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EDIT: Fly and Nightbloom posted b4 I could 'double post' ~~> ty.
Yes (to beatnik) I used to go to 'coffee shops' before Starbucks® -n- Starburst®.
My reply is, "I've asked that you shun me in this thread, thanks. That goes for you also, yes?

Barotix, Greetings~!

I would agree with your results and appreciate the information (and education) about Social Traps.
Props and cud-o's to you.

I couldn’t help but notice the similarities to Game Theory and “The Prisoner Dilemma”.
To me, what you are attempting to do with your math is better conceived with Iterated Prisoner Dilemma models or, to coin a phrase, 'two dimensional Social Traps'.
When looking at impact of group size in dual social grouping models, and especially when decision rule is used (like we are attempting to do on SRF) larger groups perform better in moving from uncoop to coop because larger groups reduce uncertainty in the random process of strategy selection.

In other words, cooperative styles amongst ‘legits’ of all flavors are necessary.
Driving a certain few ‘bots’ from a single server might be nice (and certainly is good for the ego and bragging rights, maybe) but it does little or nothing to relieve the overall problem.

Intro to economics classes can touch on Game Theory and “TPD” (The Prisoner Dilemma) which is a very simple game, actually invented by Albert Tucker, and goes something like this:

The interesting thing about the scenario is that there’s a temptation to “defect” (rat on your partner) but it only works (pays off for the first) if the other guy doesn’t do it.
If both defect, the result for both players is worse than if they had both “cooperated” (remained silent), but better for SRF, of course.
In other words, selfish opportunism screws things up for both players.

We see this in action here on SRF almost every week that I’ve observed / watched.
Robert Axelrod’s specialty was the ‘iterated prisoners’ dilemma’, where two or more players play multiple rounds of the basic “TPD”, remembering history and trying to maximize their results according to divergent strategies.

The bottom line is in the long term (and as you have stated) selfish opportunistic (cheater / bot / liar) strategies are not optimal.
The best strategies over the long term are those that encourage mutual cooperation, not pure competition.
This ‘spirit’ of coop will also be of use when comparing various flavors of ‘legit’ and their modes of ‘shunning’. They are the best strategies because they give the biggest payoff. The bigger the coalition, the greater the solidarity, the better for all legits everywhere.

The problem with both models is that we are assuming ‘zero-sum’ models, that it is a system where participant’s gain or loss is exactly balanced by the losses or gains of the other participants.

Here’s a real life example of TPD:

Edward Spellman posed the question.
“Ask Marilyn” answered.
(Marilyn vos Savant is listed in the Guinness Book of World Records Hall of Fame for the highest IQ)¹


Marilyn’s answer, which has the stranger playing twice as many tails as heads and winning $1 in six plays, is wrong .IF. the opponent elects to play a pure strategy of tails all the time!

In that case, the stranger and her opponent break even. Given the beautiful stranger’s strategy of playing twice as many tails as heads, what she wins depends on her opponent’s strategy. If the opponent plays heads and tails randomly, 50–50, the stranger will win $1 for every six plays, as Marilyn stated. Nothing in the problem as stated, however, would stop the opponent from playing tails all the time. In this case, they would break even (the stranger’s winnings, on average, would be 2 + 2 – 1 – 1 – 1 – 1 = 0).

[spoiler]Beautiful Stranger’s Strategy
Heads Tails
Opponent’s Strategy
Heads 3 –2
Tails –2 1

Let x be the probability that the opponent plays heads,
and 1 – x the probability that the opponent plays tails.
It is analogous to the stranger playing heads with
probability y and tails with probability 1 – y.
The expected rewards for the opponent are then 3x + (–2)(1 – x) against heads,
and –2x + (1)(1 – x) against tails.

The opponent’s optimal strategy is given when these two expected rewards are equal, i.e., when
3x + (–2)(1 – x) = –2x + (1)(1 – x).

Solving this equation gives the strategy (3/8, 5/8). In other words, on average, the opponent should play three heads and five tails. By following this strategy, the opponent would lose a minimum of 1/8 of a dollar per game. Analogously, the optimal strategy for the stranger is obtained by solving the following equation for y:
3y + (–2)(1 – y) = –2y + (1)(1 – y).

The optimal strategy for the stranger is (3/8, 5/8). She, too, should play, on average, three heads and five tails, for an average winning per game of 1/8 of a dollar.

If the stranger plays her optimal strategy of (3/8, 5/8) and her opponent plays pure heads, the opponent will win (3/8)(3) + (5/8)(–2) = –1/8 dollar per game and the stranger will win 1/8 dollar per game. Similarly, if the stranger plays her optimal strategy of (3/8, 5/8) and her opponent plays pure tails, the opponent will win (3/8)(–2) + (5/8)(1) = –1/8 dollar per game and the stranger will win 1/8 dollar per game.

Given that, if the stranger plays her optimal strategy of (3/8,5/8) and her opponent plays either a pure strategy of heads or a pure strategy of tails, the stranger will win, on average, 1/8 of a dollar per game. In fact, any linear combination of these pure strategies on the part of her opponent will still result in the stranger winning 1/8 of a dollar per game. Hence, if the stranger plays, on average, three heads and five tails, then no matter what strategy her opponent plays, she will win an average of 1/8 of a dollar per game, or $1 in eight games.

Marilyn’s suggested strategy of (1/3, 2/3) for the stranger is not optimal and makes the outcome of the game dependent on the strategy chosen by her opponent. Consider the following pairs of pure strategies for the opponent and resulting outcomes for the stranger if she follows Marilyn’s recommended strategy of (1/3, 2/3):

Opponent plays heads always, stranger wins (1/3)(–3) + (2/3)(2) = 1/3 dollar per game.

$1 per 8 games vs. 1/3 per game
$1 per 8 games vs. 8/3 per 8 games
$1.00 < $2.67 therefore bots lose to purist style play

It's simplified (because I can't cope with the math) but IMO the point is valid.
Math for "Does Marilyn Know Her Game Theory?"
by By Francis J. Vasko and Dennis D. Newhart²


Anybody wanting to do more research? You could explore the boundaries of Axelrod’s results in the IPD. Under certain conditions, Tit For Tat or its variants seem optimal. Where are the boundaries with regard to ratio of cooperators, defectors, and others? What others? Make a guess, then try to defend it. Alternatively, you could try something similar with another of the four classic games - Deadlock, Stag Hunt, or Chicken.

Another one of Axelrod’s results was that the only time opportunistic strategies do work is when there’s a high percentage of naive always-cooperate players for them to fleece. "Neutral Legits" are indeed part of the problem. So there you have it. From very basic game theory to real-life economics, to SRO and SRF. Social Traps and Game Theory runs the gauntlet. The difference is the simple matter of "Trust". It is a significant difference.

Lots more information found at: The Heretical Press <~~~ It's not just math-n-games-n-stuff, there's stuff about sex there too

Again, props and cud-o's to you Barotix.
~Grandpa


____________________________________
credits: ¹Parade Magazine, March 31, 2002
²Francis J. Vasko is a Professor of Mathematics at Kutztown University in Kutztown, Pennsylvania. Dennis D. Newhart is a research consultant with International Steel Group in Bethlehem, Pennsylvania.