When you come to the 2^100 forks in the road...

In some simple games, it is easy to spot Nash equilibria. For example, if I prefer Chinese food and you prefer Italian, but our strongest preference is to dine together, two obvious equilibria are for both of us to go to the Chinese restaurant or both of us to go to the Italian restaurant. Even if we start out knowing only our own preferences and we can’t communicate our strategies before the game, it won’t take too many rounds of missed connections and solitary dinners before we thoroughly understand each other’s preferences and, hopefully, find our way to one or the other equilibrium.
 
But imagine if the dinner plans involved 100 people, each of whom has decided preferences about which others he would like to dine with, and none of whom knows anyone else’s preferences. Nash proved in 1950 that even large, complicated games like this one do always have an equilibrium (at least, if the concept of a strategy is broadened to allow random choices, such as you choosing the Chinese restaurant with 60 percent probability). But Nash — who died in a car crash in 2015 — gave no recipe for how to calculate such an equilibrium.
 
By diving into the nitty-gritty of Nash’s proof, Babichenko and Rubinstein were able to show that in general, there’s no guaranteed method for players to find even an approximate Nash equilibrium unless they tell each other virtually everything about their respective preferences. And as the number of players in a game grows, the amount of time required for all this communication quickly becomes prohibitive.
 
For example, in the 100-player restaurant game, there are 2&100 ways the game could play out, and hence 2^100 preferences each player has to share. By comparison, the number of seconds that have elapsed since the Big Bang is only about 2^59.
 

Interesting summary of a paper published last year that finds that for many games, there is not clear path to even an approximate Nash equilibrium. I don't know whether this is depressing or appropriate to the state of the world right now, it's probably both. Also, it's great to have mathematical confirmation of the impossibility of choosing where to eat when with a large group.

Regret is a fascinating emotion. Jeff Bezos' story of leaving D.E. Shaw to start Amazon based on a regret minimization framework is now an iconic entrepreneurial myth, and in most contexts people frame regret the same way, as something to be minimized. That is, regret as a negative.

In the Bezos example, regret was a valuable constant to help him come to an optimal decision at a critical fork in his life. Is this its primary evolutionary purpose? Is regret only valuable when we feel its suffocating grip on the human heart so we avoid it in the future? As a decision-making feedback mechanism?

I commonly hear that people regret the things they didn't do more than the things they do. Is that true? Even in this day and age where one indiscretion can ruin a person for life?

In storytelling, regret serves two common narrative functions. One is as the corrosive element which reduces a character, over a lifetime of exposure, to an embittered, cynical drag on those around them. The second is as the catalyst for the protagonist to make a critical life change, of which the Bezos decision is an instance of the win-win variety.

I've seen regret in both guises, and while we valorize regret as life-changing, I suspect the volume of regret that chips away at people's souls outweighs the instances where it changes their lives for the better, even as I have no way of quantifying that. Regardless, I have no contrarian take on minimizing regret for those who suffer from it.

In that sense, this finding on the near impossibility of achieving a Nash equilibrium in complex scenarios offers some comfort. What is life or, perhaps more accurately, how we perceive our own lives but as a series of decisions, compounded across time.

We do a great job of coming up with analogies for how complex and varied the decision tree is ahead of us. The number of permutations of how a game of chess or Go might be played is greater than the number of atoms in the universe, we tell people. But we should do a better job of turning that same analogy backwards in time. If you then factor in the impact of other people in all those forks in the road, across a lifetime, what we see is just as dense a decision tree behind us ahead of us. At any point in time, we are at a node on a tree with so many branches behind it that it exceeds our mind's grasp. Not so many of those branches are so thick as to deserve the heavy burden of regret.

One last tidbit from the piece which I wanted to highlight.

But the two fields have very different mindsets, which can hamper interdisciplinary communication: Economists tend to look for simple models that capture the essence of a complex interaction, while theoretical computer scientists are often more interested in understanding what happens as the models grow increasingly complex. “I wish my colleagues in economics were more aware, more interested in what computer science is doing,” McLennan said.

