Results for “solve for equilibrium”
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The Liberal Radicalism Mechanism for Producing Public Goods

The mechanism for producing public goods in Buterin, Hitzig, and Weyl’s, Liberal Radicalism is quite amazing and a quantum leap in public-goods mechanism-design not seen since the Vickrey-Clarke-Groves mechanism of the 1970s. In this post, I want to illustrate the mechanism using a very simple example. Let’s imagine that there are two individuals and a public good available in quantity, g. The two individuals value the public good according to U1(g)=70 g – (g^2)/2 and U2(g)=40 g – g^2. Those utility functions mean that the public good has diminishing utility for each individual as shown by the figure at right. The public good can be produced at MC=80.

Now let’s solve for the private and socially optimal public good provision in the ordinary way. For the private optimum each  individual will want to set the MB of contributing to g equal to the marginal cost. Taking the derivative of the utility functions we get MB1=70-g and MB2= 40 – 2g (users of Syverson, Levitt & Goolsbee may recognize this public good problem). Notice that for both individuals, MB<MC, so without coordination, private provision doesn’t even get off the ground.

What’s the socially optimal level of provision? Since g is a public good we sum the two marginal benefit curves and set the sum equal to the MC, namely 110 – 3 g = 80 which solves to g=10. The situation is illustrated in the figure at left.

We were able to compute the optimum level of the public good because we knew each individual’s utility function. In the real world each individual’s utility function is private information. Thus, to reach the social optimum we must solve two problems. The information problem and the free rider problem. The information problem is that no one knows the optimal quantity of the public good. The free rider problem is that no one is willing to pay for the public good. These two problems are related but they are not the same. My Dominant Assurance Contract, for example, works on solving the free rider problem assuming we know the optimal quantity of the public good (e.g. we can usually calculate how big a bridge or dam we need.) The LR mechanism in contrast solves the information problem but it requires that a third party such as the government or a private benefactor “tops up” private contributions in a special way.

The topping up function is the key to the LR mechanism. In this two person, one public good example the topping up function is:

Where c1 is the amount that individual one chooses to contribute to the public good and c2 is the amount that individual two chooses to contribute to the public good. In other words, the public benefactor says “you decide how much to contribute and I will top up to amount g” (it can be shown that (g>c1+c2)).

Now let’s solve for the private optimum using the mechanism. To do so return to the utility functions U1(g)=70 g – (g^2)/2 and U2(g)=40 g – g^2 but substitute for g with the topping up function and then take the derivative of U1 with respect to c1 and set equal to the marginal cost of the public good and similarly for U2. Notice that we are implicitly assuming that the government can use lump sum taxation to fund any difference between g and c1+c2 or that projects are fairly small with respect to total government funding so that it makes sense for individuals to ignore any effect of their choices on the benefactor’s purse–these assumptions seem fairly innocuous–Buterin, Hitzig, and Weyl discuss at greater length.

Notice that we are solving for the optimal contributions to the public good exactly as before–each individual is maximizing their own selfish utility–only now taking into account the top-up function. Taking the derivatives and setting equal to the MC produces two equations with two unknowns which we need to solve simultaneously:

These equations are solved at c1== 45/8 and c2== 5/8. Recall that the privately optimal contributions without the top-up function were 0 and 0 so we have certainly improved over that. But wait, there’s more! How much g is produced when the contribution levels are c1== 45/8 and c2== 5/8? Substituting these values for c1 and c2 into the top-up function we find that g=10, the socially optimal amount!

In equilibrium, individual 1 contributes 45/8 to the public good, individual 2 contributes 5/8 and the remainder,15/4, is contributed by the government. But recall that the government had no idea going in what the optimal amount of the public good was. The government used the contribution levels under the top-up mechanism as a signal to decide how much of the public good to produce and almost magically the top-up function is such that citizens will voluntarily contribute exactly the amount that correctly signals how much society as a whole values the public good. Amazing!

