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A one player extensive-form game with perfect information.  The player’s name is Zeno. The game has an infinite horizon.  For every non-negative integer N there is a node at which Zeno chooses either to Continue or Quit.  If he Quits at node N his payoff is -N/(N+1). If he continues he moves on to node N+1.

There is also a terminal node at infinity.  This node is reached if and only if Zeno Continues at all finite nodes.  The payoff at infinity is 1.

Here is the story:  Zeno stands at the starting line of a Marathon.  After running the distance he decides whether to quit, etc.  His goal is to finish the Marathon and run into the arms of his proud and adoring fans.  If he doesn’t get to the finish line (the node at infinity) then all he has done is make himself tired with no compensating adoration.  The farther he runs before quitting the more tired he is.

The game has a unique subgame perfect equilibrium:  Zeno completes the Marathon.  But it has another strategy which is unimprovable by a one-stage deviation:  Zeno quits at every opportunity.

This latter strategy has a nice behavioral interpretation.  Zeno lacks confidence in his determination to complete the Marathon.  In particular he wants to complete it but he expects that if he runs another half of the distance he will wind up quitting once he gets there so why bother.  And indeed the reason he knows he will quit after running half the distance is that he knows that when he gets there he will know that after running another half the distance he will still quit so why bother.

This is a great example for teaching the One Stage Deviation Principle, which asserts that strategies that are unimprovable are also SPE.  The OSDP requires the game to be continuous at infinity.  The Marathon game is not continuous at infinity.

To make it continuous at infinity, assume that Zeno’s fans will be almost as proud of him if he runs 26.1999 miles as they would be if he ran the remaining one-millionth of a mile.  If so, then Zeno’s payoff from nearly completing the Marathon is positive and the Quitting strategy becomes improvable.

On Saturday The New York Times published the story that Donald Trump Jr together with Paul Manafort and Jared Kushner met in Trump Tower with a Russian Lawyer.  That was basically the entire content of the story in terms of new information being reported.  The rest of the story was recap of allegations about collusion together with some hint-hint dot connecting.

Junior responded by acknowledging the meeting and saying that it was about Russian adoptions.

The Times followed up on Sunday by reporting that this was in fact a lie, that Junior was promised information about Hillary Clinton that would be valuable for his campaign.

Junior acknowledged this, but minimized the significance of the meeting through a number of statements.

Finally the Times was set to publish accounts of an email thread that apparently showed that Trump was told in advance that this was an effort by the Russian government to provide information that would help his father get elected.

Before they could do that Junior published the actual emails himself.

Someone, either the Times’ source, or the Times journalists themselves had all of that information at the very beginning.  And rather than do the normal journalistic thing of reporting what they knew they released it in little bits.

The first bit was barely meaningful to every reader in the world except for Trump, Manafort Kushner.  It was a message that we have some information that you might not like and it was a challenge to find the right response.

Their dilemma was that first and foremost they don’t want to admit to have colluded with the Russian government.  But, if that was going to be proven anyway they would rather not first lie about it and then have to admit it.

They tried lying.  The Times released another little piece which did two things.  First it proved they lied, and second it proved that they have more information than they had in their original story.

Now Junior and Co. had to guess just how much information.  They guessed wrong.  Indeed the Times had all of the information and in the end Junior was forced to admit what he could have admitted at the beginning and along the way he was caught in two lies.  Indeed in the end he pre-empted the Times revelation by revealing everything himself.

This is a very clever tactic by journalists who are technically doing the journalistically-ethical thing of publishing only the truth,  but being strategic about it by publishing in little pieces to maximize the damage, probably because the Trump administration has made them the enemy.

Note how truly powerful this tactic is once it has been deployed.  The next time the Times has some but not all of the information that would prove guilt they will again release a little bit of it.  Trump will have to guess again how much they are holding back.  Trump will have to trade off the probability of being caught in another lie (if The Times truly has all the dirt) versus credible denial (if they don’t).  If used optimally, this bluffing tactic can get the subject to pre-emptively confess (i.e. to fold to extent the poker analogy) even when the damaging evidence isn’t there.

(One could write a simple dynamic Bayesian persuasion model to calculate the Times’ optimal probability of bluffing in order to maximize the probability that the subject’s best-response is to pre-emptively confess.)


Everyone who has armchair-theorized why movie theaters don’t sell assigned seats in advance is now obligated to explain why this has changed and how that’s consistent with their model.

I will start.  My theory was based on the value of advertising to movie-goers who must arrive early to get preferred seats and then are a captive audience.  This has become significantly less valuable now that said movie-goers can bring their own screens and be captive to some other advertiser.

Indeed today at the movies we arrived on time to our assigned seat, there were no ads and just a few previews.  (Spoiler alert:  the movie with Stringer Bell and the Titanic girl is going to suck, Bladerunner is going to be great and Wonder Woman was awesome for the first and last 10 minutes but apart from that was basically Splash meets Hot Lead and Cold Feet.)


