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April 20th, 2015, 02:27 AM   #1
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From: Milan

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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..!!!
Neha is offline  
 
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