Naturally there are a few issues. The optimal solution is a Nash equilibrium which may not be easy to find as everyone must take into account everyone else’s actions to reach equilibrium (an iterative process may help). The mechanism is also potentially vulnerable to collusion. We need to test this mechanism in the lab and in the field. Nevertheless, this is a notable contribution to the theory of public goods and to applied mechanism design.

Hat tip: Discussion with Tyler, Robin, Andrew, Ank and Garett Jones who also has notes on the mechanism.

Talking to your doctor isn’t about medicine

On average, patients get about 11 seconds to explain the reasons for their visit before they are interrupted by their doctors. Also, only one in three doctors provides their patients with adequate opportunity to describe their situation…

In just over one third of the time (36 per cent), patients were able to put their agendas first. But patients who did get the chance to list their ailments were still interrupted seven out of every ten times, on average within 11 seconds of them starting to speak. In this study, patients who were not interrupted completed their opening statements within about six seconds.

Here is the story, here is the underlying research.  Via the excellent Charles Klingman.

Now solve for the telemedicine equilibrium.

Friendship with telepathy

Imagine that people could read each other’s minds, at least once they knew each other and focused on each other’s presence in a common physical space.  They can’t do this perfectly or with full transparency, but still they have a much better idea what the other person is thinking and feeling than what they receive today from external signals.  They can even “feel” those thoughts from the other at some times, leading to potential embarrassment, both.in positive and negative ways of course.  Still, some noise remains, so you are never sure just how intentional, explicit, or sincere a “sampled thought” might be.

Solve for the equilibrium:

1. Many people would develop thicker skins, as they would learn what others really thought of them.  They also would tolerate more evil thoughts from others, though at the margin most people still would try to look better rather than worse.

2. A large minority of people, for instance potential child molesters, could not go out in public very much.

3. Sometimes we would meet people and, before initiating a friendship, decide to “get everything out of the way.”  Think all the bad (and good?) thoughts up front, and acknowledge this mutually.  Make it clear that this is your standard practice with all your friends.  Then, if the person later on catches you having a particular thought, you can just say, or intuit, back to them: “Of course I am thinking of stealing a dollar from you.  I thought that on the very first day we met, right after wishing you didn’t get that big raise.  You’re simply sampling residual memories from all the intentional sins we committed together when initiating our friendship.  We did that so subsequent negative signals aren’t really new signals at all.”

And it’s not just thoughts: people preemptively might do everything they are afraid others might discover they are thinking.  Get it out of the way.  Restore that pooling equilibrium, as they say.  Make sure everyone has every thought, using action if need be.

4. A boss hiring a new worker may try to prevent the worker from going through this “mind clearing” process early on.  The worker may try to do it.  And trying to engage in “mind clearing” with your boss may not be such a negative signal if everyone has unacceptable thoughts of some kind or another.  We’re just trying to get back to an equilibrium where those thoughts don’t matter so much.  Is that so terrible?

What else?

5. You might keep special friends, with whom you don’t act out or think through all the possible suspicions in advance.  In essence they would be “surprise friends.”  We would call them surprise friends because you would sample their thoughts in real time and with some degree of surprise.  Those sampled thoughts actually would contain significant new information about what the person was thinking about you.  Having a surprise friend might be considered a sign of courage.

6. Alternatively, people might simply prefer dopey friends, namely those with weak telepathic abilities.

7. Other people will form vice groups, somewhat akin to current gangs.

8. Note that if you can interpret the bad thoughts of others in a truly Bayesian manner (“well, that may sound horrible, but most of the other people are thinking something much worse…”), it is harder for other people to engage in the signal-jamming equilibrium of transmitting all bad thoughts in advance.  You would take their signal-jamming as a very negative signal of what their true thoughts are like, and thus the better people would refrain from signal-jamming.  At the margin, thoughts would become relevant again, including bad thoughts.

Is there thus a positive or negative social value to an individual turning more Bayesian in this setting, and thus discouraging the signal-jamming in advance?

What else?

What if sleep was a commodity?