  1. One reason time seems to go faster when you are older. “Has it already been a year?” You have so many more things going on and only a few of them can reside in working memory. When some milestone brings a buried one back to the surface it feels like time has passed more quickly than if it were on your mind the whole time.
  2. A 50 meter tall swimmer would win every race.  Generally taller swimmers have less ground to cover and so the distance is shorter for them.  Is there any kind of race other than swimming like that?
  3. If you have your brain cut into two parts so that one side is unaware of what the other is doing can you tickle yourself?

The anticlimax that is/will be the Comey testimony proves something I have always thought about skeletons in the closet. They should be released early when not everyone is paying attention.

The premise is that outrage is something that needs to be coordinated. Its not enough for everyone to feel outraged. Its not even enough for everyone to know everyone is feeling outraged.  The feeling of outrage has to be common knowledge. Only that way enough people know that when they act on their outrage there will be enough others acting on their outrage for it to be a movement that can have impact.  (Outrage is a scarce resource.)

So skeletons released sometime in the past when nobody was actually looking for skeletons is a way to dampen that coordination. Because then when the time comes and people are actually focused on you and any skeletons you might have, the old already-uncloseted skeletons can’t have the same impact as a brand new one released right now when everyone sees it for the first time.  They are “old news” (and its no wonder that’s a go-to line of defense against resurrected skeletons.)  Strategically everyone infers that since the skeletons didn’t cause outrage at the time they must not be that outrageous to that many people and so they are not a call to outrage now.

So despite the several outrageous things in the Comey statement, they are all old news and that feeling of anti-climax is a symptom of the above logic. If Comey had not previewed his testimony in the preceding weeks but instead dropped it as one brand new bombshell on TV in front of a Super Bowl audience (paging Michael Chwe) the same skeletons would cause significantly more outrage.

An interesting corollary is that leaks are actually Trump’s ally. Leaking the scandal little by little through varied and segregated media channels is a way of getting the skeletons out with minimal impact well in advance of any chance of outrage.

(There’s a new paper by Gratton, Holden and Kolotilin that also looks at bombshells but I think the argument is a little different.)

  1. Watch for the key leading indicator of impending Presidential downfall:  the Vice President going silent.  We will reach a point where the VP’s objective switches from defending the President to preserving his own viability as President.  Right around that turning point he will try his best to avoid having to comment.
  2. That means that before reaching that point, Democrats will do their very best to get him to comment while they still have a chance.  Knowing this of course makes the VP want to hide even sooner, etc.  The unraveling may have already reached back to the present moment.
  3. At some point the VP himself becomes a threat to the President because Republicans in Congress will try to find the smoothest path to a fresh Presidency with the possibility of delivering on their agenda intact.  This will involve coordination with the VP.
  4. That means the President himself will try to get the VP to publicly support him in order to ensure that the VP is tarred with the same brush, removing the above branch of the tree and maintaining the threat of a messy impeachment proceeding that congressional Republicans will want to avoid.  Of course the first sign that the President needs the VP is the first signal to the VP that his best respond is to run far away, accelerating the unraveling further.
  5. This implies another leading indicator of impending doom.  There will come a time when its the GOP that wants to hasten the proceedings and the Democrats will try to slow it down.
  6. Trump of course is the major wild-card (sic) in all of this.  He has no loyalty to anybody and he has a massive megaphone whether he is in office our out.  There is the prospect of Trump busting out tapes of conversations with GOP leaders expressing support.  There is the possibility that he publicly turns on Pence before actually being removed from office.
  7. And of course the GOP is by no means out of the water once Trump is gone.  He will be tweeting.  He will have his “tapes”.  He could even run again.

This paper by Finkelstein, Hendren, and Shepard finds that the uninsured have such a low willingness to pay for health insurance that they wouldn’t even cover the costs they impose on insurers:

But for our entire in-sample distribution – which spans the 6th to the 70th percentile of the WTP distribution – the WTP of marginal enrollees still lies far below their own expected costs imposed on insurers for either the H or L plans. For example, a median WTP individual imposes a cost of $340 on the insurer for the H plan, but is willing to pay only about $100 for the H plan. This suggests that textbook subsidies offsetting adverse selection would be insufficient for generating take-up for at least 70% of this low-income population. Coverage is low not simply because of adverse selection but because people are not willing to pay their own cost they impose on the insurer.

Large subsidies would be required to achieve universal coverage.  And this is not correcting a market failure, its paying for something that the uninsured are revealing it would be inefficient to provide.

Except when you look at the likely reason.

Individuals choosing to forego health insurance exercise the ability to utilize uncompensated care; this externality from insurance choice raises a potential Samaritan’s dilemma rationale (Buchanan, 1975) for providing health insurance subsidies by using government taxes to internalize the externality imposed on the providers of uncompensated care when individuals choose to remain uninsured.

