1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Mathematical Game Theory (Von Neumann Morganstern Utility)

  1. Dec 8, 2014 #1
    1: If u: omega---> reals is a Von Neumann Morganstern Utiliy function and L is a lottery, prove that expectation E is "linear" ie: E(Au(L)+B)=AEu(L)+B

    2. Given none:

    3. The attempt at a solution: My attempt at a solution has gone nowhere. I found a stanford and princeton game theory notes that went into it, but I could exactly follow.

    I found in a book that if E[v(c)]=v(E[c]) the person is risk netural and they're risk neutral iff VNM Utility function is linear.

    I'm really grasping at straws here though.

    Here is where I've found my information, but I haven't been able to translate anything into a formal proof.
    http://web.stanford.edu/~jdlevin/Econ 202/Uncertainty.pdf
    and finally this book which seems to be the best (see theorem 3.9.1)
    http://books.google.com/books?id=nv...orgenstern utility function is linear&f=false

    I would love a shove in the right direction. thx
  2. jcsd
  3. Dec 8, 2014 #2


    User Avatar
    Homework Helper

    ## L=\sum p_i C_i ## where ## \sum p_i = 1 ## would be the expected value for the Lottery L with probabilities p_i corresponding to possible payouts C_i.
    ##E(Au(L)+B) ## is the expected value ... which is ##\sum p_i (Au(C_i)+B)##, where A and B are constants.
    You should be able to change this to the form you were looking for using basic properties of sums and products.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted