INTRODUCTION Sometimes an idea is so old it seems new. That�s the case with this �roundtable� discussion, an idea that I originated back in the 1960s in my old Dip zine, XENOGOGIC. In the days before personal computers and the internet roundtable discussions were the way for Diplomacy hobbyists to exchange their knowledge, opinions and ideas about a variety of topics. It worked fairly simply: A topic would be proposed and distributed to interested readers; Comments would be returned to me and then distributed to all those who had responded; Those individuals would be invited to comment on everybody else�s comments; and The entire discussion would be published for the hobby at large. Times have changed in nearly fifty years. This time I used the Facebook World Diplomacy 2014 group for the discussion. I posted the following question, �Are any of you interested in game theory and related subjects as they relate to the game Diplomacy? If so, please contact me� on the group site and waited to see what happened, hoping I�d get a nibble or two by way of a response. Within a short time Doug Kent made a couple of comments and then Eric Hunter joined the discussion and it quickly took on a life of its own. In the next 15 hours or so six people contributed to the discussion and 26 people saw at least part of it. It was interesting to see Dippers trying to grapple with the question, which quickly became a discussion centered on the question, �Is Diplomacy a zero-sum or a non-zero-sum game?� I was amused to see what I thought was a simple mathematical question become an argument over semantics. I didn�t notice that the discussion changed anyone�s mind but I am hoping the discussion got some people thinking about the topic; and that this will contribute to our discussion of robotics and Diplomacy. I also hope the success of this round table will lead to other, similar events in the future. Thanx to Kent, Hunter, Desper, Burgess and Abbott for their contributions to the round table; and to all who participated, even if only vicariously. The following is a summary of the transcript. Douglas Kent: Aren't you a little old to be messing around with theories? Time to stick with sure things. Laurence Peery: You're never too old to stop learning and I haven't dabbled in game theory since I was in college and working with RAND. I'm just looking for a simple answer to a simple question Is Diplomacy a non-zero-sum-game or a zero-sum-game? Douglas Kent: You're never too old to stop learning? That's a double negative, confirming what I said....you are too old to learn. Douglas Kent: And the answer is yes. Laurence Peery: Oh, and one detail, why? Eric Hunter: I would think it is non-zero-sum. Douglas Kent: Because if it was no it wouldn't be yes. Eric Hunter: Not everyone places the same value on solo vs a draw, and not everyone differentiates between the value of a small draw and a large draw to the same degree if at all. It is also quite common for people to think a loss to one opponent is worse than a loss to a different opponent. Laurence Peery: You mean some players would rather beat Edi than me? Amazing. Who would have thought it Eric Hunter: I actually meant some folks would rather see Adam Daniel solo, than see me share in a draw. Laurence Peery: That's because of all those years you've spent living in the shadow of Three Mile Island. Dan Mathias told me that. Rick Desper: Diplomacy is a zero-sum game in the sense that it has 34 SCs. And if one player gains a center, another one loses it. That's analogous to poker, when there's a fixed, finite number of chips at the table. Whether people "feel differently" about different types of results isn't really the point. A person may feel great about moving knights around on the chess board. But that's not the purpose of the game. Eric Hunter: Looking at Diplomacy as a game about SC counts completely misses the point. Turkey giving Russia a Center so he can build F StP/NC, and keep England from sending his Fleets south to seal Gibraltar, is a plus for Turkey, not a minus. Laurence Peery: Yes, there's no easy answer I think. Two-sided games might be zero-sum but when you get into multi-player games it becomes more complicated. I found some interesting web sites on this topic but nothing particularly about Dip. James Burgess: The game theory of multiplayer games is pretty complex and not for the faint of heart. Studying it more seriously and writing a book on it is one of my potential post retirement projects. There is some dip history on the question, mostly by Danny Loeb and Matt Sundstrom's masters thesis