Dane emails me:

This is a speculative solve-for-the-equilibrium-type question that I’d love to get your thoughts on:

Imagine there was a technology that allowed essentially frictionless harvesting, selling, and buying of (non-perishable) human sleep. Essentially, anyone can strap in to a machine, be put to sleep, and their time/sleep would be harvested in a way that their time sleeping could be used by anyone else who would then get all the benefits of that sleep but instantaneously instead of sleeping themselves, maybe through a painless injection or a drink perhaps.

Imagine also that this technology was relatively non-capital-intensive, or at least, cheap enough that all humans were potential suppliers/buyers of sleep. Call them sleep-workers and sleep-consumers.

Additionally, there’s nothing “free” about the technology. Any sleep-worker’s or sleep-consumer’s lifespan would be unaffected in terms of calendar time. Instead, there would be a zero-sum transfer of waking hours between persons. Even an “around-the-clock” sleep-worker could only net 16 hours of saleable sleep per day. The other 8 hours would have to go to meeting their own sleep needs.

How would this market evolve? How would society evolve? What is the market price for an hour of sleep? How would norms around sleep-working and sleep-consuming evolve? How would the economic indicators evolve (GDP, productivity, inequality, etc)? Which jobs could or could not compete with non-consciousness? How would the welfare state then evolve? How much inter-temporal saving of sleep would there be? Should prisoners be allowed to sleep-harvest for their entire sentences? Would we allow them? Would it be ethical to farm never-conscious humans for the sole purpose of harvesting sleep? Etc…

Dental DNA Beatle rent-seeking markets in everything

A DENTIST who bought John Lennon’s tooth is looking for potential love children of the late-Beatle in a bid to stake a claim to his £400million estate.

Dr Michael Zuk, 45, from Alberta, Canada, purchased the legendary songwriter’s decayed molar at auction in 2011 for around £20,000…

Speaking with The Sun Online, the dentist has sensationally revealed that he plans to stake a claim to the music icon’s vast estate using DNA from the body part.

He said: “I am looking for people who believe they are John Lennon’s child and have a claim to his estate and hopefully I can legitimise their claim.

“John was a very popular guy who was having sex with lots of women and I doubt birth control was on his mind.

…“I would ask anyone who is participating to sign a commission agreement which would mean if they were related they would pay my company a percentage of their inheritance.

“Like a finder’s fee.”

Here is the story, via Michael J.

P.s. Solve for the equilibrium.

*The Trade*

This book is about what I call the Trade, the growing international business of political kidnappings, according to the US Treasury the most lucrative source of income, outside of state sponsorship, for illegal groups. But it’s more than about money. It is about my attempt, yes, to find the answer to two questions which have haunted me for nine years: Who kidnapped me, and why?

That is from Jere Van Dyk, The Trade: My Journey into the Labyrinth of Political Kidnapping.

Solve for the equilibrium, as they say.  The puzzle, of course, is why there are not more kidnappings for revenue.

Malthusian dog markets in everything

An effort that animal rescuers began more than a decade ago to buy dogs for $5 or $10 apiece from commercial breeders has become a nationwide shadow market that today sees some rescuers, fueled by Internet fundraising, paying breeders $5,000 or more for a single dog.

The result is a river of rescue donations flowing from avowed dog saviors to the breeders, two groups that have long disparaged each other. The rescuers call many breeders heartless operators of inhumane “puppy mills” and work to ban the sale of their dogs in brick-and-mortar pet stores. The breeders call “retail rescuers” hypocritical dilettantes who hide behind nonprofit status while doing business as unregulated, online pet stores.

But for years, they have come together at dog auctions where no cameras are allowed, with rescuers enriching breeders and some breeders saying more puppies are being bred for sale to the rescuers.

Here is more from Kim Kavin at WaPo, substantive throughout with photos and video.  In essence, somebody has solved for the equilibrium.

For the pointers I thank Tom Vansant and Alexander Lowery.

