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From the fantastic blog, Letters of Note.
Circa 1986, Jeremy Stone (then-President of the Federation of American Scientists) asked Owen Chamberlain to forward to him any ideas he may have which would ‘make useful arms control initiatives’. Chamberlain – a highly intelligent, hugely influential Nobel laureate in physics who discovered the antiproton – responded with the fantastic letter seen below, the contents of which I won’t mention for fear of spoiling your experience. Unfortunately, although I can’t imagine the letter to be anything but satirical, I’m uninformed when it comes to Chamberlain’s sense of humour and have no way of verifying my belief. Even the Bancroft Library labels it as ‘possibly tongue-in-cheek’.
Via The Volokh Conspiracy, I enjoyed this discussion of the NFL instant replay system. A call made on the field can only be overturned if the replay reveals conclusive evidence that the call was in error. Legal scholarship has debated the merits of such a system of appeals relative to the alternative of de novo review: the appelate body considers the case anew and is not bound by the decision below.
If standards of review are essentially a way of allocating decisionmaking authority between trial and appellate courts based on their relative strengths, then it probably makes sense that the former get primary control over factfinding and trial management (i.e., their decisions on those matters are subject only to clear error or abuse of discretion review), while the latter get a fresh crack at purely “legal” issues (i.e., such issues are reviewed de novo). Heightened standards of review apply in areas where trial courts are in the best place to make correct decisions.
These arguments don’t seem to apply to instant replay review. The replay presumably is a better document of the facts than the realtime view of the referee. But not always. Perhaps the argument against in favor of deference to the field judge is that it allows the final verdict to depend on the additional evidence from the replay only when the replay angle is better than that of the referee.
That argument works only if we hold constant the judgment of the referee on the field. The problem is that the deferential system alters his incentives due to the general principle that it is impossible to prove a negative. For example consider the (reviewable) call of whether a player’s knee was down due to contact from an opposing player. Instant replay can prove that the knee was down but it cannot prove the negative that the knee was not down. (There will be some moments when the view is obscured, we cannot be sure that the angle was right, etc.)
Suppose the referee on the field is not sure and thinks that with 50% probability the knee was down. Consider what happens if he calls the runner down by contact. Because it is impossible to prove the negative, the call will almost surely not be overturned and so with 100% probability the verdict will be that he was down (even though that is true with only 50% probability.)
Consider instead what happens if the referee does not blow the whistle and allows the play to proceed. If the call is challenged and the knee was in fact down, then the replay will very likely reveal that. If not, not. The final verdict will be highly correlated with the truth.
So the deferential system means that a field referee who wants the right decision made will strictly prefer a non-call when he is unsure. More generally this means that his threshold for making a definitive call is higher than what it would be in the absence of replay. This probably could be verified with data.
On the other hand, de novo review means that, conditional on review, the call made on the field has no bearing. This means that the referee will always make his decision under the assumption that his decision will be the one enforced. That would ensure he has exactly the right incentives.
Each Christmas my wife attends a party where a bunch of suburban erstwhile party-girls get together and A) drink and B) exchange ornaments. Looking for any excuse to get invited to hang out with a bunch of drunk soccer-moms, every year I express sincere scientific interest in their peculiar mechanism of matching porcelain trinket to plastered Patricia. Alas I am denied access to their data.
So theory will have to do. Here is the game they play. Each dame brings with her an ornament wrapped in a box. The ornaments are placed on a table and the ladies are randomly ordered. The first mover steps to the table, selects an ornament and unboxes it. The next in line has a choice. She can steal the ornament held by her predecessor or she can select a new box and open it. If she steals, then #1 opens another box from the table. This concludes round 2.
Lady #N has a similar choice. She can steal any of the ornaments currently held by Ladies 1 through N-1 or open a new box. Anyone whose ornament is stolen can steal another ornament (she cannot take back the one just taken from her) or return to the table. Round N ends when someone chooses to take a new box rather than steal.
The game continues until all of the boxes have been taken from the table. There is one special rule: if someone steals the same ornament on 3 different occasions (because it has been stolen from her in the interim) then she keeps that ornament and leaves the market (to devote her full attention to the eggnogg.)
Theoretical questions:
- Does this mechanism produce a Pareto efficient allocation?
- Since this is a perfect-information game (with chance moves) it can be solved by backward induction. What is the optimal strategy?
