Game Theory -- Modeling the Spirituality Forum

The purpose of this thread is to explore ideas for constructing a game theoretical model of this forum.

A game model, in essence, is comprised of a set of players, a set of potential strategies -- possibly cooperative or competitive -- that each may invoke, and a set of competing goals that players try to acheive through application of their chosen strategies.

I would like to begin by offering some thoughts that I've had as a result of observing this forum (and its previous incarnation) and brainstorming about how to organize my findings.

First, regarding the players, I could see us modeling either individual posters or denominations of faith as players in the game. I suppose that it would even be possible to have a heterogenous mix of posters and denominations.

Among the goals the players attempt to achieve are:
1. Converting other players to one's belief system
2. Avoiding being converted
3. Helping others to avoid conversion.
4. Performing God's work by preaching
5. Crusading for reason and rationality by refuting claims of faith

Now for modeling strategies, which is really what got me brainstorming.
Let us begin by pondering some questions: For a Catholic who wants to convert an Atheist to Christianity, would that Catholic rather have or not have a Protestant also trying to convert the subject to Christianity? How does the "quality of play" of the Protestant affect the Catholic's decision on this matter? Would the Catholic rather have the Protestant be convincing or uncredible? Should the Catholics and Protestants compete or cooperate against the Weak Atheists? Should the Catholic invoke reason and rationality against the Protestant in hopes of securing a common ground with the Weak Atheist? Once the Weak Atheist is converted through cooperation of the Catholic and Protestant, should they maintain and strengthen their cooperative strategy, or decide to compete and win the Weak Atheist over to their particular denomination?

Of course, all of these questions must be answered with respect to achieving some optimal combination and level of the goals.

It should be clear that the game is rich in complexity, and several interplaying factors must go into an analysis of what a proper strategy is for any player in the game.

Next, I would like to entertain suggestions for refining the player and goal aspects of the model, as well as thoughts about what sorts of strategies make sense to model, and which instances of those you predict to be good or bad.

In theory,
Dr. S

I've never been involved in anything like this before, so pardon me if I misunderstand the processes, but I'm interested in taking part.

If I might tackle the players then. I feel that rather than grouping players under headings that are too broad (atheist/christian etc.), or limiting the players to single choices, one might choose a team of players, within which there would be a selection of differing skills. Since this is the spirituality forum, there seems to be two topic types which will influence team choice:

1) If it is a topic of, for example, Christian doctrine, then the choices are likely to result in a team comprised of players of similar abilities, ie: all Atheist or all Christian.

2)If the topic is one of questioning to reach an unknown position, which has yet to be settled on, then one may like to have a mix of players in the group

The skills each player might have could be modelled fairly easily on real characters, but for the moment, can I suggest they might be something like the following:

1)Language
2)Reasoning
3)Subject Knowledge
4)Deflection
5)Humour
6)Faith
7)Cross-Referencing

I'm sure there are more, but they escape me for the moment. There might also be special skills useable maybe once in a thread per player, like 'Double-Team' or 'Ridicule'. I'm not sure how much of a game this should be and how much of a model, so I'm wary of elaborating in too fantastical a manner. Am I on th eright track? If so, I'll post some more later once I've had a think. If I'm missing the point of this, could you elaborate some more?

Originally posted by Starrman
I've never been involved in anything like this before, so pardon me if I misunderstand the processes, but I'm interested in taking part.

If I might tackle the players then. I feel that rather than grouping players under headings that are too broad (atheist/christian etc.), or limiting the players to single choices, one might choose a team of players ...[text shortened]... later once I've had a think. If I'm missing the point of this, could you elaborate some more?

Sounds like a non-zero- sum game to me.

This is all very complicated. Can we just have a lottery and dispose of someone?

Originally posted by frogstomp
Sounds like a non-zero- sum game to me.

What exactly is a non-zero-sum game?

Originally posted by Starrman
What exactly is a non-zero-sum game?

one that has levels of victory
like tactical, strategic and overwhelming
some times all sides can claim some level of victory
scores always ad up to a positive number
in contrant is chess
chess is a zero sum game and the possible scors ad to zero

Do you have any more information on this sort of thing? Links etc?

Originally posted by Starrman
Do you have any more information on this sort of thing? Links etc?

A basic overview is at: http://en.wikipedia.org/wiki/Game_theory

Originally posted by DoctorScribbles
The purpose of this thread is to explore ideas for constructing a game theoretical model of this forum.

A game model, in essence, is comprised of a set of players, a set of potential strategies -- possibly cooperative or competitive -- that each may invoke, and a set of competing goals that players try to acheive through application of their chose ...[text shortened]... sense to model, and which instances of those you predict to be good or bad.

In theory,
Dr. S

You've missed off a very important goal... that of just plain $h!@ disturbing. Creating maximum chaos and disrupting the 'game' to the greatest degree possible. Bonus points should be available for actually driving someone crazy through your comments, subterfuge, sarcasm and bitching.

The game is won if a naked Darfius retires to a clock tower with a 30-06 and starts pumping round after round into his fellow students chanting "There is a God! Behold my glory!"

Originally posted by Starrman
I'm not sure how much of a game this should be and how much of a model, so I'm wary of elaborating in too fantastical a manner.

Have no such fear. Nothing is too fantastical for the Spirituality forum, after all. And how much more so for a theoretical model of such a place! Let your fantasies run wild. That's how great ideas are born. (Ref. the bar scence depicted in A Beautiful Mind.)