is well worth reading. Matt's in the Chicago mob, Danny Loeb is hard to find. The DipAI people also have thought about it some. In my view the zero sum game aspect is not that important — it's odd number of simultaneously movement. The game breaks down with even numbers, someday I'll give that a proper proof Eric Hunter: Dip is clearly not a zero-sum game. Rick takes a Center from me, he gains, I lose, zero-sum. Except I disband, leaving a hole in the stalemate-line, and Edi Solos, so by gaining a Center, Rick loses, too. QED Laurence Peery: Thanx for both comments. James Burgess: So in Eric's proof he needs Edi as the third player. That's quite essential actually. Three player dip though, would be boring, but seven is just about the right complex tradeoff. Will J Abbott: Of course, the complexity skyrockets with the negotiations. What I've seen as the biggest problem with Dip computer games has been that negotiations are inherently stylized. Yes, some of them have been tactically idiotic, but negotiating with the program his usually boring. If we all were playing a a game, I could go to Jim-Bob and talk to him about anything in any matter. We could talk about moving to the Channel or attacking Turkey or even how that Italian player may be a newbie, but she's getting the hang of it quickly and defended against France well. These are not transactions that can be easily stylized. Furthermore, they aren't necessarily zero sum. Sometimes information only has value if it is shared with the right person. Eric Hunter: Pay attention to the board, but play against the players. I've had people throw solos because they thought I was thinking about eliminating them, even when I had no intention of doing so. The Game just isn't zero-sum. Laurence Peery: Please see my comment at the top. Well, that didn't work so I'll put it here. I was looking for a volunteer to write something on this topic for the DEC TDP but if nobody objects I'd like to use your comments as the basis for that discussion. You're welcome to elaborate or edit them if you like. The main thing I wanted to do was open this discussion and keep it simple as possible. I think it would be a good companion piece to the article on robotic Diplomacy I'm mulling over. And, if anyone is interested, I'm still looking for a volunteer to write the lead article on this. Thanx. Will J Abbott: I have no problem with you using my comments above or any others I make. Laurence Peery: Thanx. I wasn't even thinking of this at the start but as I read the comments I realized it was doing exactly what I wanted; and a lot less effort for all of us. I may try this approach in the future for other topics that lend themselves to group discussion. Actually, now that I think about it this revives an old tradition from my original Dip zine, XENOGOGIC back in the 1960s when I�d do a �roundtable discussion�� on different topics and people would contribute their thoughts. Remember, in those days we didn�t have computer, internet, etc. so it took a lot longer to put one together, but people liked them. Will J Abbott: I have no problem with you using my comments above or any others I make. Probably a good idea as people who are intimidated by the thought of writing an article may not be by the thought of commenting. So to restart discussion, how does Diplomacy as a zero-sum or nonzero-sum game relate to objectives other than winning? I know the latter is a great big ball of fire ants for some people but that some people play for things other than 18 centers, at least in some games, happens. Eric Hunter and Rick Desper have alluded to this relationship above. Laurence Peery: Mea culpa. For years I've followed the teachings of an old California politician named Jesse Unruh who said, "I'd rather be a kingmaker than a king any day." That's the way I feel about Dip. I get more of a kick out of helping somebody, especially a newbie, win a game; or perhaps keeping somebody who xxxx-ed me off from winning, then I do from actually winning a game myself. Rick Desper: Eric, you haven't exactly proven that Diplomacy isn't zero-sum. You're just showing that the naive away of assigning values according to SC counts is wrong. My point is that there's a _way_ to look at Diplomacy as a zero-sum game, and that's worthwhile. You could also define the value of a game to be 1=win, 0=loss, 1/n = value of n-player draw to each player. Indeed, many scoring systems do something like that, with a different value for the win and various scores in a draw. Dave Maletsky's "Carnage" system does that. The player in nth pace with k