- How can this possibly be more fun than quarters?
Auction sites are popping up all over the place with new ideas about how to attract bidders with the appearance of huge bargains. The latest format I have discovered is the “lowest unique bid” auction. It works like this. A car is on the auction block. Bidders can submit as many bids as they wish ranging from one penny possibly to some upper bound, in penny increments. The bids are sealed until the auction is over. The winning bid is the lowest among all unique bids. That is, if you bid 2 cents and nobody else bids 2 cents, but more than one person bid 1 cent, then you win the car for 2 cents.
In some cases you pay for each bid but in some cases bids are free and you pay only if you win. Here is a site with free bidding. An iPod shuffle sold for $0.04. Here is a site where you pay to bid. The top item up for sale is a new house. In that auction you pay ~$7 per bid and you are not allowed to bid more than $2,000. A house for no more than $2,000, what a deal!
I suppose the principle here is that people are attracted by these extreme bargains and ignore the rest of the distribution. So you want to find a format which has a high frequency of low winning bids. On this dimesion the lowest unique bid seems even better than penny auctions.
Caubeen curl: Antonio Merlo.
After a day of conference talks, but before drinks arrive, game theorists have been known to debate whether what is known as Zermelo’s theorem was actually proved by Zermelo. Eran Shmaya (who is always fun to talk to with or without drinks) decided to go and look at the paper (recently translated) and all but strips Zermelo of his theorem.
So, Zermelo clearly did not set out to prove his eponymous theorem. But was he aware of it ? I guess the answer depends on what you mean by being aware of a mathematical statement (were you aware of the fact that any even number greater than 2 can be written as a sum of a prime number and an even number before you read this sentence ?). But I do believe that some of the logical implications in Zermelo’s paper only make sense if you already assume his theorem.
Via kottke, Clusterflock gives five simple rules for effective bidding on eBay:
Step One:Find the product you want.
Step Two:
Save the product to your watch list.
Step Three:
Wait.
Step Four:
Just before the item ends, enter the maximum amount you are willing to pay for the item.
Step Five:
Click submit.
This is called sniping. That’s a pejorative label for what is actually a sensible and perfectly straightforward way to bid. eBay is essentially an open second-price auction and sniping is a way to submit a “sealed” bid. It’s a popular strategy and advocated by many eBay “experts.” But does it really pay off?
Tanjim Hossain and I did an experiment (ungated version.) We compared sniping to another straightforward strategy we call squatting. As the name suggests, squatting means bidding your value on an object at the very first opportunity, essentially staking a claim on that object. We bid on DVDs and randomly divided auctions into two groups, sniping on the auctions in the first group and squatting on the other.
The two strategies were almost indistinguishable in terms of their payoff. But for an interesting reason. A lot of eBay bidders use a strategy of incremental bidding. That’s where you act as if you are involved in an ascending auction (like an English auction) and you bid the minimum amount needed to become the high biddder. Once you are the high bidder you stop there and wait to see if you are outbid, then you raise your bid again. You do this until either you win or the price goes above the maximum amount you are willing to pay.
Against incremental bidders, sniping has a benefit and a cost (relative to squatting.) You benefit when incremental bidders stop at a price below their value. You swoop in at the end, the incremental bidders have no time to respond, and you win at the low price.
The cost has to do with competition across auctions for similar objects. If I squat on auction A and you are sniping in auction B, our opponents think there is one fewer competitor in auction B and more opponents enter auction B than A. This tends to raise the price in your auction relative to mine. In other words, squatting scares opponents away, sniping does not.
We found that these two effects almost exactly canceled each other out for auctions of DVDs. We expect that this would be true for similar objects that are homogeneous and sold in many simultaneous auctions. So the next time you are bidding in such an auction, don’t think too hard and just bid your value.
Now, I am still trying to figure out what I am going to do with all these copies of 50 First Dates we won in the experiment.
Steven Landsburg set 10 questions for honors graduates at Oberlin College. #8 is a great undergraduate game theory exercise:
Question 8. The five Dukes of Earl are scheduled to arrive at the royal palace on each of the first five days of May. Duke One is scheduled to arrive on the first day of May, Duke Two on the second, etc. Each Duke, upon arrival, can either kill the king or support the king. If he kills the king, he takes the king’s place, becomes the new king, and awaits the next Duke’s arrival. If he supports the king, all subsequent Dukes cancel their visits. A Duke’s first priority is to remain alive, and his second priority is to become king. Who is king on May 6?
visor volley: BoingBoing.