They are going to emergency rooms, receiving charity, etc.  The low revealed willingness to pay comes from the fact that that formal health insurance would crowd out the informal health insurance they are receiving for “free”.  But of course the cost is borne by somebody and should be added to the welfare calculation.

Perhaps we should stop thinking of health insurance as solving a traditional market failure but instead think of it in the same terms as flood insurance.  Flood insurance is federally mandated for residences in flood plains.  The logic is very simple.  When there is a flood, those affected will receive assistance whether they have insurance or not.  Therefore the only way to get them to internalize any of these costs is to require them to pay in advance, in the form of flood insurance.

When politicians argue against health insurance mandates because they take freedoms away ask them to argue against mandatory flood insurance on the same terms.

Beanie bob:  MR

Yesterday just before the start of a seminar I went to the thermostat to try to warm up the room.  The speaker saw me fiddling with it and nodded with approval.  I said nothing, turned up the heat and returned to my seat.

The thing is, she couldn’t see whether I was raising the temperature or lowering it.  She just assumed that I would be moving the temperature in the same direction as her preference.  And of course with good reason.  We both want a comfortable room.  We each get private signals about whether the room is currently too cold or too warm.  Our private signals are correlated. If her private signal suggests the room is too warm then she knows that more likely than not my private signal says the same thing, and since I am acting on my private signal and nothing more I am most likely adjusting the thermostat exactly how she wants it.

I know all of this and therefore I strictly prefer to say nothing about what I am doing.  By saying nothing I allow her to continue to believe that I am doing what she wants me to do even though I don’t know for sure what it is she wants.  Her signal of course could be different than mine.  If instead I tell her I am raising the temperature then in the best case I am just confirming what she already believed and nothing is gained.  But there is the risk that I inform her that actually I am doing the opposite of what she wants and then we have a conflict.

Her seminar was awesome.

NYT on whether to filibuster Gorsuch now or wait:

The substantive stakes now are relatively low: Judge Gorsuch appears to be very conservative, but so was Justice Scalia. Confirming Judge Gorsuch would merely preserve the ideological status quo on the closely divided Supreme Court. Should the confirmation move ahead, all 52 Republican senators will probably stick together, bolstered by a few Democrats from conservative-leaning states. Those are enough votes to easily clear the way for confirming Judge Gorsuch — and all future nominees — by a simple majority.

But the dynamics could play out differently in a second situation: Judge Gorsuch is confirmed, but the filibuster rule survives. If Mr. Trump then gets to nominate a successor to a moderate or liberal justice, the substantive stakes would be much higher.

The framing for the filibuster fight would be different at that point. It would focus on whether the nominee would provide a fifth vote to overrule the Roe v. Wade abortion rights precedent and create a new conservative majority on other highly charged topics, like guns, affirmative action and the rights of same-sex couples.

Under that second possibility, it may not be inevitable that the filibuster rule falls. Red-state Democrats would be less likely to break ranks, and institutionalist or moderate Republican senators, like Susan Collins of Maine and Lisa Murkowski of Alaska, might be more reluctant to vote to change the chamber’s longstanding rules.

If red state Democrats and Collins and Murkowski can do backward induction, filibustering now or later is equivalent.

Also, if Republicans use the “nuclear option”, this reveals their type to Kennedy who may then defer retirement so he is not replaced by a Trump appointee.


A few weeks ago, I went to a meeting.

There was a part of the meeting where some open-ended information was disseminated and very general comments were sought. Now, one possibility when you make a comment is that it leads to interesting responses and a “whole if bigger than the sum of the parts” dynamic develops. Let us call this the brainstorming case. (This is the scenario that is meant to occur in research seminars.)

Much more likely is the “every action has an equal reaction” case where you talk, others respond but really the discussion goes nowhere and you wish no-one had talked in the first place. Let us called this the BS case. Casual empiricism suggests that the BS case is much more common than the brainstorming case.

This fact implies that comments should be taxed to internalize the negative externality but with taxation impossible we have to rely on morality to create incentives. Any moral individual should take into account the horrific effect of their casual comments. Even a rational decision-maker should take the negative feedback loop into account – in this sense, the BS case helps rational individuals take the horrific effects of talking at meetings into account. However, even this does not account for the acute suffering of the innocent by-listener so the moral individual should ratchet up the threshold for talking yet further.

Of course, this does not happen. There are always one or two people who have to talk. This is valuable not because of what they say but because of what others do not say. Namely, the people who do NOT talk are to be celebrated. They either see through the logic above and are quite moral or, to add another dimension, they are nice and kind of shy. Either case, these are nice people. Hang out with them. Meetings with just these people might be quite productive so put them on committees.







There was 20 seconds left, Vanderbilt had just scored a layup to go ahead by 1 and Northwestern’s Bryant Mcintosh was racing to midcourt to set-up a final chance to regain the lead and win the game.  Vanderbilt’s Matthew Fisher-Davis intentionally fouled him, sending McIntosh to the line and the commentators and all of social media into a state of bewilderment.  Yes, we understand intentionally fouling when you are down 1 with 20 seconds to go, but when you are ahead by 1?

