Ask MetaFilter questions tagged with gametheory

You ate ALL MY PIZZA!

contessa — Fri, 04 Sep 2009 11:58:49 -0800

Is there a mathematical, economic, logical or game-theory name/description for the following scenario? Let's say you have two pairs of people: Pair A and Pair B.

Both pairs are ordering pizza. Pair A will not eat meat toppings, whereas Pair B wants meat toppings. Collectively all four decide to order two pizzas: one with no meat toppings (pizza #1) and one with meat toppings (pizza #2).

When the pizzas arrive, Pair A of course will only eat pizza #1. But Pair B are not committed carnivores; in addition to pizza #2 (which only they prefer) they also want to eat slices from pizza #1.

At the end of the meal, Pair A have had to struggle to get a "fair" share of pizza #1, whereas Pair B have helped themselves to both pizzas.

What's this called? (Besides "being jerks"?)

Game theory games, in theory

TheSecretDecoderRing — Fri, 14 Aug 2009 03:00:42 -0800

I'm currently reading a book on game theory ("Rock Paper Scissors" by Len Fisher), and am considering putting together a series of a few quick games/demonstrations for when it's my turn to do a weekly motivational/informative session at work. Any ideas? Prisoner's Dilemma, Free Rider, Chicken, etc. There's about a 15-minute time limit, and I'd like the games to be easily presented and executed, and have an obvious application to their everyday lives in and out of work.

We have about 20 people, and ideally I'd separate them into small groups for one or two games, and individual for others.

One possibility is the one where separated groups have to independently plan when and where to meet in a city. Another is something along the lines of the doughnuts in the office, which I think was used in Freakonomics.

And we usually dole out small prizes at the end, so if there are any other ways to determine who wins them (whether it's cumulative of all the games, or a separate contest at the end just for the prizes), that'd be helpful too.

And if you've participated in a memorable game theory game that may be too complex or elaborate for this purpose, I'd still like to hear it. Thanks.

Prisoner's Dilemma citation

arcticwoman — Wed, 01 Jul 2009 12:33:32 -0800

How do I cite the originators of the Prisoner's Dilemma (in my thesis) when it looks like none of them actually published anything on it? The Stanford Encyclopedia of Philosophy says this:

Puzzles with the structure of the prisoner's dilemma were devised and discussed by Merrill Flood and Melvin Dresher in 1950, as part of the Rand Corporation's investigations into game theory (which Rand pursued because of possible applications to global nuclear strategy). The title “prisoner's dilemma” and the version with prison sentences as payoffs are due to Albert Tucker, who wanted to make Flood and Dresher's ideas more accessible to an audience of Stanford psychologists. Although Flood and Dresher didn't themselves rush to publicize their ideas in external journal articles, the puzzle attracted widespread attention in a variety of disciplines. Christian Donninger reports that “more than a thousand articles” about it were published in the sixties and seventies.

I can't find any direct citations, any original articles where this game was formulated/formalized. When I look at research that has used the PD, most don't bother to cite anyone for the formulation of the game. Am I just missing something? Do I just cite (for example) the 1993 Poundstone book where the origination is described?

Game theory for people who like words and pictures?

vizsla — Mon, 26 Jan 2009 13:27:33 -0800

Best books, websites, lecture series on game theory and its applications for smart people who understand mathematics but can't stand trawling through pages of unnecessary complex formulae?

No one twisting his arm....

scarylarry — Wed, 17 Sep 2008 23:09:33 -0800

What bands sound like Game Theory? One of the only good things to come out of a past relationship was exposure to Game Theory, close to my current favorite band. I have acquired all their albums by methods both legal and illegal, and I just love their sound and their unflagging intelligence.

What other bands should I listen to? These can predate GT or be more contemporary. I'm searching for songwriting that is as simultaneously intelligent and, for lack of a better word, *quirky* as Scott Miller's.

Were I answering this question, I guess I'd suggest Big Star, The Soft Boys, early REM, and the Unicorns/Islands. I hope this gives some idea where I'm coming from.

One thing I love about Game Theory, too, is that they've *nearly* fallen by the wayside. I'd love to resurrect a band from the 70s, 80s, or 90s that I would have no way to discover without asking this question; the more obscure the better, I suppose.