Originally posted by DoctorScribbles
The purpose of this thread is to explore ideas for constructing a game theoretical model of this forum.

A game model, in essence, is comprised of a set of players, a set of potential strategies -- possibly cooperative or competitive -- that each may invoke, and a set of competing goals that players try to acheive through application of their chose ...[text shortened]... sense to model, and which instances of those you predict to be good or bad.

In theory,
Dr. S

Number 2 is not one of by objectives.

Originally posted by Starrman
Do you have any more information on this sort of thing? Links etc?

there a programable A.I. text game... called Brainiac at sorceforge


it might be adaptable and the info on it might give you an idea of what constitutes a goal oriented game

Originally posted by DoctorScribbles
Have no such fear. Nothing is too fantastical for the Spirituality forum, after all. And how much more so for a theoretical model of such a place! Let your fantasies run wild. That's how great ideas are born. (Ref. the bar scence depicted in A Beautiful Mind.)

This is going to be one hell of a difficult model to solve.

It must also be a dynamic game in which different strategies are played over time, resulting in equilibrium paths.

Overview
Now one (not really so simple) way to model this would be to consider the struggle between the Holier-Than-Thou Alliance (HTT) and the Rationals. These groups compete each period for converts (a fraction from a unit measure continuum of Undecideds). At the end of each period (must be defined), HTT and Rationals convert some fraction of undecideds depending on their strategies. In the next period we have a new pool of Undecideds to convert.

Utilities/Payoffs

A utility function for a member of the HTT would be a function of the fraction of all players that are HTT, the fraction of HTT that are members of their particular cult, and a personal satisfaction term which gives increased weight to the second fraction in periods where the member plays differentiate. The form must be such that in equilibrium players face a tradeoff between focusing on converting more xtians through cooperating and persuading these converts to their cult (The function must be seperable in these inputs.).

A utility function for a Rational consists of an entertainment term which rises with the comedic value of mocking HTT's as well as component which rises with the fraction players that are enlightened Rationals.

Strategies

HTT: In any given period each member of the HTT can choose cooperate or differentiate.
----> cooperate: This strategy specifies joining in a unified multidenominational assault on the Rationals and also giving Amen's to each others posts.
----> differentiate: Do not participate in the group assualt and instead focus on turning more of the current period HTT converts to that players particular cult. Perhaps a Protestant could point out that the Catholic Church is really a led by Satan, or a Catholic could remind new converts that Protestants are heretics that left the One True Church.

Rationals:
----> reason: This strategy calls for rationals to band together in patient, reasoned refutation of the HTT's superstitious claims. This increases the fraction of undecideds that choose Rationality in a period.
----> mock: Here Rationals increase their individual utilities at the expense of seeming as ridiculous as the HTT. This decreases the expected return on converts, but increases the utility of current members highlighting their intellectual superioty to the HTT.

Outcomes
The fractions of converts to HTT and the Rationals is determined by the following equation:

HTTCon = 50% + (% of HTT that play cooperate - % of Rationals that play reason)

RationCon= 1 - HTTCon

The fractions of HTTCon that choose Protestant and Catholic are determined by these equations.
HTTCat: (# of Catholics that play differentiate) / (# of all HTT players that play differentiate)
HTTPro: 1 - HTTCat

So the more Catholics and Protestants cooperate the more they increase their fraction of converts. However, if one HTT member (say Protestant) plays differentiate and the rest play cooperate, then all the HTT converts from that period become Protestants! If however most Catholics and Protestants play differentiate, this backbiting causes the Rationals to gain a greater percentage of converts.

In equilibrium HTT members must find a balance between gaining xtian converts and shoring up these converts into their One True Faith.
Rationals must balance certain utility from mocking HTT's and the potentially greater utility from freeing undecideds.

I can already think of many improvements to this, but they could get wildly complicated. For instance, members of HTT's and Rationals could move into the Undecided pool. From here they could go to Rational or HTT or remain Undecided. We would need to incorporate some factor that allowed for decoversion.

Playing Reason repeatedly could cause could have diminishing returns over time. Thus at some point, Rationals will become tired of countering the brainwashing techniques of HTT. Or perhaps playing Mock could have some potential to upset HTT's and drive a wedge into their alliance so that fewer HTT members play cooperate and instead choose differentiate.

We could also make the equilibria Weak Perfect Bayesian Nash Equilibria, where members have beliefs about how all other members will play. This seems particular fitting given the nature of this forum.

Ok, well please check the math. I think though with well-specified preferences we could make this work.

Originally posted by telerion
This is going to be one hell of a difficult model to solve.

It must also be a dynamic game in which different strategies are played over time, resulting in equilibrium paths.

Overview
Now one (not really so simple) way to model this would be to consider the struggle between the Holier-Than-Thou Alliance (HTT) and the Rationals. These groups compete ...[text shortened]... please check the math. I think though with well-specified preferences we could make this work.

Great post. I think you have made some very insightful observations and formulations. I will mull these over and post again tomorrow.

Originally posted by Hand of Hecate
You've missed off a very important goal... that of just plain $h!@ disturbing. Creating maximum chaos and disrupting the 'game' to the greatest degree possible. Bonus points should be available for actually driving someone crazy through your comments, subterfuge, sarcasm and bitching.

The game is won if a naked Darfius retires to a clock tower ...[text shortened]... ing round after round into his fellow students chanting "There is a God! Behold my glory!"

It's not the only goal he's missed.

How about the goal of creating tolerance?

And I know that's not even the last one either.

MÅ¥HÅRM