From: "Jonathan W. Hoyle"
Subject: Re: 0-sum N-Person Game Theory
Date: Tue, 28 Sep 1999 13:40:56 -0400
Newsgroups: sci.math
>> Is there no such thing as 'Optimal Strategi' for N-person games
>> with N>2?
You are correct, there is not necessarily an optimal strategy when n>2,
if we mean by "optimal" that in a symmetric game the expected return is
no less than 0. In the example I gave with n=3, the "solution" strategy
can result in a negative return if, for example, two players conspire
on strategy. If Player #1 chooses to always bet, and Player #2 chooses
some other predefined critical betting point (I won't bother with the
algebra), then Player #3 will have a negative expected return if he
plays the solution strategy.
Granted, Player #1 loses a lot more, but if there was collusion prior to
the game that Players #1 & #2 will split the wins & losses, they come
out net in the positive. Note that this collusion involves only
agreeing on strategy, no "cheating" involved.
==============================================================================
From: hrubin@odds.stat.purdue.edu (Herman Rubin)
Subject: Re: 0-sum N-Person Game Theory
Date: 29 Sep 1999 16:01:05 -0500
Newsgroups: sci.math
In article <37F06DF0.D354F1DE@intel.com>,
Michael Jørgensen wrote:
>Go over that again, please:
>Is there no such thing as 'Optimal Strategi' for N-person games with N>2?
>What have I missed?
If we allow payments, the solution set of such a game consists
essentially of two coalitions. which will play against each
other to maximize their payoffs in the resulting two-person
game, and divide the proceeds within each coalition. There
are many ways this can be done, and there are considerable
discussions about which of these are "fair". Books on game
theory go into this.
>Herman Rubin wrote:
>> In article <37EEECB3.10D0@kodak.com>,
>> Jonathan W. Hoyle wrote:
>> >Are there any good books you recommend on 0-sum n-person Game Theory
>> >with N>2? Most of the books I have seen out there deal mostly with
>> >N=2. In particular, I am considering a continuous infinite strategy
>> >model, rather than discrete finite model.
>> There are books discussing this, and there are discussions of
>> what can be called "solutions". But there is no clear solution
>> to any such game.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558