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April 20th, 2015, 03:27 AM  #1 
Newbie Joined: Apr 2015 From: Milan Posts: 1 Thanks: 0  How can I normalize a vector to sum to a certain value?
Dear all, I have been reading the discussions posted on this forum and it has been very helpful, many thanks for that..!!! I am trying to reproduce the results of the paper: Designing human agents that act like human agents: A Behavioural approach to bounded rationality by W.Brian Arthur (1991). On page 354 of this paper four points are mentioned, my doubt is limited to the 4th point. I can not understand how to calculate the 4th point. For the sake of convenience I will write the entire 4th point preceded by the previous 3 points. PROBLEM DESCRIPTION: Set of N actions exist, from 1 to N. A vector of strength S_t is associated with every action at every time 't'. The current sum of these strength is C_t (the component sum of S_t) and the initial vector S_0 is strictly positive. The probability p_t represents the agent's probablities of taking actions 1 through N at time t. At each time t, the agent: 1. Calculates the probablity vector as the relative strengths associated with each action. It sets, p_t = (S_t/C_t) 2. Chooses one action from the set according to the probablities p_t and trigger that action. 3. Observes the payoff received and updates strengths by adding the chosen action j's payoffs to action j's strength. That is, where action j is chosen, it sets the strength to S_t + beta. Where, beta = payoff(j)*e_j (e_j is the jth unit vector) 4. Renormalizes the strengths to sum to a value from a prechosen time sequence. In this case, it renormalizes strength to sum to C_t = C*t. (Where t could also be raised to a value v) QUESTION: I dont understand how to renormalize the strength to a sum ? I have read: http://en.wikipedia.org/wiki/Normalization_(statistics) and every page it pointed me towards but no luck. I am really stuck with this and will appreciate any help..thanks a ton..!!! 

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normalize, sum, vector 
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