## Archive for the ‘**Game Theory**’ Category

## Screwtape discusses voting

*My Dearest Wormwood,*

After receiving your most recent letter, on your advice I watched the video on quick and easy voting for normal people. I am surprised that this comes as a revelation to you, since We who are down below routinely allow our charges to vote for a wide variety of things using what our patients semi-jokingly refer to as the Chicago Method (“Vote early and often”) and what your video refers to as Approval Voting.

And, as befitting our station, we scrupulously respect their votes whenever suits our mood. Which is more often than not, because all voting methods have flaws. Surely Our Father has taught you all the details of Arrow’s Impossibility Theorem, which has dozens of applications to suffering and gaming. I myself learned it at an early age.

(A more pedantic member of our kind – although I doubt you will ever encounter one – may state that Arrow’s formal proof does not strictly apply here. Math is a realm of The Enemy – and as such I have no done no more than dabble, lest I be accused of heresy again – but I believe the idea generalizes. I will check with several experts I am dining on tonight).

Whenever a vote is proposed, you should of course make sure the outcome is as you desire. The stakes are high!

The video numbers make for a poor example for more interesting applications, so let us juggle them a bit. Surely even a youngster such as yourself is familiar with creative accounting?

- The five vegetarians prefer: Veggies, Burgers (w/Veggie option), Steak (in that order)
- The three carnivores prefer: Steak, Burger, Veggie
- The lone Burger guy prefers: Burger, Steak, Veggie

In all cases the 1st two are “acceptable,” so burgers get nine votes, and is an acceptable compromise.

First of all, note the obvious flaw with the system. *It punishes excellence*. This means that, despite all of its problems, you should suggest Approval Voting whenever possible. Your goal should be to promote mediocrity and lazy thinking in all aspects. Do this consistently and your patients will always dine out on the most milquetoast and bland meals possible, never taking chances, never risking sublime beauty!

Do not mistake my critique of this system – which is done as a general exercise to instruct my favorite nephew – for a serious criticism!

Now, let us make a small change.

If, on the final restaurant named, people don’t vote on something acceptable because they prefer the currently winning option. Now, so long as Burgers are listed last, Veggies will win, because the Vegetarians, being more delighted with the currently winning option (named first or second), decline to raise their hands for Burgers. Which will now lose 5-4, despite being a unanimous winner before!

Then simply force those shuffling carnivores towards their tofu. Demand their happiness while they respect the group’s decision. Be sure to smile broadly as you choke down your okra. Sing praises towards democracy, which levels all of our patients in the same way that water always strives for the lowest resting place.

(As to my prior criticism, I simply state that while Vegetarian restaurants can be excellent in theory, much like excellent non-alcoholic beer it does not occur in practice).

As always, he who sets the vote order (and he who votes slowest, deciding after others who have raised their hands) has an immense amount of control, particularly if they well judge the preferences of others.

These tricks (along with a few more which I dare not reveal, lest this letter is intercepted) will let you control the outcome with ease, which is why we are serving a slightly maggoty meatloaf for the thousandth night in a row instead of the exquisite venison or lovely pouched trout, both clearly visible in the cafeteria.

*Your affectionate uncle,*

*Screwtape*

[H/T to Chris Farrell’s twitter feed]

My first (semi-joking) comment was that the Tao of Gaming method was to have everyone list all their options, then reject them all and walk away. This prevents mediocre games, although I admit that also has problems. I had thought I tweeted a joke about that but, much like Screwtape, I prefer the old method and send my messages encoded in the pitches and volumes of screams, although I do keep up with the times and try to limit my conversation to at most 140 screams.

An amusing coincidence — I was already thinking about the Impossibility Theorem earlier today, since my side project incorporates a quote by Kenneth Arrow in the next chapter.

## Olympic Losing to Win

Slate has an article on the Badminton thing at the Olympics. (Short Form — Several teams deliberately lost matches and were disqualified by the World Badminton Federation).

The article proposes the “Let the best winner pick their opponent” method, but any bridge player who follows the world championships knows that isn’t a Panacea. You won’t tank to go from 1st to 2nd, but *you’ll tank from 4th to 5th*.