But it was a brilliant move and it failed only because the worst-case scenario (for Vanderbilt) realized:  McIntosh made two clutch free throws and Vanderbilt did not score on the ensuing possession.

(Before we get into the analysis, a simple way to understand the logic of the play is to notice that intentionally fouling late in the game very often is the right strategic move when you are down by a few points and there is no reason that should change precipitously when the point differential goes from slightly negative to slightly positive.The tactic is based on a  tradeoff between giving away (random) points and getting (for sure) possession.  The factors in that tradeoff are continuous as a function of the current scoring margin.)

Let p be the probability that a team scores (at least two points) on a possession.  Let q be the probability that Bryant McIntosh makes a free throw.  Roughly, the probability that Vanderbilt wins if they do not foul is 1-p because Northwestern is going to play for the final shot and win if they make a field goal.

What is the probability that Vanderbilt wins when Fisher-Davis fouls? There are multiple, mutually-exclusive ways they could win.  First, McIntosh might miss both free-throws.  This happens with probability (1-q)^2.  The other simple case is McIntosh makes both free-throws, a probability q^2 event, in which case Vanderbilt wins by scoring on the following possession, which they do with probability p. Thus, the total probability Vanderbilt wins in this second case is q^2p.

The third possibility is McIntosh makes one free-throw.  This has probability 2q(1-q). (I am pretty sure McIntosh was shooting two, i.e. Northwestern was in the double bonus, but if it was a one-and-one this would make Fisher-Davis’ case even stronger.)  Now there are two sub-cases.  First, Vanderbilt could score on the ensuing and win.  Second, even if they don’t score, it will be tied and the game will be sent into overtime. Let’s say Vanderbilt wins with probability 1/2 in overtime, a conservative number since Vanderbilt had all the momentum at that stage of the game.

Then the total probability of a Vanderbilt win in this third case is 2q(1-q)\left[ p + \frac{1-p}{2}\right].  Adding up all of these probabilities, Vanderbilt wins using the Fisher-Davis foul with probability

(1-q)^2 +  2q(1-q)\left[ p + \frac{1-p}{2}\right] + q^2p

Fisher-Davis made the right move provided the above expression exceeds 1-p.  Let’s start by noticing some basic properties.  First, if p = 1 then fouling is always the right move, no matter what q is.  (If Northwestern is going to score for sure, you want to foul and get possession so that you can score for sure and win.)  If q = 0 then again fouling is the right strategy, regardless of p.  (If he’s going to miss his free-throws then send him to the line.)

Next, notice that the probability Vanderbilt wins when Fisher-Davis fouls is monotonically increasing in p. Since the probability (1-p) Vanderbilt wins without fouling is decreasing in p, the larger it is the better the Fisher-Davis gambit looks.

Finally, even if q = 1, so that McIntosh is surely going to sink two free-throws, Fisher-Davis made the right move as long as p > 1/2.

Ok so what are the actual values of p and q.  McIntosh is an 85% free-throw shooter so q = .85.  Its harder to estimate p but here are some guidelines.  First, both teams were scoring (at least two points) on just about every possession down the stretch of that game.  An estimate based on the last 3 minutes of data would put p at at least .7, in any case certainly larger than 1/2.

More generally, I googled a bit and found something basketball stat guys call offensive efficiency.  It’s an estimate of the number of points scored per possession.  Northwestern and Vanderbilt have very similar numbers here, about 1.03.  A crude way to translate that into the number we are interested, namely probability of at least 2 points in a possession, is to simply divide that number in half, again giving p > 1/2.  (This would be exactly right if you could only ever score 2 points.  But of course there are three-point possessions and one-point possessions.)  A third way is to notice that Northwestern was shooting a 49% field goal percentage for the game.  This doesn’t equal field goals per possession of course because some possessions lead to turnovers hence no field goal attempt, and on the other side some possessions lead to multiple field goal attempts due to offensive rebounds.

So as far as I know there isn’t one convincing measure of p but its pretty reasonable to put it above p = 0.5 at that phase of the game.  This would be enough to justify Fisher-Davis even if McIntosh was certain to make both free throws.  (I used Wolfram Alpha to figure out what p would be required given the precise value q = .85 and it is about .45).

Finally, even if p is below .45 say around .4 it means that the foul lowered Vanderbilt’s win probability but not bvery much at all. Probably less than every single time in the game that someone missed a shot.  Certainly less than a few seconds later when LaChance missed the winning shot on the final possession.  Its interesting how in close games the specific things we focus our attention on when in fact pretty much every single play in the game turned out to be pivotal.

