Thinking more about the two "tuning parameters" GOB just described: deposit reserve ratio, and max profit %. I am wondering how many degrees of freedom this system actually has.
inputs: (D) deposit amount, (R) deposit reserve ratio, (M) max profit %
outputs: (P) profit, (V) variance of profit, (C) counter-party risk
If I increase D, holding R and M fixed, then P, V and C go up, I think.
If I decrease R, holding D and M fixed, then P and V go up, but C stays fixed.
If I increase M, holding D and R fixed, then P and V go up, but C stays fixed.
How exactly is decreasing R different than increasing M?
Depends on exactly what you define D, R, P and V to be.
IF:
D= total deposit, including coins held offsite
R= deposit reserve ratio where R is % of coins held AT justice
P= expected investment growth rate
V= investment variance
THEN:
If I increase D, holding R and M fixed, then P stays constant, V stays constant (if bet sizes grow relative to it, which won't be the case, so it probably decreases) and C goes up.
If I decrease R, holding D and M fixed, then P and V stay constant (given I don't get auto-divested), but C decreases (fewer coins help at JD).
If I increase M, holding D and R fixed, then (due to Kelly Criterion):
a) if M increases and is <1%, then P and V go up, and C stays fixed.
b) if M > 1% and increases, then P goes down, V goes up and C stays fixed.
c) if M < 1% and increases to >1%, then P can increase or decrease depending on the exact numbers, V goes up, and C stays fixed.
Does that make sense? If you change the definitions of DRP&V I'll redo it.
Yes, given your way of defining D (I was defining D as what you actually sign over to JD, which is why my logic table looks a bit different). But maybe your first line is wrong:
"If I increase D, holding R and M fixed, then P stays constant, V stays constant (if bet sizes grow relative to it, which won't be the case, so it probably decreases) and C goes up."
Wouldn't increasing D lead to an increased share of the pie and thus larger values of P, V and C?
When you talk about increasing M, I noticed that you are applying the Kelly Criterion based on the sum of the reserves held at JD and those held offsite (your definition of "D"). So, I think proves that it is OK--and in fact necessary for profit maximization--to have a max bet % greater than 1% of the reserves held at JD (i.e., the number dispayed on the website). It's OK because there are other reserves that will flow into JD should the ones currently controlled by JD become depleted.
And participants who "fakes reserves" by more than a factor of 2, like you point out, would be expected to burn through the smaller amount of funds that actually possess and bust. Darwinism.
Thanks for the further info on the Kelly criterion, BTW!