The Editor and the Readership
Well, what shall I talk about this time? No ideas? Okay, I'll tell you. I'll talk about me. It seems to be a common fallback topic for 'zine editors as far as I can tell. But before I launch into this topic (in which I do hope you will find at least a little interest), let me justify why I think I really am the best thing to talk about this issue.
First of all, let's look at the Pouch Deposits column. The original idea for the column was for me to present a topic for discussion, then to publish the correspondence which I received concerning that topic in the next issue. Unfortunately, the volume of on-topic correspondence was such that this didn't seem to be working out. The Deposits column, at least for now, seems to be wholly a repository for comments on articles in past issues. Now I'm not complaining (though I do wish I'd have gotten more responses to my topics), but I figure if I'm not going to get a lot of on-topic responses, I may as well spend this issue talking about something you don't know anything about. Like me. (Maybe this'll teach you!)
Second of all, as you all know, I've been a busy boy lately, kind of out of the Dip loop for a while, and we can all thank the many others who have taken up the slack at The Pouch when I was unable to pull the rope myself. So I thought it right to update you on my activities now that I'm back where I want to be, in the Dip world. I hope that there will be some useful information in here for you, because I have big plans.
So let's get right to it. First of all, let me apologize to all the people who were in the two games I was forced to abandon when real life got out of hand. I have one particular power and one particular Master in mind especially, and I hope they know who they are. I slowly scaled back my activity to two games, one of which I was perpetually late in (and which ended recently -- darn that Joan Artes for stabbing me before I could stab him!) and the other which went on a long hiatus and is only now getting re-started. So basically, I've been off the board for a couple months or more.
But I've been Mastering, and am still at the helm of something like six games. I hope that my crunch didn't affect any of the players who depend on me. Luckily, we had a lot of judge outages recently, and this helped. :-)
Anyway, instead of getting into exactly why I was so pressed for time that even Diplomacy (gasp!) had to take a back seat, let's look forward and discuss what I plan to do now that I'm back. I've been busy re-filling my plate.
First off, it's nice to be reading and contributing to the rec.games.diplomacy newsgroup again. (Didja miss me, guys?) The Internet hobby seems to be growing by leaps and bounds now with the explosion of new Web-users (hello, out there!) and the newsgroup is still doing a great job accommodating everyone.
Second of all, there's your favorite magazine, The Pouch. Let's talk a bit about this. A couple of the regular contributors missed the deadline for the Fall Movement issue so badly that this Retreat issue came out. Now I'm not upset at all about this, because I know how it is, and in one case (John Woolley) I myself know why he's been unable to get to it.
So the philosophy of what a "regular contributor" will be is in flux. I still like the idea that these contributors would have something in every Movement and Adjustment issue, but it may not always happen. At the same time, I'm very reluctant to demote anyone from "regular contributor" status, especially because "The Big Dipper" and the "Sherlock Holmes, Consulting Detective" series are among my favorite. Basically, anyone who will write a series and get them to me whenever he or she can will be a "regular contributor."
As far as these two specific series go, since I'm John's best friend, I know what he has in mind for Sherlock's second case, and I thought that if I got the time before he did that I could throw it together. My Victorian-Edwardian writing would prove no match for his, however, and then I never found the time anyway. Do look for The Great Detective to be reappearing soon, though. Hopefully in the Winter issue. And as for Mr. Crandlemire and The Dipper, he has already promised (for the Winter issue) an article whose topic interests me greatly.
Speaking of The Pouch, I don't know if you noticed (it's mentioned on the front page of The Pouch), but The Pouch has been rated four stars (out of four) by The Magellan. And I didn't even know they knew we existed. I guess there are people with good taste everywhere.
Combine this with the fact that another set of Webpages under my control was recently named to the infamous and hilarious List of Useless WWW Pages (and the Webpage set in question isn't even ready for company!), and you can see that I'm one proud papa indeed!
But let's get back to what I'm doing. How many of you are familiar with Payola Diplomacy? Well, one of my missions is to make sure that you all raise your hands when that question is asked. Look for an article in the next issue of this magazine which goes into deep detail discussing the Payola variant, and in the meantime, look for me as the "Swissbankmeister" in various games around the 'Net. The one game I'm actually playing is a "Tin Can" game, meaning that it is Payola and it is Blind. Two -- two -- two variants in one! And I must tell you, it seems to be about the best way to play which I have found.
What do you care about this? How does this affect you? Well, maybe it doesn't (except for that part about the article I plan to finally get to for next issue, which will convert you to a Payola player if you're not already one), but then again, maybe it does. One of the first things I did on my reacquisition of useful spare time was to inquire about the possibility of adding support for Payola to the judge. This has grown into my unofficially joining the judge-maint team with some lofty goals -- adding Blind, adding Payola, and then some. Look for these changes as soon as Larry Richardson makes them. Oh, okay, I'll help him. :-)
Last but not least, and growing out of this judge-coding urge, is my own deep-seated need to create a Web interface for the judge, one of which will run right up here at The Pouch. As some of you know, Joseph Cheek already has a Dip Web site established with hand-adjudicated games. He will be writing an article for the next Pouch discussing his experiences! As for my own infant effort to integrate such pages with an existing or re-worked judge, I'm chock full of ideas on what it will look like, and I was going to fill this article a bit with some of this, but I'll stop here, and just say that if you're interested in participating, please don't hesitate to get in touch.
