# Tag Based Co-operation in Artificial Societies

## Ph.D. Thesis - David Hales 2001

## Error in chapter 9

It has been pointed out to me by serveral readers that that probablistic analysis given in chapter 9 is not correct.
Specifically Eq. 9.6 and 9.7 are not correct. Hence a more detailed analysis seems to be required that takes account of the tag-group dynamics
in some way. This is still an open issue.

Comments kindly supplied by Tamas Vinko, Rameez Rahman, Hiroto Yonenoh (see e-mail below)

[Back to David Hales Home Page]
from hyonenoh@sk.tsukuba.ac.jp

to David Hales

date 9 October 2009 11:09

subject Re: About "Cooperation Without Memory or Spaace:Tags,Groups and the Prisoner's Dillemma"

Dear. Dr. David Hales,

I've read chapter 9 of your thesis I got at:

http://cfpm.org/~david/thesis/index.html

I've learned a lot from your thesis. Thank you!

I have a question.

Equation (9.6) in page 169 reads:

pti(n) = 2/(n-1) ... (9.6),

It seems Eequation (9.6) represents a sort of probablityprobability.

But, if n = 2, pti(n) = 2, which cannot be a probability.

Is there some restriction for the value of n?

Is pti(n) something other than probability?

Also,

equation (9.7) in page 169 reads:

pmoti(n,m) = pti(n)*pmo(n,m) ... (9.7)

pmo(n,m) is the probability that "more than one agent( n > 1 )" will

be mutated into a co-operator over a single generation.

On the other hand, pti(n) is the probability that "those two ( and only

two n = 2 ) agents" will interact producing a mutually co-operative

outcome.

In other words, while pmo(n,m) requires "n > 1 ", pti(n) requires "n = 2

".

So, I'm afraid that equation (9.7), which represents that pmoti(n,m) is

computed by multiplying pmo(n,m) by pti(n), isn' t valid, if n does not

equal to 2.

These months, I have tried to derive the expected average number of

generations required before two cooperative agents perform a game

interaction.

It would be grateful if you kindly give me your advice.

Yours sincerely.

---------------------------------

Hiroto Yonenoh

Graduate School of Systems and Information Engineering, University of

Tsukuba,

Tennoudai 1-1-1, Tsukuba, Ibaraki 305-0006, Japan

e-mail: hyonenoh@sk.tsukuba.ac.jp

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##### Last Updated: Sept 2010