The bridge system advances 8, with the 1st seed getting the pick of 5th-8th. Suppose that the teams are rated on strength (higher number is better). In theory, that means that you should have:

- 100
- 95
- 90
- 85
- 80
- 76
- 73
- 70

after the qualifying. But bridge has some element of luck. (Presumably, so does Badminton). Suppose that we say that the #3 team did poorly (but well enough to qualify) and the #7 team did great.

- 100
- 95
- 73
- 85
- 80
- 90
- 76
- 70

Now, assuming rational selection (you always want to pick the weaker opponent), The favorites pick the #8 seed (as before) but now the #2 picks the 7th seed and the #3 picks the 5th seed. Poor #4 seed (skill=85) is

playing up!. So they tank and lose a match, now look at it

- 100
- 95
- 73
- 80
- 85
- 90
- 76
- 70

Now (because they lost a match) they get to play the lucky #3 (skill 73), and the new #4 seed gets to play the #90. None of which isn’t to say that the Badminton idea is terrible, just that this isn’t as easy to solve as you’d expect.

Letting the #1 seed pick any opponent (not just 5-8) does solve this a bit, but brings up some hard feelings when the #2 seed picks the #3 seed, and the 3rd seed doesn’t get to pick.

## President’s Day Web Walking

- Michael Chwe’s manuscript on “Folk Game Theory,” which analyzes Jane Austen,
*Oklahoma!*, Brer Rabbit, and other popular stories from a game theoretic perspective, is certainly interesting. Although I’m stunned that the opening sentence of his manuscript isn’t “It is a truth universally acknowledged, that a single man in possession of a good fortune, is not in a Nash Equilibrium.” (or some variant). [Hattip to Cheeptalk] ~~By my calculation~~, the odds of one partnership in bridge having NO high card points between them happens roughly once in every~~21,700~~hands. So that’s why it was the talk of the bridge club last week.**Update**— You know, there are 16 honor cards, not 12. So by my corrected calculation it’s once every 1,950,000 hands.**Update Squared**— Half that. Once every 975,000 hands. See below- I do enjoy strategy articles based off of massive data analysis of online games. Even for a trifling like 7 Wonders.
- My pointless quest up the total fan count leaderboard for Rock Band 3 continues apace. I was going to pre-order the Squier pro-guitar from Amazon, but apparently Best Buy has an exclusive. What are ya’ll doing for that? (If anything).

So, how’s your weekend going?

## The Predictioneer’s Game

I recently picked up The Predictioneer’s Game. This is yet another of the countless books trying to cash in on the Freakonomics/Malcolm Gladwell/TED trend[1]; but what the hell, it deals with game theory.

Cutting to the chase — this is more of a book to get from the library. I may go digging into some of the referenced books/articles, because I would like to see more details on modeling real world negotiations based on various desired outcomes works, but this book doesn’t have the details. (At least not yet). It is a pretty breezy read, though. Still, if you are interested in game theory and want to one-up that guy who tries to act interested in science and stuff [2], then you may be interested.

Summary — If you build a complicated game theoretical model that takes numerous actors, and rates them on knowledge, desired outcome, and how much influence they exert, you can model it pretty damn well.

(A quick glance at scholar.google.com does make me think that the author actually knows stuff. So I should be humble.)

[1] By which I mean, books that flatter you and pretend to make you think you have some stunning insight without actually providing any details that would give you a stunning insight.

[2] Again, without actually knowing math.

## Game Theorist — “Dumb is the new Smart”

An interesting article points out that even game theoreticians don’t believe their own results (when money is on the line).

a research team repeated the experiment using professional game theorists playing for real money. But even among game theorists, game theory failed

One hypothesis is that you can get good results by playing dumb. If your opponent knows you are totally rational, then they have to give up a lot to keep from getting screwed. (This particular example deals with the Traveler’s Dilemma, but it applies to the Prisoner’s Dilemma, as well).

I remember a book that dealt with various puzzle aspects of Game Theory as told by Sherlock Holmes, et al. One passage discussed the prisoner’s dilemma, after a clever person tries to use it with real prisoners. When it doesn’t work, he goes to Holmes, who then sighs and calls forth one of the prisoners.

“So you know that it’s always better [to defect].”

“Yes, guv’ner.”

“Then pray explain to [this doofus] why you don’t.”

“Me mates would beat me senseless.”

Glad to see the theoreticians catching up.

Now to just figure out how this relates to unconvincing cylons, and the applications will be endless!

