How to Survive on a Desert Island

March 7, 2012 Leave a comment

Fish exhibiting swarming behavior. Or, what I imagine Bayes_Bots to look like.

For the last few months, a team and I have been aggressively competing* in the 2nd Social Learning Strategies Tournament. Here’s what it’s all about:

Suppose you find yourself in an unfamiliar environment where you don’t know how to get food, avoid predators, or travel from A to B. Would you invest time working out what to do on your own, or observe other individuals and copy them? If you copy, who would you copy? The first individual you see? The most succesful individual? The most common behaviour? Do you always copy, or do so selectively? If you could refine behaviours, would you invest time in that or let others do it for you? What if you then migrated – would you rely on your existing knowledge, or copy the locals?

The team consisted of a rocket scientist, a mathematician, a genetic engineer, and me.  Fortunately, the other three had enough brainpower to help us put together something interesting to submit.

The deadline for submission was Feb 28, 2012. Our team ended up using Baysian economics to put together a competitor.  If you’re interested, the abstract overview is below.

Bayes_Bots makes decisions based on the expected payoff of the moves in her arsenal: Observe, Innovate, Exploit, and, in the appropriate extension, Refine.  To decide which move to use, Bayes_Bots will look at the distribution of the learned payoffs from Innovate, and Observe.  Bayes_Bots uses Bayesian inference, to learn these distributions: she assumes that the values learned from Innovate and Observe can be modeled by an exponential distribution, and given a distribution on the payoffs associated with each arm, the means of the Observed distributions will follow a Beta distribution, while the payoffs from Observe follow an exponential distribution.  Bayes_Bots will discount older information as less reliable, using Pc as the probability that a given strategy’s payoff changes.

Bayes_Bots will Innovate rarely.  However, she will always Innovate on her first turn; this will help provide new raw information to the collective population of agents.

Observe_who. In the observe_who strategy, Bayes_Bots will not change her strategy.  The assumption is that information is equally valuable from all other agents in the field, regardless of their age, number of times they’ve been observed, etc.

Refine. Bayes_Bots will Refine one of her high-payoff moves at least once, in order to understand what benefit that might have to her overall expected payoffs.  Otherwise, Bayes_Bots will not change her strategy; if other agents refine their strategies, Bayes_Bots will learn the refined payoff.

Localization/Demes. When Bayes_Bots changes to a new deme, she will discard information about the distribution of payoffs from observed strategies.  She will retain information regarding the distribution of payoffs from innovated strategies, as well as the distribution of the means of the observed strategies, as these pieces of information are assumed to be useful across all demes.

If you want to read the full entry, let me know – I’m happy to share out the doc.  It also has our very complex math and equally complex Python code.

*by “aggressively competing” I mean “meet at a coffee shop once a week to pretend we know what we’re talking about and eat chocolate.”

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Game Theory of the Burning Man Lottery

February 1, 2012 11 Comments

Burning Man is difficult to describe. Having never been to this event, I gather it’s a temporary city in the desert, full of art and often lacking in clothing.  Despite the somewhat disconcerting description, Burning Man is very popular.  To deal with this demand, Burning Man came up with a fairly convoluted lottery system.

The lottery system chosen by Burning Man is, like everything else related to this community, unconventional.  Let’s talk through some options Burning Man Organization could have used to deal with the increased demand for these tickets.

Players

    Burning Man Organization (BMORG) – the organizers of the event. If this were a traditional event, their goal would be to make money. However, BMORG also values fairness and equality, as well as access to the event. They just need enough money to host the event.
    Burners – the attendees of the event. Their motivation is fairly simple: they want to attend the event.

Constraints

    Really just one: number of Burners who can attend.  From what I can gather, this is approximately 53,000.

Possible Solutions -or- How can tickets be fairly distributed?

First Come, First Serve.  The easiest way to distribute tickets: BMORG sells tickets until there are none remaining.  This is the strategy they used until this year. It was discarded because tickets were selling out too quickly. Remember when I mentioned BMORG values fairness, equality, and access to the event? A first-come-first-serve model didn’t support that.

