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