Here is a passage from Ariel’s interesting and thought-provoking review:

“The following famous quote is taken from a letter written by John Maynard Keynes to Roy Harrod in 1938: “It seems to me that economics is a branch of logic, a way of thinking”; “Economics is a science of thinking in terms of models joined to the art of choosing models which are relevant to the contemporary world.” Economists enjoy discussing this question. I sometimes wonder if the question of whether economics is a science is about the commitment of economics to certain standards or whether it is actually about gaining entry into that prestigious club called Science.

Dani takes the question seriously and declares: “Models make economics a science” (p. 45). He rejects what he describes as the most common justification given by economists for calling economics a science: “It’s a science because we work with the scientific method: we build hypotheses and then test them. When a theory fails the test, we discard it and either replace it or come up with an improved version.” Dani’s response: “This is a nice story, but it bears little relationship to what economists do in practice. . . ” (p. 64). He also admits that “. . . [economic] methods are as much craft as they are science. Good judgment and experience are indispensable, and training can only get you so far. Perhaps as a consequence, graduate programs in economics pay very little attention to craft” (p. 83).”

Here is the link.


In Chicago Tribune (edited by paper in some ways that make it less clear!).

Main Point: Way Trump reacts to #grabyourwallet campaign against Nordstrom shows he is (1) easily provokable and (2) emotionally connected to his “brand”.

Terrorists as much as activists aim to provoke and have learned that Trump-branded properties worldwide are good targets if they aim to inflame Trump.

Interesting WashPo article re Germany truck attack:

Islamic State officials have explicitly sought to link such attacks to the larger goal of making Europe intolerable for faithful Muslims. A 2015 article in the group’s English-language magazine, Dabiq, warned that the terrorists would soon begin targeting the West with the aim of deliberately provoking a backlash against Muslims living there.

“Muslims in the West,” the article said, “will quickly find themselves between one of two choices: they either apostatize and adopt the [Western] religion . . . or they emigrate to the Islamic State and thereby escape persecution.”

Somewhat consistent with our paper but generates some new questions – unlike Al Qaeda, ISIS is a near state not a terrorist group. The main threat to its survival is Western tacit support to a Putin-Assad (and Trump?) coalition against ISIS. If these terrorists attacks lead to such a  coalition, provocation will backfire.

The poll aggregators were wildly off as they gave Hillary Clinton an over 90% chance of winning. Nate Silver was the most pessimistic because of his theory of correlated forecasting errors:

State outcomes are highly correlated with one another, so polling errors in one state are likely to be replicated in other, similar states….If Clinton loses Pennsylvania despite having a big lead in the polls there, for instance, she might also have problems in Michigan, North Carolina and other swing states.

The correlating factor appears to be the white working class vote which abandoned Clinton in the Rust Belt States. For reasons we do not yet fully understand, this vote for Trump did not appear in polls. The polls were then all off the mark in all Rust Belt states.

The others poll aggregators assumed independence and gave less thought to a simple theory of voting that might generate independence let alone whether such a theory might be plausible. If they hand, it would have led them to a more plausible way to look at the data, like Silver, and hence better predictions.

(HT Georgy Egorov though I may not be doing justice to his point.)

Evangelical Christians knew who Trump was, had seen the videos and ads and yet still voted for Trump. Their main issue is the make-up of the Supreme Court and Trump gave them a list of potential nominees they liked . He was more likely to choose an anti-abortion justice than Hillary. So, the vast majority worked out their constrained optimal choice and went for it.

Greens could register a protest vote for Jill Stein in the election or choose between one of two electable candidates. No doubt, Jill, if elected, would have tried to implement a first-best environmental policy (and failed to get it past a Republican Congress) but realistically it was choice between Hillary getting nothing done or Trump ripping up the Obama legacy. The obvious legacy of interest to Greens is the Paris agreement and this is now the Paris disagreement. And in Michigan and Wisconsin, Hillary’s margin of loss is smaller than Jill Stein’s vote. Of course, this is not enough – Robby Mook would have to have had the foresight to get Beyonce to come to Philly not Cleveland.

So why are Evangelicals better than Greens at this kind of reasoning? Are Greens just crazier? My colleague Jorg Spenkuch found a clever way to measure the fraction of crazy Greens in Germany – I think he finds it is 60%. Not sure if he has a way to measuring crazy German Evangelicals (if they exist)! Another theory would be based on learning. Evangelicals have been around the block a while and have learned the optimal strategy but Greens have not. But a counterargument is the Gore vs Bush Florida battle where Ralph Nader played a crucial role. Surely the Greens voters could remember having screwed up the election of the person who would have been the best President on the environment ever? I parry this thrust by positing the Greens who voted for Jill Stein are so young that Bush v Gore is not part of their recalled history.

HT Krugman


How do you assess whether a probabilistic forecast was successful?  Put aside the question of sequential forecasts updated over time.  That’s a puzzle in itself but on Monday night each forecaster will have its final probability estimate and there remains the question of deciding, on Wednesday morning, which one was “right.”