I should probably also say that I already know and love the Loud Family. Otherwise, I'm all ears!

I look forward to the aural candy to come.

Help me use game theory to better understand my workplace

brandnew — Wed, 30 Jan 2008 04:12:46 -0800

Help me use game theory to better understand the seemingly irrational behavior at my workplace I have a fascination with trying to understand the behaviors of my co-workers in the context of game theory. I love the workplace - it's a wonderful zoo of seemingly odd, irrational, and puzzling human behavior. I have my own anecdotal theories about why things play out as they do, but I'm looking for more solid scientific evidence and theories. Basically I want to understand the rationality behind my co-workers' seemingly irrational behavior.

For example, one curiosity I have had lately is for those co-workers who voluntarily dilute their salaries by working long hours. Interestingly, they often seem to be the same people who nit pick about their starting salaries down to the hundredth dollar. I remember reading long ago about a game theory called something like "jackpot theory". Supposedly a reason workers work long hours is in anticipation of obtaining their bosses' salaries. However, often, like the casino games, the odds are largely against them.

What are some sites or books I can use to better understand workplace game theory? Who are the major research bodies for this area of research? What are some of the more interesting game theories that have emerged recently? How does one use this information to "game" the system?

BTW I have a science and math background, so I'm not afraid to read research papers, if necessary.

mathematics chess book?

randomizer — Thu, 18 Oct 2007 16:21:49 -0800

is there a book on the mathematics of chess? i've been looking for a book that deals with the mathematics or/and game theory of chess, but i'm not having much luck. is there a chess book that deals with the mathematics/game theory?

What is this addictive game structure called?

argybarg — Sun, 29 Jul 2007 10:23:41 -0800

There's a certain fiendishly addictive structure in video (and other) games, and I'd like to know if anyone has named it or researched it. I'm not much of a gamer, but I have stayed up some very late nights playing Civilization and (wayy back) X-Com: UFO. There's a very basic structure to those (and many other) games, one I'd like to research and especially try to apply to the classroom. But I don't have a simple term for that structure, and I wonder if anyone knows one.

I'll try to describe the form: By taking on challenges, you gain new skills, technologies and opportunities to build; which in turn expand your ability to take on novel challenges; which get you new skills, technologies and opportunities to build; which let you take on novel challenges which ... and so on ad infinitum.

(The Tech Tree for Civilization IV might give a notion of the branching-upward structure. Each new technology makes you better able to move towards the next, which makes you better able to move towards the next...)

It's probably a basic cycle in many games (Dungeons and Dragons, perhaps Settlers of Catan). Most of these games are turn-based -- but just calling them turn-based doesn't capture that loop of attainment-leading to challenge-leading to attainment (getting that next thing that will help you fight to get that next-next thing) that makes these games so addictive.

I'd love to put that mechanism to use in the classroom, but I don't know if A) anyone has invented a generally accepted term for it; and B) if it has been researched or modeled in idealized form. Any help is most welcome. (Brainstorming what it ought to be called -- feh. I can do that.)

Is there an optimal selection strategy for a white elephant gift exchange?

23skidoo — Sun, 17 Dec 2006 12:29:39 -0800

Mathematically speaking, is there an optimal strategy towards gift selection while opening gifts during a white elephant gift exchange? Could I have done better than a creme brulee set?

Here's what happened at the office white elephant.

Instructions were that the gifts were to be "new or gently used", which at least had me thinking that some people would buy new gifts. I knew that I bought a new gift. I watched two people wrap theirs, so I knew that at least two people were bringing complete crap.

The "can only be stolen twice" rule was in effect. When it was my turn to pick (13 out of 23), there was nothing I wanted that had only been stolen once (that is, if I stole it, it was still possible that someone might steal it from me, and end up taking it home). The only thing available that I wanted was a bottle of whiskey. I didn't take it because I thought it was valuable, and that if I stole it, it would immediately be stolen from me. I took a creme brulee set instead, hypothesizing that by taking what I percieved to be a desirable gift, someone else would soon pounce on it, knowing that they could steal it and they would go home with it. I was just buying time, hoping that by the time my creme brulee set got stolen, that I would be the third person to have the whiskey.