Highest Bidder. Tickets are auctioned off to whomever wants to pay top dollar for them.  This would capture the maximum amount of profit, while allowing Burners to indicate their willingness to pay for tickets. However, the Burning Man community tends to shy away from extreme-capitalist strategies.  This distribution option wouldn’t allow everyone equal access to the event.

Pure Lottery. A completely random, completely fair option. While this doesn’t allow for any sort of price discrimination on the part of the Burners, I’m honestly not sure why this method wasn’t chosen.

Hybrid Model -or - the solution they chose. The “Lottery” BMORG ended up with is a hybrid model of the three above options. You can read about it in detail here. A quick summary:

  • Round 1: Pure lottery, $420 per ticket. 3,000 tickets sold. Limit 4 tickets per entry.
  • Round 2: Pure lottery. Tickets sold in three tiers: $$390, $320, and $240. If you entered the lottery at a higher level, you were also entered into the lottery for the lower pricing levels. This captures willingness to pay of Burners. 40,000 tickets sold. Limit 2 tickets per entry.
  • Round 3: First-come-first-serve model, $390 per ticket. 10,000 tickets to be sold. Limit 4 tickets per entry.

Several Burners, knowing they weren’t guaranteed tickets this year, entered the Round 2 lottery several times, hoping one of their entries would garner them tickets. As a result, the pool of applicants was artificially inflated, generating a surge of false demand. The results of the Round 2 lottery were revealed yesterday. Right now, there are a lot of unhappy Burners who didn’t get tickets.

My Proposal -or- Not A Perfect Solution

Situations in which demand outstrips supply are tricky. For something like Burning Man, where people feel such an intense connection with the event, distributing tickets can become a very complex matter.

That being said, here’s a solution I like.  Again, it isn’t perfect, but it touches on a lot of the constraints and player values.

Of the 53,000 tickets, randomly distribute 47,700 of them, for free, via a random lottery. Fair, equitable, and allows equal access to all demographics. (I got to 47,700 because it’s 90% of the available tickets).

Auction the remaining 5,300 tickets to the highest bidder. The implication here is that the average price someone would be willing to pay for an auctioned ticket would be enough to offset the tickets given away for free. In this case, that price would be around $4,000 per ticket.  While that seems outrageous, I gather that there are some who would be willing to pay that much, especially if their ticket allowed nine other Burners to attend Burning Man for free.

Recap

The problem both Burners and BMORG face is too much demand for a product with limited supply. The motivations of each group are similar: attend a great event. However, the path to that outcome, for each group, are just different enough that seemingly simple problems like this become very complex, very quickly.

If you were solving the Burning Man Lottery problem, what solution would you propose?

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Separating Facebook users: 4.74 Degrees

January 11, 2012 5 Comments

Remember my less-than-epic, although very entertaining, quest to confirm or deny the famous Six Degrees of Separation experiment, originally conducted by Stanley Milgrim?  My goal was to send out letters, as in the original experiment, and have those recipients do their best to get those letters to a named someone in Boston.  Each link in the chain would write down their name on the letter, and, by the end, we’d have a list of how many people the letter went through to get to that final person.

You might remember that not one letter made it to my contact in Boston.

Many other groups have turned to Facebook to answer the question. Several failed, fake, or ineffective “Six Degrees” Facebook groups have popped up.

However, just a few months ago, the University of Milan partnered with Facebook to report that the average number of acquaintances separating any two people in the world was not six, but 4.74.

The new research used data from 721 million Facebook users, more than one-tenth of the world’s population. Facebook posted the results on their data facebook page.

From the New York Times article:

The experiment took one month. The researchers used a set of algorithms developed at the University of Milan to calculate the average distance between any two people by computing a vast number of sample paths among Facebook users. They found that the average number of links from one arbitrarily selected person to another was 4.74. In the United States, where more than half of people over 13 are on Facebook, it was just 4.37.

That being said, Facebook users are probably a self-selected bunch.  In this case, the people who use Facebook are those who have online access and choose to use Facebook.  They might be better connected individuals than those who do not use Facebook.

