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Game theory, mixed strategies

  1. Apr 29, 2010 #1
    1. The problem statement, all variables and given/known data
    I am trying to study a mixed-strategy phenomenon form the book:
    Game Theory Evolving:A Problem-Centered Introduction to Modeling Strategic Interaction (Second Edition)
    by Herbert Gintis. There is an example (The Prisoner's Dilemma) which looks as follows:

    [PLAIN]http://img199.imageshack.us/img199/1092/img1sh.jpg [Broken]

    where P=1, R=0, T=1+t, S=-s and s,t>0.

    There are two players Alice and Bob. They both play C with alpha and beta probabilities respectively.
    The author claims that payoffs to Alice and Bob are:

    [PLAIN]http://img696.imageshack.us/img696/3070/img1ye.jpg [Broken]

    However, I think this is wrong and there should not be alpha multiplied by beta, just at the beginning of the right-hand side - it stems from the fact that since R=0 then alpha multiplied by beta and 0 is equal to 0. Am I correct? I think that, the zero factor which is at the end of right-hand side, should be next to alpha multiplied by beta right at the beginning of the RHS.

    2. Relevant equations

    3. The attempt at a solution

    In the other example:
    [PLAIN]http://img709.imageshack.us/img709/4764/img1yk.jpg [Broken]

    the payoff's are following:

    [PLAIN]http://img402.imageshack.us/img402/4696/img1hr.jpg [Broken]

    Therefore, I think there might be a mistake in the first example.
    Last edited by a moderator: May 4, 2017
  2. jcsd
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