Sunday assorted links

1. Is the scientific paper obsolete?

2. Solve for the goat equilibrium.

3. They are still not telling us what happened in Havana (or elsewhere).

4. Prosecution before Roe vs. Wade.  And a British case.  And Ross Douthat on Kevin Williamson.  And Henry on said topic and conservative intellectuals more generally.

5. “Subvocalization signals are detected by electrodes and turned into words using AI.”

6. Jonathan Zittrain on a fiduciary approach for Facebook (NYT).

You would have thought armed conflict with Russia would be a bigger story

That is the topic of my latest Bloomberg column, here is one excerpt:

The relative lack of attention being paid to the news that U.S.-backed forces killed 200 to 300 Russian mercenary soldiers this month in Syria seems like a non-barking dog to me.

In many years, this might have been the most disruptive story, holding the headlines for weeks or maybe months. Circa February 2018, it didn’t command a single major news cycle.

What outsiders know about the event is still fragmentary, but it sounds pretty ominous. One Bloomberg account notes: “More than 200 contract soldiers, mostly Russians fighting on behalf of Syrian leader Bashar al-Assad, died in a failed attack on a base held by U.S. and mainly Kurdish forces in the oil-rich Deir Ezzor region.” It is described as the biggest clash between U.S. and Russian forces since the Cold War. It seems that the Russian mercenaries are pretty closely tied to the Russian government.

And:

One Russian commentator called this event “a big scandal and a reason for an acute international crisis.” American foreign policy expert Ian Bremmer noted, “At some level, it’s startling that isn’t the biggest news of the year.” Yet I have found that I know plenty of well-educated people, with graduate degrees and living in and near Washington, who aren’t even aware this occurred. The story has fallen into a memory hole, in part because neither the Americans nor the Russians wish to escalate the conflict.

Is this unusual affair a one-off, or an indication of a more basic shift in the world? I am starting to believe the latter.

Finally, do solve for the equilibrium:

As the tolerance for particular instances of conflict rises, the temptation to allow or initiate such conflicts rises, if only because the penalties won’t be so large. Eventually more parties will experiment with violent sorties.

Here is further coverage from The Washington Post, from today, the most detailed article to date, but it is already way down on their front page.

Chicago’s land tax and how the city survives being such a fiscal mess

https://twitter.com/Austan_Goolsbee/status/958696452125024256

But wait, isn’t Chicago a fiscal mess? How about the state of Illinois?  It remains the case that living in Chicago is still remarkably affordable, and many of the neighborhoods have wonderful food, buildings, and offer a relatively safe (not always) and walkable environment.  You may even hope to find a parking spot.

I would put it this way: there are many ways to impose a Georgist land tax, fiscal insolvency being one of them.  Very wealthy people and institutions know that if they relocate to Chicago, they will be required to ante up for the final bill.  And so they stay away.  For a city of its size and import, Chicago just doesn’t have that many billionaires, nor do I think a rational billionaire should consider moving there.

In other words, there is a pending wealth tax.  Either directly or indirectly, this will place fiscal burdens on Chicago land, the immobile factor.  And this keeps down rents in Chicago now.

Overall, I do not recommend this fiscal course of action, and Chicago may well become a worse city due to eventual insolvency at the local and state levels.  Still, if you are wondering how it is that Chicago is so affordable — and wonderful — right now, this is part of the answer.

I also should note that not every neighborhood in Chicago benefits from this equilibrium, as in some parts gentrification is difficult to come by.

Monday assorted links

1. According to this estimate, non-searchers lose about a penny on the dollar (pdf).

2. The culture that is Portland how much should companies accommodate the homeless?

3. Solve for the equilibrium: “A UK supermarket chain will sell pasta, crisps, and rice for just 10p to reduce food waste.”

4. Potatoes reduced the number of civil wars.

5. Why a lot of important research is not being done (NYT).

6. What will the Mideast peace plan look like? (NYT)

7. Shoot your Bitcoins off into space, and Cryptokitties is now the most popular application on Ethereum.