Importantly, this study raises questions about definitions like “friend,” “acquaintance,” or “guy you met one time on the bus.”  Which of those actually counts as a connection?

Either way, it’s pretty exciting to know that we’re only a few introductions away from people like Hugh Laurie and David Cameron.*

*If anyone here is Facebook friends with them, let me know.

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Game Theory of Black Friday

November 25, 2011 1 Comment

If you’re reading this real-time, you’re probably not out shopping.

Black Friday, the day after Thanksgiving, is a day of shopping madness, and is sometimes considered the beginning of the Christmas shopping season. Most major retailers open extremely early andd offer promotional sales to kick off the shopping season.

A few days ago on NYT, Robert H. Frank described Black Friday as a retail race to the bottom in terms of a zero-sum or negative-sum game:

In recent years, large retail chains have been competing to be the first to open their doors on Black Friday. The race is driven by the theory that stores with the earliest start time capture the most buyers and make the most sales. For many years, stores opened at a reasonable hour. Then, some started opening at 5 a.m., prompting complaints from employees about having to go to sleep early on Thanksgiving and miss out on time with their families. But retailers ignored those complaints, because their earlier start time proved so successful in luring customers away from rival outlets.

Tyler Cowen, of MarginalRevolution, has a different opinion.  Based on the fact that early December has in general the cheapest prices of the year, not Black Friday, he says:

Dare I suggest that some people like waiting in those lines with their thermos cups and stale bagels.  You could try to argue they are “forced to do so,” to get the bargains, but in a reasonably competitive world  each outlet will (roughly) try to maximize the consumer surplus from visiting the store, including the experience of waiting in line.

All I know is that a few of my colleagues were more excited to go home for Black Friday than for Thanksgiving on Thursday.

Wondering why Rebecca Black’s face is the photo for this post?  Check out the commercial below.  Read about it here.

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Economics of this Halloween party

October 28, 2011 Leave a comment

On Saturday, I’ll be attending the Ghost Ship Halloween party, mainly because several of my good friends are going.  I was wrangled into the party a few weeks ago when one of them sent out an email directing us to the ticketing website.

This post is about the cleverness of the Ghost Ship’s ticketing strategy.

The pricing structure looked something like this*:

  • Super Early-bird Presale: $25
  • Early-bird Presale: $30
  • Regular Presale: $35
  • Presale: $40
  • Last Chance Presale: $45

*I couldn’t remember what the names of each tier were, so I made them up. You get the idea.

These weren’t actually time-sensitive tickets; sales for each tier all ended a few days before the party. At the time the tickets were posted, you could purchase any one of these options.  I could theoretically purchase the Super Early-bird Presale or the Last Chance Presale.  Obviously, given the option, I’d prefer to purchase the less expensive ticket.

So, why wouldn’t everyone purchase the Super Early-bird Presale tickets?  Well, there were only a limited number of tickets at each pricing tier.  And those coming to the website closer do the date of the party would see which tiers sold out.  So, when I got to the website, the pricing structure looked more like this:

  • Super Early-bird Presale: $25 Sold Out
  • Early-bird Presale: $30 Sold Out
  • Regular Presale: $35 Sold Out
  • Presale: $40 Sold Out
  • Last Chance Presale: $45

I quickly purchased a ticket because, well, look at the ticket sales – a lot of people were apparently going to this party.

What’s going on here?  Ghost Ship was doing something pretty clever – they were using the ticket sales to publicly indicate how many people were purchasing tickets to the party.  The ticket sales were an indicator of the party’s popularity.

Not only that, but they were playing off of a phenomenon we discussed last week: Loss Aversion.  Tickets for Ghost Ship were selling out quickly, and I didn’t want to lose the opportunity to purchase one and attend the party … so I bought one.

There’s more to this story about ticket sales, such as the black market for tickets on Craigslist that erupted shortly after the final tier sold out, or the limited number of more expensive tickets available at the door (encouraging people to show up early), or the awesome costumes we made.  But this post is long enough as it is.

Happy Halloween!

Edit: This post got written up on the WePay blog!  Check it out here.

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