Give no credibility to pronouncements by, say 538, that they correctly forecasted X out of 50 states.  According to 538’s own model these are not independent events.  Indeed the distinctive feature of 538’s election model is that the statewide errors are highly correlated.  That’s why they are putting Trump’s chances at 35% as of today when a forecast based on independence would put that probability closer to 1% based on the large number of states where Clinton has a significant (marginal) probability of winning.

So for 538 especially (but really for all the forecasters that assume even moderate correlation) Tuesday’s election is one data point.  If I tell you the chance of a coin coming up Armageddon Tails is 35%, you toss it once and it comes up Tails you certainly have not proven me right.

The best we can do is set up a horserace among the many forecasters.  The question is how do you decide which forecaster was “more right” based on Tuesday’s outcome?  Of course if Trump wins then 538 was more right than every other forecaster but we do have more to go on than just the binary outcome.

Each forecaster’s model defines a probability distribution over electoral maps. Indeed they produce their estimates by simulating their models to generate that distribution and then just count the fraction of maps that come out with an Electoral win for Trump.  The outcome on Tuesday will be a map.  And we can ask based on that map who was more right.

What yardstick should be used?  I propose maximum likelihood.  Each forecaster on Monday night should publish their final forecasted distribution of maps.  Then on Wednesday morning we ask which forecaster assigned the highest probability to the realized map.

That’s not the only way to do it of course, but (if you are listening 538, etc) whatever criterion they are going to use to decide whether their model was a success they should announce it in advance.

It was great to wake up this morning and find that Oliver Hart and Bengt Holmström were awarded the Nobel Prize in Economics for 2016. Their research is the bread and butter of modern economic theory and hence is taught in all first-year PhD microeconomics courses and more applied versions are taught to MBAs in electives on organizational economics.

Let me begin with the work of Bengt Holmström. The prize announcement begins with his work on the principal-agent model with moral hazard: An agent privately chooses an action that impacts the welfare of a principal. The principal observes noisy signals of the action and rewards the agent as a function of the signals to align incentives. Holmström asks: Which variables should be included by the principal is her performance measure and which should be omitted? In the “sufficient statistic” result, he shows that variables should be included if and only if they contain information about the action. Adding more signals into a performance measure would add superfluous noise into payments which the a risk-averse agent would have to be compensated for. On the other hand, subtracting informative signals from a performance would eliminate useful information for aligning incentives.

This result poses a puzzle which Bengt turns to in later work: Real-world contracts are rarely as complex as the informativeness principle would suggest. Why is that the case? In joint work with Paul Milgrom, Holmström introduced the multi-task principal agent model. The main innovation was to allow the agent to perform multiple tasks and to substitute from one to the other. Holmström and Milgrom show that in certain circumstances it is better not to may pay responsive to performance. Suppose someone working in a fast food restaurant can look after the kitchen or sell burgers. Burger sales are measurable but time spent looking after the kitchen is not. Then making pay depend on burger sales can backfire as the agent substitutes away from looking after the kitchen. Better to have low-powered incentives which are relatively flat in burger sales.

Bengt has made at least two other seminal contributions to moral hazard models. In his work on moral hazard in teams he shows that it might be impossible achieve total value maximizing outcomes when joint output is measurable but individual output is not. In his career concerns model, he shows that an agent trying to prove he is high ability to a market might work too hard at the start of his career and then tail off at the end. All these papers are workhorses of applied theory. They show Holmström’s flair of coming up with models that serve as vehicles for others to make interesting contributions to understanding incentives.

I want to end my appreciation of Bengt Holmström by pointing out that several of these papers were written when he was an Assistant Professor in the MEDS Department at Kellogg. Roger Myerson has already won a Nobel Prize for the work he did when he was in MEDS.

Oliver Hart took contract theory in a different direction by emphasizing the role of property rights. In the principal-agent model, the principal might be an employer and the agent an employee. Or the principal might be one firm and the agent an independent subcontracter. In other words, the model cannot address the question of when trade should take place within a firm or across two firms. Building on some informal ideas of Oliver Williamson, Oliver Hart with Sandy Grossman and John Moore used the idea that contracts are incomplete to offer a unified theory of the optimal allocation of property rights. The key idea is that ownership of an asset confers residual rights of control so you can use it for production should a relationship break down. Suppose a buyer and a seller are trading a widget. They can both invest ex ante to increase the value of trade but because contracts are incomplete they must haggle over the price ex post. This means both are subject to hold-up: the benefit of any costly investment is shared with the other trading party. Hence, both will underinvest. This underinvestment is mitigated by the fact that if a player owns an asset he can use it to trade with others so at least he can capture some value from his investment. So, if one player’s investment is particularly important for value creation he should be own all the assets and employ the other – so we have an integrated firm. If both players’ investments are important, then they should both own assets and then we have trade across two independent firms.