## Game Theorist — “Dumb is the new Smart”

An interesting article points out that even game theoreticians don’t believe their own results (when money is on the line).

a research team repeated the experiment using professional game theorists playing for real money. But even among game theorists, game theory failed

One hypothesis is that you can get good results by playing dumb. If your opponent knows you are totally rational, then they have to give up a lot to keep from getting screwed. (This particular example deals with the Traveler’s Dilemma, but it applies to the Prisoner’s Dilemma, as well).

I remember a book that dealt with various puzzle aspects of Game Theory as told by Sherlock Holmes, et al. One passage discussed the prisoner’s dilemma, after a clever person tries to use it with real prisoners. When it doesn’t work, he goes to Holmes, who then sighs and calls forth one of the prisoners.

“So you know that it’s always better [to defect].”

“Yes, guv’ner.”

“Then pray explain to [this doofus] why you don’t.”

“Me mates would beat me senseless.”

Glad to see the theoreticians catching up.

Now to just figure out how this relates to unconvincing cylons, and the applications will be endless!

## Rational Agents should *Win*

I don’t know if I’ve linked to Overcoming Bias before or not. It doesn’t deal with gaming, but is interesting and sometimes deals with tangential items of interest (especially to game theory).

Today they are talking about Newcomb’s Paradox (which I first encountered in a math class in middle-school. Thanks, Martin.)

And the following jumped out:

Nonetheless, I would like to present some of my motivations on Newcomb’s Problem – the reasons I felt impelled to seek a new theory – because they illustrate my source-attitudes toward rationality. Even if I can’t present the theory that these motivations motivate…

First, foremost, fundamentally, above all else:

Rational agents should WIN.

Don’t mistake me, and think that I’m talking about the Hollywood Rationality stereotype that rationalists should be selfish or shortsighted. If your utility function has a term in it for others, then win their happiness. If your utility function has a term in it for a million years hence, then win the eon.

But at any rate,

WIN. Don’t lose reasonably,.WIN

{I’m adding them to the blogroll and cleaning up some old URLs).

## Basic polynomino theory?

Little Princess Tao wanted to play Ubongo. So we played. (She finished most puzzles in time, and often beat me).

This got me to thinking about polyominoes. I can look at a basic grid arrangement and a set of -ominoes and tell if it’s impossible by counting squares, and some arrangements because of parity issues. But I suspect that with some thought I could knock out more possibilities. Are there other tricks? Is there a good reference for the theory behind this that doesn’t involve massive math?

The fact that Wikipedia had nothing leads me to believe I’m spelling this wrong, or missing a technical term.

## Interesting Textbook on Markets, Game Theory & Auctions

Via Newmark’s Door, I skimmed an interesting book available online:

Markets, Games, and Strategic Behavior:

Recipes for Interactive Learning, an economics text on game theory and the like. I just skimmed it, but there were some interesting experiments on market bubbles. As usual, the games are theory, not fun. *But* I now think that someone could make a great game about stag hunting.

## The Power of Nash Compels You!

The Fury of Dracula showed up this week. I’ve never played the original, so the release didn’t excite me, but I did glance at the rules. The basic mechanism reminds me of Scotland Yard, and then I read the combat section.

Oooh, it’s a decision matrix. Chock full of game theory. But it gets better. The matrix is actually done with cards, and each player has a base number of cards. The hunters have 3, and Dracula has 3 during the day, but 8 at night. But the hunters (and possibly Drac, I’m not sure) may have some cards beyond what the started with, which means that your opponent may or may not be able to make some choices.

I think this is an innovation; it’s certainly new to me. You also have a one-turn delay. Once you pick a tactic, you can’t use it during the next round. Combat keeps going until one side escapes, dies or a certain number of stalemates occur in a row.

Unfortunately, Fury of Dracula adds dice as well. Each entry in the matrix has two outcomes depending on who wins the die roll, but ties are not re-rolled (the cards have an initiative number to break ties). There’s also multiple combat if several hunters corner Drac … they each play a card and Dracula picks his opponent. If Dracula wins, you resolve his card against his opponent. If the hunters win, they pick which card to use.

So you have a reasonable “find the villian” game, and then a decision matrix with hidden information.

Interesting, in theory. No idea if it works in practice … but I hope to find out.

*And yes, I realize the title plays on the Exorcist. I couldn’t think of a good vampy quote.*