Subject: Game Theory, RPGs and Real-Life

From: Shlomi Fish <[email-masked]>
Date: Thu, 21 Mar 2002 12:52:01 +0200 (IST)

Yesterday evening I took the Moed Beith Exam of Game Theory. All in all
the course was very interesting, especially when I had to learn it on my
own, from the Open University books. I found it irritating that the Exam
was not an open book one and that one question in each test required us to
detail very long proofs. I heard there is a similar situation in other
courses of the math faculty.

But that's not the main theme of this message. What is, is my musings on
how well we can use Game Theory concepts to model a role-playing game, and
by extension real-life. In a role-playing game, each player play the role
of an imaginary character, and there is one special character called the
game master, who explains what happens to the character at any given
point. It's very similar to doll play, except for the fact that there is a
GM who acts as an objective arbitrator in telling the players what is
going on, and that there are rules that govern the success or failure of
the players' actions. (usually with the aids of dice).

Now, let's suppose the characters walk in a complex of rooms and encounter
a door. They can:

1. Open the door.
2. Try to pick its lock.
3. Walk Away.
4. Eavesdrop.
5. Knock on the door.
6. Sing the Kum-ba-ya outside the door.
7. Mark the door in some way.
8. Wait to see what's happening.
9. Look through the keyhole.
10. Do something and then do something else if it fails.
11. Etc.

The number of options at any given situation is practically infinite.
While a good game master is determinstic and knows exactly what happens
for any given situation the players' reach and for every action they take,
there is still a very large number of situations which can be reached.

Game Theory models work on a finite set of strategies, or such that
follow a certain pattern. This is not the case for a role-playing game.

Now, I believe real-life is usually closer to a role-playing game than to
a Game Theory model. I.e: at many given points, a person can come up with
many creative solutions, in manners that do not give way for a game-like
model. Thus, thinking in terms of Game Theory concepts can usually lead to
over-simplified (e.g: yes/no or purely numberic) models, and otherwise
lame behaviour.

Regards,

	Shlomi Fish

----------------------------------------------------------------------
Shlomi Fish        [email-masked]
Home Page:         http://t2.technion.ac.il/~shlomif/
Home E-mail:       [email-masked]

"Let's suppose you have a table with 2^n cups..."
"Wait a second - is n a natural number?"

---

From: Nimster <[email-masked]>
Date: Thu, 21 Mar 2002 13:37:45 +0200

----- Original Message -----
From: "Shlomi Fish" <[email-masked]>
To: "Hackers-IL" <[email-masked]>
Sent: Thursday, March 21, 2002 12:52 PM
Subject: [hackers-il] Game Theory, RPGs and Real-Life

[Snipped: Good luck to Shlomi]

> the players' actions. (usually with the aids of dice).

I do not know Game Theory, but you should note most RPG's don't have a
"goal" per say. You play with the idea of having fun and coming close to
your token's demeanor and attitude (what one would call Ofi in Hebrew, which
translates to character, so we get into some ambiguity with terms).
Classically, in games such as the famous Dungeons and Dragons, you were
usually sent on some goal- but it was completely up to the GM if he wanted
to play a goal-based game or one that simply immitates life in a
pseudo-medieval world. I can imagine one of the basic requirements from a
Game Theory "game" is to have a goal, an ending or method to measure
progression. That's something that doesn't necessarily exist in RPGs.

[Snipped: example]

> over-simplified (e.g: yes/no or purely numberic) models, and otherwise

That is, I imagine, the goal of RPGs. To come as close to "life", even if by
life we mean the life of kittens on Mars. In fact, to become as close as
possible to that purpose, many RPGs today are played without any "system
rules" as we know them from the classic RPG's (again, "Dungeons and Dragons"
is an example), those which describe your token with a number of scaled and
pre-set attributes (Strength, Intelligence, Skills, etc.) or use arbitrary
die rolls to decide everything that goes on in the game world: The only rule
is the GM's understanding of "who you are" ("I'm a neat hacker, kinda like
Shlomi F." as opposed to "I have intelligence of 15 and strength of 8*pi")
and the physics (meta-physics included) of his world ("You fall and spring
your ankle" as opposed to "You fall and lose 1D4.5 damage"). This, they
hope, brings them as close to a realistic imitation of life.

-Nimster

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From: "Nadav Har'El" <[email-masked]>
Date: Thu, 21 Mar 2002 17:41:33 +0200

On Thu, Mar 21, 2002, Shlomi Fish wrote about "[hackers-il] Game Theory, RPGs and Real-Life":
> I found it irritating that the Exam

:)

> follow a certain pattern. This is not the case for a role-playing game.

I'm note sure what you're trying to say... Even in a role-playing game,
there's some practical limit to what kind of instructions you can give in
each step. For example, you shouldn't need to explain your action to the
GM for more than 1 minute. In that one minute you can not say more than (say)
100 words, so you can only utter (say) 100^100 different instructions in
that time. This is a finite number...
In reality, the number of "logical" instructions you can come up with is
much, much, smaller. Say, 1000 (game theory would not be interested in
steps that do not make any sense and nobody would take them). It's probably
safe to say that 99% of the time 10 of these instructions would be chosen
and 0.9% more can be approxmiated by one of these 10 instructions. So if
you only allow these 10 instructions, you might be able to model te game
quite well...

When you make approximations, you always have to prove that your
approxmations are valid (the Physics teachers I had probably never heard
this rule ;)), but you *can* do approximations and models. You can achieve
much stronger results that way, that you'd be unable to achieve otherwise.

A breakthrough in Game Theory, Physics, or any other science, can be to
find a new model that better approximates reality than previously known
models. See, for example, Einstein's General Relativity, John F. Nash's
"Nash Equalibrium" (see the movie? :)), and most scientific breakthroughs
of the century.

-- 
Nadav Har'El                        |      Thursday, Mar 21 2002, 8 Nisan 5762
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |I have an open mind - it's just closed
http://nadav.harel.org.il           |for repairs.

---

From: "Orna Shemesh" <[email-masked]>
Date: Sun, 24 Mar 2002 10:37:46 +0200

> follow a certain pattern. This is not the case for a role-playing game.

In more advanced courses you will find models for infinite strategies,
either as a range
of real numbers (for example, a price offered at an auction) or just as a
really infinite range of strategies,
treated simply as "strategy space".

Orna.

---

From: [email-masked]
Date: Sun, 24 Mar 2002 22:43:44 +0200

Hey,
	You've have a discussion lately regarding game theory.
I would like to find some documentation on the subject, either on the web, or if you can recommend some basic books.

Eli Shemer(app).

---

From: "Orna" <[email-masked]>
Date: Mon, 25 Mar 2002 09:11:25 +0200

I have not looked in the web for it, but the most basic and well known book
is "Game Theory", by Mas-Colell.

Orna.
----- Original Message -----
From: <[email-masked]>
To: <[email-masked]>
Sent: Sunday, March 24, 2002 10:43 PM
Subject: Re: [hackers-il] Game Theory, RPGs and Real-Life

> I would like to find some documentation on the subject, either on the web,
or if you can recommend some basic books.
>
> Eli Shemer(app).
>
>
>
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