Debt and equity confer decision rights in different ways. So, Oliver Hart’s way of looking at control rights has proved to be very fruitful in corporate finance. But there is a lot to be done. In particular, without a theory of why contracts are incomplete there is a tension between the lessons of mechanism design and the ideas in Grossman-Hart-Moore. This tension was pointed out by Maskin and Tirole. Eric Maskin was my PhD advisor at Harvard and Oliver arrived at Harvard just as I graduated. At that point, my friend, co-author and advisor Tomas Sjöström, who was sitting at the podium during the announcement as he is on the Nobel Committee, was an assistant professor at Harvard and I would visit to work with him. We became interested in Oliver’s ideas and also knew of the Maskin-Tirole critique. So, Tomas and I wrote a few papers studying optimal decision rights when agents can collude or renegotiate inefficient outcomes without falling afoul of the Maskin-Tirole critique. I continue to work on these questions still. I would never have worked on those papers without Oliver’s seminal insights to build on. So, I am particularly happy personally with this prize.


Trump excites the “base” but not independents or traditional Republicans who believe in free markets etc. The temptation for Congressional Republicans up for election is to use “strategic ambiguity” and have their cake and eat it. That is, say you support the Republican Presidential nominee but not embrace his positions, e.g like Ayotte and McCain. This way, you hope ticket-splitters vote for you to check and balance Hillary.

Unfortunately, Obama moves second. He will say Trump is unfit to be President, is not a Republican and will tar supporters with the same brush. This way he will seek to slice off the base vote from the non-base. A vote for a supporter is a vote for Trump. How will they check and balance a demagogue when they are not splitting with him now? Also – and somewhat unexpectedly – Trump is helping Obama out here by refusing to endorse Congressional Republicans employing strategic ambiguity. He refuses to endorse Ayotte and McCain because of criticisms etc. Hence,he is signaling to his base not to support them (not sure if his strategy makes sense but I will take him at face value).

So, on the one hand, Obama will attack anyone on the fence by saying they support Trump (hoping to peel off independents, “real” Republicans and ticket-splitters) and Trump will attack anyone on the fence by saying they do not support him (hoping his base will not support them?!!).

So, strategic ambiguity is going to backfire so you have to pick a side. Which side? Can you win if you support him and he loses your state? If the answer is a likely Yes, you support Trump (e.g. Rubio) and if it is a No, you Dump Trump. The more likely your state is to go for Hillary, the more plausible your “I will check and balance Hillary” argument and the less costly it is to Dump Trump. Hence, Toomey and Ayotte are likely in this category. If the state is 50-50 like AZ, your choice is difficult, eg McCain, but you have to pick a side otherwise both may not vote for you.




  1. Suppose one forecaster says the probability Trump wins is q and the other says the probability is p>q.  If Trump in fact wins, who was “right?”
  2. Suppose one forecaster says the probability is q and the other says the probability is 100%.  If Trump in fact wins, who was right?
  3. Suppose one forecaster said q in July and then revised to p in October.  The other said q’ < q in July but then also revised to p in October.  Who was right?
  4. Suppose one forecaster continually revised their probabilistic forecast then ultimately settled on p<1.  The other forecaster steadfastly insisted the probability was 1 from beginning to end.  Trump wins.  Who was right?
  5. Suppose one forecaster’s probability estimates follow a martingale (as the laws of probability say that a true probability must do) and settles on a forecast of q.  The other forecaster‘s “probability estimates” have a predictable trend and eventually settles on a forecast of q’>q.  Trump wins.  Who was right?
  6. Suppose there are infinitely many forecasters so that for every possible sequence of events there is at least one forecaster who predicted it with certainty.  Is that forecaster right?

What I wrote yesterday:

When Fox broadcasts the Super Bowl they advertise for their shows, like American Idol. But those years in which, say, ABC has the Super Bowl you will never see an ad for American Idol during the Super Bowl broadcast.

This is that sort of puzzle whose degree of puzzliness is non-monotonic in how good your economic intuition is.

If you don’t think of it in economic terms at all it doesn’t seem at all like a puzzle. Try it: ask your grandpa if he thinks that its odd that you never see networks advertising their shows on other networks.  Of course they don’t do that.

When you apply a little economics to it that’s when it starts to look like a puzzle. There is a price for advertising. The value of the ad is either higher or lower than the price. If its higher you advertise.  If its another network that price is the cost of advertising. If its your own network that price is still a cost: the opportunity cost is the price you would earn if instead you sold the ad to a third-party.  If it was worth it to advertise American Idol when your own network has the Super Bowl then it should be worth it when some other network has it too.

But a little more economics removes the puzzle.  Networks have market power.  The way to use that market power for profit is to artificially restrict quantity and set price above marginal cost. (The marginal cost of running another 30 second ad is the cost in terms of viewership that would come from shortening, say, the halftime show by 30 seconds.)

When a network chooses whether to run an ad for its own show on its own Super Bowl broadcast it compares the value of the ad to that marginal cost.  When a network chooses whether to run an ad on another network’s Super Bowl broadcast it compares the value to the price.