One of the least enjoyable tasks of a journal editor is to nag referees to send reports. Many things have been tried to induce timeliness and responsiveness. We give deadlines. We allow referees to specify their own deadlines. We use automated nag-mails. We even allow referees to opt-in to automated nag-mails (they do and then still ignore them.)
When time has dragged on and a referee is not responding it is typical to send a message saying something like “please let me know if you still plan to provide a report, otherwise i will try to do without it.” These are usually ignored.
A few years ago I tried something new and every time since then it has gotten an almost immediate response, even from referees who have ignored multiple previous nudges. I have suggested it to other editors I know and it works for them too. I have an intuition for why it works (and that’s why I tried it in the first place) but I can’t quite articulate it, perhaps you have ideas. Here is the clinching message:
Dear X
I would like to respond soon to the authors but it would help me a lot if I could have your report. I realize that you are very busy, so if you think you will be able to send me a report within the next week, then please let me know. If you don’t think you will be able to send a report, then there is no need to respond to this message.
Why is blackmail illegal? Sure it’s mean and all but what makes it a crime? This article raises some questions about the legal scholarship behind blackmail. (The background is the Letterman case.)
Whether or not this is how Hollywood really works, Shargel does have a point of logic. The reasoning that makes blackmail illegal–and a great many other similar business activities not illegal — is something that’s never been satisfactorily explained by legal scholars. It remains a paradox of the law. That said, Halderman and Shargel shouldn’t hold their breath until January, when a judge will rule on their motion to dismiss. Even if it makes no sense, blackmail remains a serious crime.
What about the economics of blackmail? There is one obvious economic rationale for making blackmail a crime: rent-seeking. Seeking out and producing incriminating evidence for the express purpose of ultimately keeping it secret is a waste of labor resources and should be discouraged. And this idea explains an otherwise puzzling asymmetry. That is, presumably I can legally accept payment in return for publicizing good information about you. That is tantamount to threatening not to publicize it if you don’t pay me. Whether I threaten withold good information about you or actively publicize bad information about you I am arguably doing the same thing: threatening to lower your reputation relative to what it would otherwise be.
The economic difference is that allowing blackmail leads to unproductive rent-seeking whereas allowing me to charge you for good publicity incentivizes productive information-gathering.
In rare cases blackmail is efficient. If I want you to dig up the dirt on me (perhaps to keep it out of more dangerous hands) we have an incentive problem. I can’t pay you up front because then you have no incentive to do the search. You will come back claiming that my record is so clean that despite all your efforts you came up empty-handed. Instead I would like to pay you ex post in return for the documents. But once you’ve already sunk the cost of searching, I will hold you up and try to renegotiate the fee. The information is not worth anything to you since blackmail is illegal. We would both prefer to allow you to blackmail me ex post. That way I am effectively commited to pay you for your service and you will work hard.
You can trust me to pay you for the information but now the problem is that I can’t trust you. You will show me only half of what you found and blackmail me to keep that a secret. Once you have your money you will show me the other half and blackmail me again. Forseeing this I won’t pay you the first time.
Once you think of this its hard to see how blackmail works at all and why we need to even make it illegal. The blackmailer has to somehow prove that he is not hiding any additional information. That is probably impossible because any incriminating evidence can be copied.
Maybe the problem can be solved with a reciprocal arrangement. You dig up some dirt on me and yourself. Then you offer me the following deal. I pay you the hush money and you hand over the information about you. I will pay you because in return I get a threat against you which deters you from blackmailing me again.
“You’re a cad if you break up around Christmas. And then there’s New Year’s — and you can’t dump somebody right around New Year’s. After that, if you don’t jump on it, is Valentine’s Day,” Savage says. “God forbid if their birthday should fall somewhere between November and February — then you’re really stuck.
“Thanksgiving is really when you have to pull the trigger if you’re not willing to tough it out through February.”