In fact, if you're interested in any of the things I discussed above on which I hope to work in contribution to our beloved hobby, I hope to hear from you. Let me put a special bug in your ear for help with The Pouch -- and not necessarily the kind of help (editing, etc.) which I've thankfully received recently. No, what I'm asking for is articles. For whatever reason, the contributions seem to be slower in coming to me than I was hoping, and I was foolish enough to really set myself up at the end of the year -- The Pouch is basically a monthly magazine at the end of the year (what was I thinking?), and the plan was for the Adjustment issue to be a huge extravaganza!
I'm not begging, though, because if there's one thing I've learned these last few months it's that I don't have to beg. This hobby is absolutely full of people who pitch in whenever and wherever they can, and who have continually gone to amazing lengths to help me in all my various undertakings. So I know that even if the directions of my own current efforts don't interest you, there is a whole bunch of other things which need to be done and that together, we'll get them done. Being back in the newsgroup and seeing action on all the many fronts is refreshing. I guess you guys got along okay without me after all.
But I sure missed you. It's good to be back.
I enjoyed your article "What you don't know...". Your analysis which shows how the plan will keep the players honest only works because of the numbers. In other words,
6+2 > 7+0 (1) so 0.5*8 > 0.5*7 (2) so 4 > 3.5 (3)so they remain honest (assuming rational play, maximizing expected payoff, etc.) But if the situation is such that being ambitious when the other player is conservative is say, 10, the players don't maximize payoff by remaining honest, and so the equilibrium point changes (or does it disappear?).
In other words, if the 8 and 7 in equation (2) become 8 and 10, the greater than sign becomes less than. Of course, the situation can be remedied (i.e., the sign can be flipped back) by changing the probabilities in equation (2) from 0.5 and 0.5 to unequal probabilities, which can be done by changing the instructions to the GM. If the GM rolls a die and flips a coin, and only follows the above instructions if he flips heads and otherwise tells nobody anything, your calculated probability of Dan knowing the outcome given that you don't is no longer 0.5. But note that the probability that Dan calculates for you knowing given that he doesn't know is the same as the one you calculate if you don't know. (This will matter in a minute).
So far, so good. The next level (and more realistic scenario) is one where one player has more to gain or lose by somebody defaulting than the other, leading to an asymmetric matrix. This too can be solved by changing the instructions to the GM. For instance, if you have much more to lose than Dan, the instructions to the GM can read: if the die toss is a 1, tell Shoham, if it's a two or a 3, tell Loeb, else tell nobody. Now, both you and Dan will calculate different probabilities of your opponent knowing given that you don't know, and you can compensate for asymmetric payoffs.
But the big question, assuming a realistic asymmetric matrix, is: how do you go about calculating fail values for the matrix? You may say Shoham's default would be worth 10 to him and 2 to you, whereas he might downplay this and say it would only be worth 8 to him and 4 to you. Since the amount of information you get (i.e., the probabilities you decide on) is based on the matrix values, you will both downplay your gains in a default and play up the gains of the other in a default.
Well, here's my solution. Send a letter to the GM, and tell him to roll a die...
I agree with your comments. With different numbers either the effect described won't happen, or at least the optimal probabilities to be used by the GM would be modified.
I'm not sure what "downplaying" one's gains means, since I'm assuming that Dan and I are completely aware of what a given position is "worth" to both of us.
In any case, coming up with the optimal mixed strategy is the subject of classical (or matricial) game theory.
Look at any book by Prof. Aumann.
Yours, Daniel Loeb
You said, "I'm not sure what 'downplaying' one's gains means, since I'm assuming that Dan and I are completely aware of what a given position is 'worth' to both of us." In terms of good and bad, yes, but in terms of quantifying how good or how bad, could you agree on it? For instance, you may say that if you defaulted on an agreement and took a supply center that the new position would be worth 8 to you and 4 to him. But he may look at that "stab" as having other more serious consequences and may argue that the new position would be better for you and worse for him than he stated. He may say that the new position would be worth 10 to you and 2 to him.
But even if he silently agrees with you, it's in his best interest to try to "haggle" in that way. Why? Because if he convinces you that he's right, the 10 and 2 will result in a different matrix. Thus, the die toss will have to be more biased in order to make the agreement fair (to keep you both honest). If the values are 8 and 4, your instructions to the GM may say that he tells Dan the value on a roll of 1 or 2 and tells you on a roll of 3 or 4. But with values of 10 and 2, the instructions may be to tell Dan the value on a roll of 1, 2 or 3 and you on a roll of 4.
