What: Game Theory Ninjas in Training.
When: Tuesdays at 5pm PST, starting March 27th.
Where: Google Hangouts!

If you want to join us, add me on Google+ and comment on this post. I’ll add you to the study session circle. The invite for the hangout is going to be private to those in the circle; that will help us keep the conversation relevant to the class. That said, obviously feel free to invite anyone who’s taking the class to join us.

For those in the Bay Area/near Mountain View: If you want to join me live, let me know! I’ll be in a conference room on Google campus, and am happy to share the IRL collaboration love.

Post to indicate interest is here: https://plus.google.com/u/0/106776967321860936337/posts/d8rNckNCKyB

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.

As some of you know, I ran 100 miles this weekend.  Here’s the race report.  Also, I know it’s not related to game theory at all.

The race I ran was Rocky Raccoon, a five-lap race in Huntsville, Texas. You can see the results here. I finished in 24:58:28.  Only 43% of the 415 runners finished. (Does anyone have updated stats on this?)

Lap 1: It was a dark and stormy night …

About an hour before the race started, Dad and I were sitting in the rental car.  Rain was coming down in sheets. Per the normal clichés about storms, lightening zig-zagged through the sky and thunder echoed through the forest.  We don’t get storms like this in Northern California, and I hadn’t prepared for it.

I hacked some holes into a black plastic trash bag, and used duct tape to get the extra plastic away from my legs.  In my mind, the end result looked like a superhero combination of a Catwoman costume and a steampunk bustle. In reality, it probably looked like a house getting tented for termites.

The race started at 6am. Much of the first lap was in the dark.  It took less than a mile for me to trip over a tree root, a hazard the course is notorious for.  I was already bleeding, and we hadn’t even been running for ten minutes. Somehow, this early wipe-out didn’t dampen my spirits any more than the storm did.

Every two or three miles featured an enormous, impossible-to-avoid mud puddle. I was regularly up to my ankles in mud and water. My shoes were at least damp, if not drenched, for the entire race. This would prove to cause problems later.

I don’t remember much of the first lap. There was so much running left to do, and I didn’t want to think too much about what was to come.  I do remember, around mile 8, having a bit of a panic attack.  I still had 92 miles to run.  92 miles seems a lot longer than 100 miles.

Lap 2: The Man with the Sea Dragon Compression Socks

Every so often, in a race, runners will fall into step and pace off of each other. The two runners acknowledge each other and run in silent camaraderie. No words required.

For lap 2, and some of lap 3, I found such companionship with a man whose name I still don’t know. All I know about him was that he had running spandex and compression socks that looked like sea dragon scales, so that’s how I mentally referred to him.

Somewhere during lap 2, I also met a man named Bruce. He was wearing a blue shirt with cat paw-prints on it, so, being a cat person, I had to ask about it. I learned that Bruce was from Toronto, and told him I’d be visiting in July for World Futures 2012. Bruce had heard of WFS; he’s a CIO for a large school district near Toronto with 7k faculty and 54k students, so he’d been thinking about attending.

Best part: Bruce is in the middle of deploying Google Apps for Edu for his school district. [For those who don't know, Google Apps is the part of Google I work for].  Bruce and I talked about everything from Gmail to Chromebooks to centrally-managed Android tablets. I’m somewhat embarrassed to say I drilled him for about an hour on his opinions on our products.  He seemed happy to oblige my curiosity.

Lap 3: Lothlorien in Light and Shadow

About midway through this lap, I saw the sun for the first and last time during the race. It was a wan orb, low on the horizon, mostly obscured by emaciated tree trunks. Spindly shadows reached across the dirt path.

Seeing the sun made me unreasonably happy.

Around mile 52, I realized that it was going to get dark before I got to the turnaround and could pick up a headlamp.  I ran the last 8 miles of this lap very quickly to avoid getting caught in the dark.

Lap 4: Trust

This was the lap I had been looking forward to for the last 60 miles. My thought had been that if I could just get to this lap, I’d make it the rest of the way.  This is the lap when my pacer, Georgia, joined me.

The first two-thirds of this lap were great.  It was fantastic to have someone to talk to, and Georgia was an excellent pacer. Real friendship is carrying extra caffeine Gus and a jacket for your runner.

One of the fun parts of this lap was being able to share my newly-acquired, yet very intimate, knowledge of the course. Having been around the course three times times already, I could tell her where all the turnoffs were, where the tricky roots were, and the easiest way around mud puddles.  The aid stations were at 3.1 miles, 6.2 miles, 12.2 miles, and 15.6 miles. The hardest bit was the loop between 6.2 and 12.2, because that’s a full six miles without aid.  The far timing mat was a little less than 10 miles into the loop.

There’s one stretch of the course – less than a 10th of a mile – that’s right along the lake. It’s the only part of the course with an unobstructed view of the sky. On lap four, we had front-row seats to the stars.

That short stretch is also difficult, because just a few hundred yards away, across the lake, is the finish line.  You can hear the shouts and cheers of spectators urging their runners across the timing mat. It throws into sharp relief the fact that you’re just about halfway through the lap.