Lessons from Reid Hoffman

Ben Casnocha wrote up 16 lessons he learned from Reid Hoffman after having spent years with Hoffman as his chief of staff.

Here's a portion of one:

Speed

His first principle is speed. His most tweeted quote ever is, “If you aren’t embarrassed by the first version of your product, you shipped too late.” His second most tweeted quote ever is, “In founding a startup, you throw yourself off a cliff and build an airplane on the way down.”

Practically, he employs several decision making hacks to prioritize speed as a factor for which option is best—and to speed up the process of making the decision itself. When faced with a set of options, he frequently will make a provisional decision instinctually based on the current information. Then he will note what additional information he would need to disprove his provisional decision and go get that. What many do instead – at their own peril – is encounter a situation in which they have limited information, punt on the decision until they gather more information, and endure an information-gathering process that takes longer than expected. Meanwhile, the world changes.

If you move quickly, there’ll be mistakes borne of haste. If you’re a manager and care seriously about speed, you’ll need to tell your people you’re wiling to accept the tradeoffs. Reid did this with me. We agreed I was going to make judgment calls on a range of issues on his behalf without checking with him. He told me, “In order to move fast, I expect you’ll make some foot faults. I’m okay with an error rate of 10-20% — times when I would have made a different decision in a given situation – if it means you can move fast.” I felt empowered to make decisions with this ratio in mind—and it was incredibly liberating.

Speed certainly matters to an extreme degree in a startup context. Big companies are different. Reid once reflected to me that the key for big companies like LinkedIn is not to pursue strategies where being fastest is critical—big companies that adopt strategies that depend on pure speed battles will always lose. Instead, they need to devise strategies where their slowness can become a strength.

Here's another:

When there’s a complex list of pros and cons driving a potentially expensive action, Reid seeks a single decisive reason to go for it—not a blended reason. For example, we were once discussing whether it’d make sense for him to travel to China. There was the LinkedIn expansion activity in China; some fun intellectual events happening; the launch of The Start-Up of You in Chinese. A variety of possible good reasons to go, but none justified a trip in and of itself. He said, “There needs to be one decisive reason. And then the worthiness of the trip needs to be measured against that one reason. If I go, then we can backfill into the schedule all the other secondary activities. But if I go for a blended reason, I’ll almost surely come back and feel like it was a waste a time.” He did not go on the trip. If you come up with a list of many reasons to do something, Nassim Taleb once wrote, you are trying to convince yourself—if there isn’t one clear reason, don’t do it. (An analogous belief Reid has about consumer internet business models: there’s generally one main business model. Listing a blend of possible revenue streams makes investors nervous. LinkedIn is the exception that proves this rule!)

One last gem:

12. Trade up on trust even if it means you trade down on competency.

Should you start a company with friends? All things being equal, Reid says yes, because you can move more quickly with trusted friends because you already understand how each other thinks and talks. And moving quickly? That’s critical in the early days of a startup.

But what if all things aren’t equal? If you’re choosing between working with someone who’s a trusted friend and a 7 out of 10 on competence, versus a stranger who’s a 9 out of 10 on competence, who should you pick? Answer: if the trusted friend is a fast learner, pick the trusted friend.

Trade up on trust, even if it means you have to trade down on competency a bit. In other words, choose to work with someone you know who’s a fast learner over someone who’s a bit more qualified who you do not know. Assuming the person you know and trust is in Permanent Beta, he or she can round out their gaps in skills or experience in short order.

As with sports, organizations need to be aligned in both principle and process for any particular strategy to work. Some baseball teams are more analytically driven than others, but that matters little if you can't translate analytical recommendations into on-field execution. The Tampa Bay Devil Rays seemed to be a paragon of such top to bottom alignment in recent years, one reason I'm excited Joe Maddon has moved over to manage the Cubs.

If your organization is in a position where speed matters above all else but management beats the team up over errors you'd expect them to make moving at such a pace, something will give. Nitpick people to death and don't be shocked when they suddenly move much more slowly than you'd want.