That’s from a story I heard on NPR about turkey dropping: the spike in break-ups at Thanksgiving followed by a steady period (for the surviving pairs) through the Winter months. If there is a social stigma against cutting it off between Thanksgiving and Valentine’s Day, then there may be value in that. Often social rules emerge arbitrarily but persist only if they serve a purpose, even if that purpose is unrelated to the spirit of the social norm. The post-turkey taboo plays the role of a temporary commitment that can strengthen those relationships that are still worth maintaining.
The value of a relationship fluctuates over time. Not just the total value of the partnership relative to autarky but also the value to the individual of remaining committed. The strength of a relationship is precisely measured by the maximum temptation each partner is willing to forego to keep it alive. The moment a jucier temptation appears, the relationship is doomed.
Unless there is commitment. Commitment is a way of pooling incentive constraints. A relationship becomes stronger if each partner can somehow commit in advance to resist all temptations that will arise over the length of the commitment. This transforms your obligation. Now the strength of the relationship is equal to the expected temptation rather than the most severe temptation actually realized. A social stigma against ending the relationship over certain intervals of time aids such a commitment.
Its good that commitments are temporary, but you want their beginning and end dates to be arbitrary, or at least independent of the arrival process of temptations. The total value of the relationship also fluctuates and you want the freedom to end the relationship when it begins to lag the value of being single. This is especially true in the early stages when there is still a lot to learn about the match. Over time when the value of the relationship has clarified, the length of commitment intervals should increase.
Commitments can also solve an unraveling problem. If you know that your partner will succumb to a juciy temptation and you know that its just a matter of time before a juicy temptation arrives, you become willing to give over to a just-a-little-juicy temptation. Knowing this, she is poised to give it up for just about anything. The commitment short-circuits this at the first step.
Mind Your Decisions looks at the game theory of the classic Thanksgiving showdown between Lucy and Charlie Brown.
Time after time, Lucy would bring her football to the park and entice Charlie Brown to practice some place kicks. Lucy would hold the ball, Charlie Brown would run full-steam to kick it only to have Lucy snatch the ball away at the last minute sending Charlie Brown flying, yelling ARRRRGGGHHH and landing in a heap. What a blockhead. Sure you can understand his willingness to trust her the first time, maybe even the first two times, but after that it’s pretty clear what Lucy’s objective is.
You may try to make excuses for Charlie Brown by arguing that subgame-perfection requires a great deal of strategic sophistication. But you don’t need to invoke any refinements here. The unique Nash equilibrium action for Charlie Brown is to say no. Even worse, not yanking the ball is a weakly dominated strategy for Lucy and after that strategy is eliminated, Charlie Brown has a strongly dominant strategy to walk away.
So it is not surprising that in It’s The Great Pumpkin Charlie Brown, he has finally figured this out and flatly refuses to play Lucy’s game. That’s when she goes contract theory on him.
Now we are reaching higher-order blockheadness. First of all, whether or not the contract is valid, its terms are not verifiable to a court. And Charlie Brown should be able to figure out there is something fishy about this contract. Lucy would only offer a contract if she preferred the outcome (run, don’t yank) to the outcome (walk away). But even though Lucy has never directly revealed any preference between these two outcomes, there is pretty good evidence that the worst possible outcome for Lucy would be to see Charlie Brown successfully kick.
Indeed, Lucy knew from the beginning that Charlie Brown would eventually figure out her intention to yank the ball. After that, she knows Charlie Brown will refuse to play. So if Lucy really preferred (run, don’t yank) to (walk away) then she would prevent this evaporation of trust by allowing Charlie Brown to kick the ball at least a few times, but she never did.
The only way to rationalize Lucy’s steadfast insistence on sending him flying is to assume either that (run, don’t yank) is her least-preferred outcome, or that she thinks that Charlie Brown is indeed a blockhead and unable to deduce her intentions. In either case, Charlie Brown should have viewed Lucy’s contract with deep suspicion.
Cute video from Tim Harford on the information economics of office politics.
(My theory is that in fact the managers will get stuck with cleaning coffee pots. The wage-earners are already held to reservation utility while the managers are likely earning rents. And, as illustrated in the video’s epilogue, there is no fully separating equilibrium in the “threaten to resign” game.)
You are playing in you local club golf tournament, getting ready to tee off and there is last-minute addition to the field… Tiger Woods. Will you play better or worse?