Essentially, his haggling above was haggling for information since it's the bias in the probability of getting information that establishes the equilibrium position. Now let's say he silently agrees that the matrix values are really 8 and 4. If he manages to convince you that 10 and 2 are right, you think you have established an equilibrium point where you both maximize payoff by not defaulting, but he sees his best move as one where he will maximize his payoff if he defaults. Thus, the agreed-upon values won't keep him honest.
The same argument works the other way and it's in your best interest to haggle the other way regardless of what you actually believe. If you two are really in an adversarial situation and you're both trying to maximize your payoff, haggling for more information means haggling for a higher expected payoff (if you manage to swing the matrix such that your best move is not to remain honest but to default.
So, to summarize my point, setting probabilities (i.e., instructions to the GM) is easy *given a matrix*. But the bigger problem is twofold: first, how do you get the matrix since values are subjective, not objective, and more importantly, the negotiation of matrix values is also an adversarial situation because it is to your (both you and Dan) advantages to lie, trick, misrepresent, in order to get better matrix values.
Continuing on the "downplaying one's gains" discussion, suppose that Dan and I are infinitely intelligent. Then we just make a matrix of all strategies possible to employ over the whole game. The endpoints of this "game tree" (well not actually a tree because of simultaneous movement) can be valued numerically using for example the Hall of Fame value of a win or a draw (or any other mutually agreed scoring system).
Obviously this is not in practice possible due to the incredible complexity of the game. The above is simply a "mental experiment".
The problem in estimating the values of results in a game matrix is very important.
For example, a friend of mine created a game matrix for a certain conflict in the game of Strategy. Each player had 3 "strategies". I found that for one player a certain mixture of 2 strategies dominated the third. Thus, I concluded that he should play strategy A say 30% of the time, B say 70% of the time, and never play strategy C. However, the domination was QUITE slight. With an extremely small change in the result values in the game matrix, I found that strategy C was used say 80% of the time, and strategy A say 20% of the time!
In other words, it is very hard to make firm conclusions from wishy-washy data.
[I purposely avoided giving a precise example, in order to avoid people objecting to the values I put in the matrix.]
As for your "haggling". You are modeling a slightly different type of game:
Many game theorists study such "signaling games".
For example, in Krep's Beer-Quiche game.
You make your key point when you say, "Essentially, his haggling above was haggling for information." As I pointed out, in a game of perfect information, you can't do better than the Nash equilibrium. However, by having the GM reveal selective information about some dice roll, it is possible to do better. Nevertheless, it is in each player's interest that he gets more information than the other player. Thus, even between allies there is a constant battle for information, since whoever has the most information can control the destiny of the game.
You said, in summary, that "setting probabilities (i.e. instructions to the GM) is easy *given a matrix*." Well, not that easy. The theory to set those probabilities was worth a few Nobel prizes in economics.
You put your finger right on it when you said that, "more importantly, the negotiation of matrix values is also an adversarial situation because it is to your (both you and Dan) advantages to lie, trick, misrepresent, in order to get better matrix values."
Meaning the game is a more complicated game than we originally had imagined.
Yours, Daniel Loeb
Regarding Danny Loeb's GM Coin Toss trick....
I liked this a lot.
To the first question:
Of course it's fair. I would do it if I were the GM. If I didn't, Dan and Danny would no doubt write to some third party not involved in the game. In fact, if anyone ever runs into a situation like this and wants a coin-tosser, write to me! I'll be happy to do it. (Try your GM first :-))
To the second question:
This is tricky. I gave it a little thought.
My first idea was a situation where each of a pair of allies wants to be the one who gets a center not belonging to either of them. It might be France and England quarreling over Bel in the opening. The Conservative move would be to support the other guy into Bel. The Ambitious move would be to move to Bel.
This doesn't quite yield plausible utilities, though. I think (7,2) is about right for the A/C payoffs, and (0,0) for the A/A payoffs. (Explanation: if they both go for Bel, neither gets it, the move has been wasted, although Russia and Germany are not alerted to the alliance. If England supports France to Bel, the position is excellent for France and pretty good for England, since England can more or less count on a French attack against Germany.) But the C/C option is not plausible. Germany will get Bel, and France and England will each have wasted her support move.
Without taking the time to find an actual position and area of the board, I think we want something like this:
The aggressive move is to try to enter Nth. If successful, this puts the ally in a superior position, with good chances to reap most of the spoils from the victim (and even to exert pressure thereafter on the other ally). The conservative move is to take the other available region (for France, Eng; for Germany, Nwg).
If both play Ambitious, that's worst for both. They don't make any progress, wasting the move.
If both play Conservative, then at least they manage to occupy the "pretty good" spaces (Nwg and Eng).
If one plays Ambitious and the other plays Conservative, the one who plays Ambitious is in really good shape, while the one who plays Conervative is somewhat worried about not getting his share of the goodies. Not too implausible that the utilities could work out.
It's worth keeping an eye out for actual game scenarios that fit the bill.
One of the things I like about the tactic is that it seems to apply primarily to opening and midgame situations, in contrast to the large majority of well-understood tactical ploys that apply to endgames.
Well, there you have it. Another Deposits column. Yep, it sure is.