus a sequence of 0's and 1's. Such a sequence can be considered as the binary expansion of a real number between 0 and 1. Given a set ##E## of real numbers satisfying ##0 < x < 1 \forall x \in E##, say that player 1 wins if the play corresponds to a number in ##E## and player two wins if the way corresponds to a number in ##[0,1] \backslash E##.

    Evidently the Axiom of Choice implies there exists a set ##E## for which the game has no value. Can you help me out with showing this?
  2. jcsd
  3. Nov 19, 2014 #2


    User Avatar
    Science Advisor

    1. What about ambiguities similar to 0.99999....=1, for example the two sequences 011111...... and 100000, which both correspond to the real number 0.1?

    2. If this ambiguity is resolved, it is certain that either player 1 or player 2 wins, since every real number in [0,1] lies in either E or its complement. But you meant perhaps someting else with the "value" of the game?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Game Theory Question
  1. Game theory (Replies: 3)

  2. Game theory (Replies: 7)

  3. Game theory, need help (Replies: 9)