Ultra and ISF Comparison

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Re: Ultra and ISF Comparison

Postby Cralis on Wed 11 Mar 2015 00:55

It's almost like you've been listening to some of our internal conversations. This is similar to another (more complicated) proposal we've discussed with the same net effect: the more partners involved, the less you make from each one.

Hmmmm.
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Re: Ultra and ISF Comparison

Postby szurkey on Thu 12 Mar 2015 04:14

Cralis wrote:It's almost like you've been listening to some of our internal conversations. This is similar to another (more complicated) proposal we've discussed with the same net effect: the more partners involved, the less you make from each one.

Hmmmm.

I hate to disappoint you, but I haven't been listening to your internal conversations.

The m^(n+a) has the advantage that each additional trade partner cost the the same percentage of income.

The a / (b + n) has the advantage that it is non-linear, and you lose an ever decreasing percentage of income.
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Re: Ultra and ISF Comparison

Postby szurkey on Sat 14 Mar 2015 07:10

Analytics for a / (b + n)

Assumptions:
All trade agreements are equal value (I know they're not, but it does make it much easier to do analysis)

Number of Trade Agreements (NTA)

Trade Income Multiplier (TIM) := a / (b + n)

Step Loss (SL):= 1 - [a / (b + n)] / [a / (b + (n - 1))] for all n > 1
Measure of reduction of TIM you are giving up for adding that trade agreement.

Value Loss (VL): = Step Loss * (n - 1) for all n > 1
Measure of how much income of all of all previous trade agreements you are giving up to add that trade agreement.
When TIM = Value Loss you are at the break event point. Adding that trade agreement give you NO increase in trade income.

Example, let a = 8, b = 11
Code: Select all
NTA   TIM      SL      VL
1   0.6667      
2   0.6154   0.0769   0.0769
3   0.5714   0.0714   0.1429
4   0.5333   0.0667   0.2000
5   0.5000   0.0625   0.2500
6   0.4706   0.0588   0.2941
7   0.4444   0.0556   0.3333
8   0.4211   0.0526   0.3684
9   0.4000   0.0500   0.4000
10   0.3810   0.0476   0.4286
11   0.3636   0.0455   0.4545
12   0.3478   0.0435   0.4783
13   0.3333   0.0417   0.5000
14   0.3200   0.0400   0.5200
15   0.3077   0.0385   0.5385
16   0.2963   0.0370   0.5556
17   0.2857   0.0357   0.5714
18   0.2759   0.0345   0.5862
19   0.2667   0.0333   0.6000
20   0.2581   0.0323   0.6129
The inflection point is this example is 9 trade agreements. You get no additional income by adding a ninth trade agreement.

If someone would like to pull one of their Ultra games and plug real numbers in and look at how this affects trade income, I would be very interested.
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