centers gets (8-n)*1000 + k points, except a soloist gets 28034 points. I believe David Hood's scoring system is also zero-sum. And the squared scoring system is fairly explicitly "zero-sum" since the sum of scores at a given board is 100. I don't think I have to say that being zero-sum and being C-sum, for any constant C, are mathematically equivalent for the purposes of game theory. BTW, Larry, you probably should add me to any list discussing this. I'll volunteer Jim Burgess, too. Laurence Peery: Rick, Jim had his say earlier. He know we're here. I'm all for an open discussion but I do ask that you keep in mind who is reading it. We're not all math or game theory wizards, so be sure to re-explain whatever you just said in plain, simple English for us people who still balance or checkbooks by hand Will J Abbott: For what it's worth, Rick, I get your point, and I have only the very basics of the actual mathematics of game theory. As a result I'm not going to argue that some particular zero sum or nonzero sum model is accurate to model Diplomacy. However, any way whereby someone else's gain can be your gain as well starts to suggest a kind of value creation going on. If Larry and I are playing, say, England and France respectively in a game, and Larry decides that they way that he will maximize his fun is to have me win, then it's hard for me to see the argument that Larry loses when I solo as he would like. He then gets the result he wants, and so do I. A zero-sum scoring system would give me everything and him nothing, but that happens not to be what he was playing for. Furthermore, neither my score nor my enjoyment suffers because Larry enjoyed giving me the solo. Rick Desper: Will, the thing about Diplomacy is that it doesn't have explicit end-game values other than "win", "draw" and "loss". I'm not even sure "loss" is defined. All it says about "draw" is that "all survivors share equally", and that's an instruction that is usually ignored by people who design tournament scoring systems. FWIW, chess is defined as a zero-sum game, but that's really about the most useless way to study it. Will J Abbott: Rick (and James Burgess), how developed is nonzero sum game theory? All I know is that recreational math books don't do much more than acknowledge its existence, and I'm a theologian by training. Rick Desper: Well, if you have a constant sum, then you can translate your analysis of the game to zero-sum simply by doing a linear shift. If your sum is C, and you have n players, you can shift your outcome matrix by -C/n and you have a zero sum game where any optimization strategy for the new game is essentially identical to an optimization strategy for the old game, and vice versa. Aside from that, I don't know what there is for non-zero sum game theory, other than the classic Prisoner's Dilemma. It's been a long, long time since I looked at formal game theory. The results I'm aware of don't translate to multi-player analysis. Eric Hunter: Rick is right that Dip SHOULD be zero-sum. There are 34 Centers, and the Objective, according to the rules, is to capture 18 of them. Larry's confession demonstrates part of the reason why it is not, as does Edi's ability to convince people that he is going to solo, so they might as well concede. Laurence Peery: Translated into simple DipSpeak that means "Old Farts Rule!," right Edi? Eric Hunter: Rick, you are, of course, right that tournament scoring systems often reduce the complexity of Dip by making it zero-sum, and I don't have the math or game theory background to prove that neither Dip, nor life, are zero-sum, but that doesn't mean either one is. Rick Desper: Eric, if Edi can convince people to abandon positions that are not losing positions, that fact alone doesn't mean that Diplomacy isn't zero-sum. After all, poker is obviously a zero-sum game, but bluffing is part of the game. Whether a game is zero-sum or not only refers to the range of outcomes. It doesn't tell you anything about what kinds of strategies are allowed. Like I said earlier, chess is a zero-sum game, but that fact hardly describes the intricacy of the game in an interesting fashion. Eric Hunter: Rick, the thing that makes Dip _The Game_, is the human interaction, and that isn't zero-sum. Rick Desper: I could say the same thing about poker. Laurence Peery: Bluffing? As in Blind Man's Bluff and Fog of War? Hmmm. Interesting. Larry Peery ([email protected]) If you wish to e-mail feedback on this article to the author, and clicking on the envelope above does not work for you, feel free to use the "Dear DP..." mail interface.