Well, I walked home with the creme brulee set. Was there a better move I could have made in that situation? Has anyone ever done a mathematical paper outlining what the optimal strategy is for minimizing white elephant gift unhappiness?

Deal or No Deal?

Imperfect — Tue, 18 Jul 2006 16:16:57 -0800

My workplace is doing a little motivational contest based on the TV show Deal or No Deal (stupidest name ever, IMHO). I believe I've developed a strategy for the game that's not really covered anywhere else. Am I off my rocker, or is this valid? More importantly, how else can I improve on the basic strategy? I'm not desperate to win, as I don't expect the prizes to be so top-notch that I'd absolutely kick myself for accidentally choosing the $1 case over the $1,000,000 case, so my risk-tolerance is exceptionally high. Assume infinite for probability purposes.

I do want to game the system though, as I'm kind of a twink by nature. Here's what I've come up with so far:

The basic strategy is to take the mean of all the cases remaining, and refuse the deal if the deal is less than the mean, as you stand to win on average better than what's being offered. Most of the time, if not all of the time, the banker will offer you less than the mean, so it's nearly always correct to refuse the deal.

Once you have that mean, you can also sum the number of cases remaining with prizes both below and above your mean. At this point, you have the chance that choosing another case (refusing the deal) will lower your mean and lower the next deal.

However, it seems that the banker also raises the % of the mean that they offer up to a certain point as well, to offset this kind of playing. If this is a valid strategy, how else can I improve it? If it isn't, where did I go wrong?

Reverse price auctions

Leon — Mon, 16 Jan 2006 08:28:27 -0800

Lowest-unique-bid auctions. What's the rational approach? Lowest-unique-bid auctions probably aren't auctions at all, but that's the common name for them. They work like this:

The seller places a high-value item up for "auction".

Each buyer makes one or more sealed bids.

Each bid costs the buyer some money (typically the cost of a premium-rate SMS or phone call).

The person who makes the lowest unqiue bid wins the item for that price.

So... as a buyer, what's the best approach? Bid low? Big high? Multiple bids?

Is there a "best" here at all, or is this a just a lottery by any other name?

How to give away a limited number of items as fairly as possible?

AmbroseChapel — Thu, 27 Oct 2005 19:20:16 -0800

How to give away a limited number of items as fairly as possible? I work for an organisation which sometimes gives away free books, CDs and stuff to people on a mailing list who write in and ask for them. (Long story, and no, you can't join, sorry!)

Say we have 20 books to give away. We send out that list and thirty people write in and say "I would like Book A please" etc.

I've asked them to state a preference, to make it easier. So what they do is actually say "I would like, in order of preference, Book A, Book B or Book C".

So now I've got twenty books, and thirty people asking for them.

If the matrix looked like this, there'd be no problem:



Item    1st        2nd        3rd

--------------------------------------

Book A  Person 1   Person 3   Person 4

--------------------------------------

Book B  Person 4   Person 1   Person 3

--------------------------------------

Book C  Person 2   Person 5   Person 2 

--------------------------------------

Book D  Person 3   Person 4   Person 5

--------------------------------------

Book E  Person 5   Person 2   Person 1

(Hope that comes out OK in your browser. Looks OK on preview. Monospaced font will line everything up.)

Because in that perfect world, there are five books and five people and everyone's got a first choice which is nobody else's first choice.

What happens of course is more like this:



Item    1st        2nd        3rd

--------------------------------------

Book A  Person 1   Person 3   Person 4

                   Person 2   Person 2

                              Person 7

--------------------------------------

Book B  Person 4   Person 1   Person 3

        Person 2

        Person 5

        Person 3

        Person 6

        Person 7

        Person 8

--------------------------------------

Book C             Person 5

                   Person 6

--------------------------------------

Book D             Person 4   Person 5

                   Person 8   Person 6

--------------------------------------

Book E             Person 1   Person 8

                   Person 7   

--------------------------------------

with lots of people nominating popular items, lots of "holes", and more people than items.

What would be your strategy for maximum happiness here? In other words, what's the best way to make sure the greatest number of people get their highest-number choice?