The theory of tournaments is an application of game theory used to study how workers respond when you make them compete with one another. Professional sports are ideal natural laboratories where tournament theory can be tested. An intuitive idea is that if two contestants are unequal in ability but the tournament treats them equally, then both contestants should perform poorly (relative to the case when each is competing with a similarly-abled opponent.) The stronger player is very likely to win so the weaker player conserves his effort which in turn enables the stronger player to conserve his effort and still win.
There is a paper by Kellogg professor Jennifer Brown that examines this effect in professional golf tournaments. She compares how the average competitor performs when Tiger Woods is in the tournament relative to when he is not. Controlling for a variety of factors, Tiger Woods’ presence increases (i.e. worsens, remember this is golf) the score of the average golfer, even in the first round of the tournament.
There are actually two reasons why this should be true. First is the direct incentive effect mentioned above. The other is that lesser golfers should take more risks when they are facing tougher competition. Surprisingly, this is not evident in the data. (I take this to be bad news for the theory, but the paper doesn’t draw this conclusion.)
Also, since golf is a competition among many players and there are prizes for second, third etc., the theory does not necessarily imply a Tiger Woods effect. For example, consider the second-best player. For her, what matters is the drop-off in rewards as a player falls from first to second relative to second to third. If the latter is the steeper fall, then Tiger Woods’ presence makes her work harder. Since the paper looks at the average player, then what should matter is something like concavity vs. convexity of the prize schedule.
Also, remember the hypothesis is that both players phone it in. Unfortunately we don’t have a good control for this because we can’t make Tiger Woods play against himself. Perhaps the implied empirical hypothesis says something about the relative variance in the level of play. When Tiger Woods is having a bad season, competition is tighter and that makes him work harder, blunting the effect of the downturn. When he is having a good season, he slacks off again blunting the effect of the boom. By contrast, for the weaker player the incentive effects make his effort pro-cyclical, amplifying temporal variations in ability.
Jonah Lehrer (to whom my fedora is flipped) prefers a psychological explanation.
News Corp., parent company of Fox News is reported to have made an offer for NBC Universal in competition with Comcast. Who should be willing to pay more for an upstream supplier (NBC), the downstream monopolist (Comcast), or an upstream competitor (News Corp.)?
There were no fire engines, horse-drawn or otherwise. The citizens were the fire department. Each house had its own firebuckets and in the event of a fire, everyone was meant to pitch in. That meant taking your firebucket and joining the line of people from the water tank to the fire.
Does the story so far give you a warm, fuzzy feeling? Friendly folk working together, helping each other out and living by the Kantian categorical imperative. Let me rain on your parade – I am an economist after all. The private provision of public goods is subject to a free-rider problem: The costs of helping someone else outweigh the direct benefits to me so I don’t do it. Everyone reasons the same way so we get the good old Prisoner’s Dilemma and a collectively worse equilibrium outcome.
People have to come up with some other mechanism to mitigate these incentives. In Concord, they chose a contractual solution. Each fire-bucket had the owner’s name and address on it. If any were missing from the fire, you could identify the free-rider and they were fined.
This is the story we got from the excellent tour guide at the Old Manse house in Concord. Home to William Emerson, rented by Nathaniel Hawthorne and overlooking the North Bridge, the location of the first battle of the American Revolution. (We were carefully told that earlier that same historic day in Lexington, although the Redcoats fired, the Minutemen did not fire back so that was not a real battle.) The house has the old firebuckets hanging up by the staircase.
Karthik Shashidar writes to us:
I am a regular reader of your blog, and like most of the stuff that you guys put there. Yesterday while blogging, I came across something which I thought might interest you people, hence I’m writing to you.
Recently my girlfriend and I realized that we were spending way too much time talking to and thinking about each other, and that we needed to scale down in order to give us time to do other things that we want to do. Both of us are in extremely busy jobs and hence time available for other things (including each other) is very limited, and hence the need to scale down.
I was wondering why this is not a widespread phenomenon and why more couples don’t do this “scaling down”
His analysis is here.
There is a natural force pushing couples toward too much engagement. Unilateral escalations make your partner feel good. Even if you internalize the long-run cost due to the inevitable following-suit, the slightest bit of discounting means that the equilibrium level will be above the social optimum. The usual dynamic game logic seems especially perverse here. If I am extra sweet to my sweet does she punish me for that? And what form does the punishment take, even further escalation?