Indeed even if the total time for ads is given and not under control of the network (i.e. total quantity is fixed) the profit maximizing price for ads will typically only sell a fraction of that ad time.  Then the marginal (opportunity) cost of the additional ads to pad that time is zero and even very low value ads like for American Idol will be shown when Fox has the Super Bowl and not when any other network does.

In fact that last observation and the fact that you never ever see any network advertise its shows on another network tells us that the value of advertising television shows is very low.  Perhaps that in fact tells us that the networks themselves understand (but their paying advertisers don’t) that the value of advertising in general is very low.

When Fox broadcasts the Super Bowl they advertise for their shows, like American Idol. But those years in which, say, ABC has the Super Bowl you will never see an ad for American Idol during the Super Bowl broadcast.

More generally, networks advertise their own shows on their own network but never pay to advertise their shows on other networks.  I never understood this.  But I think I finally figured it out, there’s some very simple economics behind this.

Right now at, you can read the current betting market odds for a “contested convention” and a “brokered convention.”  The definitions are as follows.  A contested convention means that no candidate has 1237 delegates by the end of the last primary.  A brokered convention means that no candidate wins on the first ballot at the convention.

Right now the odds of a brokered convention are 50%.  Note also that the odds of a Trump nomination are 50% as well.  And Trump is the only candidate with any chance of winning a majority on the first ballot (even if he doesn’t get 1237 bound delegates he will be close and no other candidate could combine their bound delegates with unbound delegates to get to a majority.)

Thus, if there is no brokered convention Trump is the nominee.  The probability of no brokered convention is 50%.  Thus the entire 50% probability of a Trump nomination is accounted for by the event that he wins on the first ballot.

In other words there is zero probability, according to betting markets, that Trump wins a brokered convention.

The odds of a contested convention are 80%. That means that betting markets think there is a 30% chance Trump fails to get 1237 bound delegates but still wins on the first round.  I.e. according to betting markets we have the following three mutually exclusive events:

  1. Trump gets to 1237 by June 7.  20% odds
  2. Trump fails to get 1237 bound delegates but wins on the first ballot.  30%
  3. Nobody wins on the first ballot and Trump is not the nominee.  50%

Donald Trump:

You are a lifelong Republican and think Trump is not a conservative. You would never vote for him. You go into the voting both and see Clinton’s name and Trump’s name. What do you do? Either you bite the bullet and vote for Clinton or you abstain. Either way you have increased the probability that Hillary wins – OK not by much but since you are in the voting booth in the first place, you’re not a fully rational voter and so you care about the infinitesimal impact you have. So, you decide to make sure she’s hamstrung by a Republican Congress. You vote for the Republican Congressional candidates.

You would vote for Cruz but suspect he is a bit nuts. You vote for the Democratic Congressional candidates to make sure Cruz is ineffective.

(Kasich would actually be best all round but has no chance of making it.)




Suppose politician C goes negative on politician M. Politician’s M’s support declines..where do his supporters go? If there are just two candidates, they either go to politician C or stay at home. But if there are three or more candidates, they might go to politician A, B, or K etc etc. So, to a first order, it is less profitable to go negative the greater the number of candidates.

This resembles the Holmstrom teams model but with unproductive effort.




From Buzzfeed:

HENNIKER, New Hampshire — In town halls, pizzerias, and high school auditoriums, hundreds of voters are carefully evaluating the three governors who have pinned their presidential hopes on Tuesday’s primary in the Granite State — Jeb Bush, Chris Christie, and John Kasich.

Some have made their choice of the three; others are still undecided. But they all agree on one big thing: The Republican Party needs a strong contender coming out of New Hampshire to take down Donald Trump.

With the stakes so high, these “non-angry voters,” as described by some, are wrestling with whether to ultimately vote for their personal favorite — one of the three governors, or go by the polls in favor of a more practical favorite, Sen. Marco Rubio.

Perhaps the GOP should adopt approval voting as suggested by my colleague Bob Weber where each voter can “approve” as many candidates as he likes.

Of course, Ted Cruz and Donald Trump would disapprove or approval voting.

My colleagues are multi-talented:

Screenshot 2015-11-03 09.04.21

Robert McDonald, Associate Dean for Faculty, and Jeff Cohen performing “Here comes the weekend” by Dave Edmunds and Nick Lowe and “What’s so funny about peace, love and understanding?” by Nick Lowe.

HT: Bob McDonald for telling me first song is also by Dave Edmunds.


Uber Drivers tried to organize a strike to demand higher pay.

Uber drivers are competing with each for fares. The smaller the number of other drivers on the road, the greater the chance a driver get business. Also, when demand for rides outstrips supply of drivers, Uber might activate surge pricing to increase supply. Not only does a driver stand to get more business, he gets a higher fare/mile. The incentives to deviate from the strike are huge.

So, in Chicago, during the supposed strike, the number of Uber Drivers on the road was huge. Surge pricing was not activated because it was not necessary.

HT: An Uber driver.

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