If I learned anything this time around it’s that, in long distance races, mood swings happen unpredictably and with no discernible cause. Miles 72 to 78 were very tough, and I’m not sure why. I had to sit down for a minute on a mound of dirt, where I spent two minutes contemplating the meaning of life with Georgia before finishing the lap.

At the impromptu rest point, I was about three-quarters done with the race. Sounds impressive, but not when that means I still had another full marathon until the finish.

Lap 5: Silence

Georgia and I finished lap 4 around midnight. I had been running for about 18 hours at that point. A sub-24 hour finish was still possible, but I knew in my heart it wasn’t very likely. I haven’t done a lot of research into this, but my intuition tells me that negative splits don’t often happen on 100-mile races.

After inhaling a chocolate donut and my first-ever mocha [which was delicious - thanks Dad!], I grabbed my iPod and took off for the last lap.

It was dark. Profoundly dark. And very, very quiet.

At this point, runners were either by themselves or running with a pacer. Everyone was spread out along the course.  Runners were exhausted, focused, and not interested in talking to othe rpeople.

All I could think about was the next step I was about to take.

When I talk about running, I often get asked about my music. Usually, I don’t listen to music. It’s distracting. When you’re this tired, any additional outside inputs or stimuli – even music – seem complicated, confusing, and overwhelming.

On this lap, I think I listened to about 45 minutes of music before I had to turn off the iPod.

The most frustrating part of this lap was that my muscles and joints felt fine, but I was unable to run. The constantly wet shoes finally taken their toll. Mud puddles had nurtured blisters on every single toe and the entire front pad of both of my feet. Each step was excruciating.

This lap reminded me of the Ave Maria sequence from Fantasia. Individual runners – little pools of light – painstakingly making a pilgrimage to the finish line. Not quickly, but inexorably, as if pulled by some external force.  And the sky is slowly turning grey.

The finish line.

There was no big celebration at the finish line. I walked across the timing pad, we took a picture, and that was that.

Epilogue: You Have My Sword, and my Bow, and My Axe

I finished the run in 24 hours and 58 minutes. I think that’s the longest I’ve been awake. I consumed more caffeine during that period than in the previous six months combined. There were highs, lows, and a lot of learning.

The hardest part of this race was not the roots, although that’s what the course is known for.  The hardest part was running in the dark. One of the reasons I like running is that it provides the opportunity to be fully immersed in nature. No technology, no distractions.  In the darkness, all you get is a tiny pool of light: just enough to see the path in front of you. There’s an entire forest, and all you get to see is some dirt and roots.  And a few headlamps twinkling in the distance. It’s hard to describe how frantic I felt at times, not being able to see anything around me.  Physically, 100 miles didn’t feel substantially different than 50. Mentally, the challenge was the darkness.

When I crewed for Mike at Badwater, he mentioned that picking a good crew is one of the most important components of a successful race. I didn’t think about it much at the time, and I didn’t understand why that would be the case until the end of the 4th lap of this race.  Going into the 5th lap, I felt like I was suffering from information overload, even though the number of ideas I had to hold in my head was very small. Case in point: I had to choose which jacket to wear on the final lap. Despite being a binary decision, this seemed like an insurmountable task, so I deferred to Georgia to help me decide. Decisions like that, so late in the race, can make or break a finish.

To sum up: I had a great crew. Dad and Georgia were incredibly supportive, upbeat, and helped me make good decisions.  Thanks so much, you guys. I could not have done it without you.

After finishing, I promptly pronounced I would never run another 100-mile race again.  Just over 24 hours later, I’m taking less of a hard line towards that assertion. While I have no immediate plans to run another 100, I could see doing it again, sometime in the distant future. Just to see how it compares to this one.

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?

Check out this report: The Economics of Piracy.  It uses data from 1500 Somalian pirates to look at the future of international piracy.  An excerpt:

Pirates would appear to be the very essence of rational profit maximizing entrepreneurs described in neo-classical economics. Expected profits determine decisions based on the information available. The supply of pirates, therefore, is closely related to the expected benefits of being a pirate and the associated risk adjusted costs.

Yep. You read that right. Pirates are economics bad-asses.

The paper, which looks primarily at Somalian pirates, explores piracy in several arenas, and concludes that incidents of piracy will substantially expand in the coming years, primarily due to the rising income disparity betwen pirates and non-pirates.

How big a problem is piracy? In 2010, the cost of piracy to the international community was between $4.9 and $8.3 billion.  Off the coast of Somalia, the total income to pirates, from piracy, was between $75 and $238 million in 2010.

Thinking about hitting the high seas as a Somalian pirate? You can expect to earn between $168,630 and $394,200 over a five year career. If you choose the next best legal alternative, you’ll probably make $14,500 – over your entire working life.  At those prices, piracy doesn’t look so bad.

To combat piracy, the paper recommends the formation of a Global Contract Group, as well as new developments to asymmetric law and law enforcement.

Check it out.  Worth a read.