Negotiating down from these heights is indeed tricky. Unilateral de-escalation is risky as Karthik discusses on his blog. The proposal could easily be read as a cold shoulder. Even assuming that both agree to scale down, how do you decide where to go? It is not easy to describe in words a precise level of interaction and this ambiguity leads to the potential for hurt feelings, if there is mis-coordination.
Some dimensions are easier to contract on. It’s easy to commit to go out only on Tuesday nights. However, text messages are impossible to count and the distortions due to overcompensation on these slippery-slope dimensions may turn out even worse than the original state of affairs.
But even setting aside all of these problems, what mechanism can you use to coordinate on a lower scale? If we both make offers and split-the-difference, then the one asking for a higher scale is going to feel hurt. Any mechanism has got to be noisy enough to hide such inequities without being totally random. The trick may be to short-circuit common knowledge. For example we could have a third party make a take-it-or-leave-it proposal and then the two partners secretly reject (if too low) or accept (if not.) The proposal is enacted only if both accept.
This ensures that when the offer is accepted, both parties learn only that each was willing to scale down to at least the same level. And when the offer is rejected, the one who was not willing to go that low will never know whether the other was, i.e. no hurt feelings.
(dinner conversation with Utku, Samson, and Hideo.)
Computer scientists study game theory from the perspective of computability.
Daskalakis, working with Christos Papadimitriou of the University of California, Berkeley, and the University of Liverpool’s Paul Goldberg, has shown that for some games, the Nash equilibrium is so hard to calculate that all the computers in the world couldn’t find it in the lifetime of the universe. And in those cases, Daskalakis believes, human beings playing the game probably haven’t found it either.
Solving the n-body problem is beyond the capabilities of the world’s smartest mathematicians. How do those rocks-for-brains planets manage to do pull it off?
Big events at Northwestern this weekend, including Paul Milgrom’s Nemmers’ Prize lecture and a conference in his honor. (My relative status was microscopic.) A major theme of the conference was market design and I heard a story repeated a few times by participants connected with research and implementation of online ad auctions.
Ads served by Yahoo!, Google and others are sold to advertisers using auctions. These auctions are run at very high frequencies. Advertisers bid for space on specific pages at specific times and served to users which are carefully profiled by their search behavior. This enables advertisers to target users by location, revealed interests, and other characteristics.
Not content with these instruments, McDonalds is alleged to have proposed to Yahoo! a unique way to target their ads and their proposal has come to be known as The Happy Contract. Instead of linking their bids to personal profiles of users, they asked to link their bids to weather reports. McDonalds would bid for ad space only when and where the sun was shining. That way sunshine-induced good moods would be associated with impressions of Big Macs, and (here’s the winner’s curse) the foul-weather moods would get lumped with the Whopper.
He is a political scientist at NYU who uses spreadsheets to predict how conflicts will be resolved. He consults for the CIA, earns $50,000 per prediction, and uses his brand of game theory to offer wisdom on questions like “How fully will France participate in the Strategic Defense Initiative?” and “What policy will Beijing adopt toward Taiwan’s role in the Asian Development Bank?”
To predict how leaders will behave in a conflict, Bueno de Mesquita starts with a specific prediction he wants to make, then interviews four or five experts who know the situation well. He identifies the stakeholders who will exert pressure on the outcome (typically 20 or 30 players) and gets the experts to assign values to the stakeholders in four categories: What outcome do the players want? How hard will they work to get it? How much clout can they exert on others? How firm is their resolve? Each value is expressed as a number on its own arbitrary scale, like 0 to 200. (Sometimes Bueno de Mesquita skips the experts, simply reads newspaper and journal articles and generates his own list of players and numbers.) For example, in the case of Iran’s bomb, Bueno de Mesquita set Ahmadinejad’s preferred outcome at 180 and, on a scale of 0 to 100, his desire to get it at 90, his power at 5 and his resolve at 90.
His model is a secret but it seems to be some kind of dynamic coalition formation model. He has predicted that Iran will not obtain a nuclear weapon owing to the rising power of dissident coalitions. In August,
He spent that morning looking over his Iranian data, and he generated a new chart predicting how the dissidents’ power would grow over the next few months. In terms of power, one category — students — would surpass Ahmadinejad during the summer, and by September or October their clout would rival that of Khamenei, the supreme leader. “And that’s huge!” Bueno de Mesquita said excitedly. “If that’s right, it’s huge!” He said he believed that Iran’s domestic politics would remain quiet over the summer, then he thought they’d “really perk up again” by the fall.
A long profile appeared in The New York Times Magazine.
You are attending a conference or other event which brings together a large group of people vaguely acquainted but not tightly connected. There is a dinner where there are many tables seating 6-8 people each. There is no assigned seating. Assuming you care about whom you will sit with, what is your strategy for finding a place to sit?
- To the extent possible, the high-status people will contract early and grab a table to themselves. This is usually possible because in groups like this it is the high-status people who are most likely to know each other well.
- Low-status people often prefer to sit with higher-status people, so they tend to play the waiting game and hop in on a table with some open seats. This usually turns out to be a bad idea (dull and awkward conversation) but it takes a few bad experiences to figure this out. By that time the lesson is irrelevant because your status has improved.
- Middle-status people have learned to care less about the status of those they dine with. And they are not yet so visible that everyone wants to sit with them just out of status-mongering. So their optimal strategy is to move early and find an empty table and sit there. They will be joined by people who are really interested in them and those are the people you want to sit with.
- The latter is generally my strategy. However, usually people don’t want to sit with me. Consistent with the logic of the strategy, this is optimal when it happens.
- There is must be something unique about weddings because there is almost always assigned seating.
- The closer people are to being total strangers the stricter the status ranking becomes, in my experience. Without anything to go on, it boils down to attractiveness. A strict, linear status ranking leads to unraveling as everyone waits to join the best table. This is when assigned seating is necessary. But I don’t think this explains weddings.
The question is ripe for experimental research.
Despite my vast legion of Twitter followers, every one of my attempts to start a new trending topic has failed to catch on. Now I think I understand why.
Suppose that your goal is to coordinate attention on a topic that seems to be on a lot of minds. Attention is a scarce resource and you have only a limited number of topics you can highlight. But suppose, as with Twitter, you see what everyone is talking about. How do you decide which topics to point to?
You probably shouldn’t just count the total number of people talking on a given subject, counting everyone equally. You might think that you would instead give extra weight to the few people that everyone is listening to. Because whatever they say is more likely to be interesting to many, and will soon be on many minds. On Twitter, those would be the people with the most followers. But there is a strong case for doing the opposite and giving extra weight to people with few followers, especially people who are relatively isolated in the social network. This is not out of fairness (or pity) but actually as the efficient way to use your scarce resource.
Efficient coordination means making information public so that not just everyone knows it, but everyone knows that everyone knows it (etc.) If we all have to choose simultaneously what to focus our attention on and we want to be part of the larger conversation, then it matters what we think others are going to focus their attention on. Coordinating attention thus requires making it public what people are talking about.
Suppose we have two topics that are getting a lot of attention, but topic A is being discussed by well-connected individuals and topic B is being discussed more by a diverse group of isolated individuals. Topic A is already public because when you see it discussed by a central figure you know that all other of her followers are seeing it to. Topic B therefore has more to gain from elevating it to the status of trending topic, which immediately makes it public.
I always knew that my Twitter followers were among the wisest. Now I see the true depth of their wisdom. By adding to my follower numbers, they reduce the weight of my comments in the optimal weighting scheme thus ensuring that the crazy things I say will be ingored by the larger network. Join the cause.
We all know about generic drugs and their brand-name counterparts. The identical chemical with two different prices. Health insurance companies try to keep costs down by incentivizing patients to choose generics. You have a larger co-pay when you buy the name brand. Except when you don’t:
Serra, a paralegal, went to his doctor a few months ago for help with acne. She prescribed Solodyn. Serra told her he’d previously taken a generic drug called minocycline that worked well. The doctor told him that the two compounds are basically the same, but that you have to take the generic version in the morning and the evening. With Solodyn, you take one dose a day.
Serra told her that if the name-brand medicine was going to cost a lot more, he’d prefer the generic. “And then she presented this card,” he says. She explained that it was a coupon, and that he should give it to the pharmacist for a break on his insurance copay.
Without the card, Serra’s copay would have been $154.28. But when he got to the pharmacy, he presented his card. “They went to ring it up at the register,” he remembers. “And when it came up, the price was $10.”
NPR has the story. Chupulla chuck: Mike Whinston.
Swoopo.com has been called “the crack cocaine of auction sites.” Numerous bloggers have commented on its “penny auction” format wherein each successive bid has an immediate cost to the bidder (whether or not that bidder is the eventual winner) and also raises the final price by a penny. The anecdotal evidence is that, while sometimes auctions close at bargain prices, often the total cost to the winning bidder far exceeds the market price of the good up for sale. The usual diagnosis is that Swoopo bidders fall prey to sunk-cost fallacies: they keep bidding in a misguided attempt to recoup their (sunk) losses.
Do the high prices necessarily mean that penny auctions are a bad deal? And do the outcomes necessarily reveal that Swoopo bidders are irrational in some way? Toomas Hinnosaar has done an equilibrium analysis of penny auctions and related formats and he has shown that the huge volatility in prices is in fact implied by fully rational bidders who are not prone to any sunk-cost fallacy. In fact, it is precisely the sunk nature of swoopo bidding costs that leads a rational bidder to ignore them and to continue bidding if there remains a good chance of winning.
This effect is most dramatic in “free” auctions where the final price of the good is fixed (say at zero, why not?) Then bidding resembles a pure war of attrition: every bid costs a penny and whoever is the last standing gets the good for free. Losers go home with many fewer pennies. (By contrast to a war of attrition, you can sit on the sidelines as long as you want and jump in on the bidding at any time.) Toomas shows that when rational bidders bid according to equilibrium strategies in free auctions, the auction ends with positive probability at any point between zero bids and infinitely many bids.
So the volatility is exactly what you would expect from fully rational bidders. However, Toomas shows that there is a smoking gun in the data that shows that real-world swoopo bidders are not the fully rational players in his model. In any equilibrium, sellers cannot be making positive profits otherwise bidders are making losses on average. Rational bidders would not enter a competition which gives them losses on average.
In the following graph you will see the actual distribution of seller profits from penny auctions and free auctions. The volatility matches the model very well but the average profit margin (as a percentage of the object’s value) is clearly positive in both cases. This could not happen in equilibrium.
I heard an interview with Reggie Jackson and Bob Gibson (former baseball greats) on NPR’s Fresh Air this weekend. They spent a lot of time talking about pitching inside and “brushing back” hitters. Reggie Jackson, a hitter, conceded that these were “part of the game.”
There is a mundane sense in which this is true, namely that not even the best pitcher has flawless control and sometimes batters get hit. But Reggie was even talking about intentional beanballs. In what sense is this part of the game?
The penalty for throwing inside is that, if you hit the batter, he gets a free base. (And your teammate might get beaned at the next opportunity.) The problem is that this penalty trigger is partly controlled by the opposition. Other things equal it gives the batter an incentive to stand a bit closer to the plate. In order to discourage this, the pitcher must establish a reputation for throwing inside when a batter crowds the plate. In that sense, intentionally throwing at the hitter is unavoidable strategy, part of the game.
So, one way to short-circuit this effect is to change the condition for giving a free base to something that is exogenous, i.e. independent of any choice made by the batter. For example, the batter gets a free base any time the ball sails more than some fixed distance inside of the plate, whether or not it actually hits the batter. Modern technology could certainly detect this with minimal error.
Whatever the merits of the claims made about Fox News by Obama’s communications team, it can be good strategy to pick a fight with your critics. To the very long list of reasons, add this one. If you can make them so angry that they lose the will to say anything at all nice about you, then you have won a major victory. For then they will have lost all (remaining) credibility.
Not game theory, but research about and even within games. Hit or miss:
One of the most high-profile projects (and most obvious recent failures) was Indiana University’s Arden: The World Of William Shakespeare, which reportedly had a grant of $250,000. It was an experimental MMO which came about via the work of Professor Ed Castronova, author of Synthetic Worlds. Castronova wondered whether the creation of a genuinely educational MMO was possible, and set up the student development project to find out. Having spent thousands of dollars on Arden it was shut down. Castronova cited “a lack of fun”.
via BoingBoing.
There is a story in the Wall Street Journal about user ratings on web sites such as Amazon or eBay. It seems that raters are unduly generous with their stars.
One of the Web’s little secrets is that when consumers write online reviews, they tend to leave positive ratings: The average grade for things online is about 4.3 stars out of five.
And some users are fighting back:
That’s why Amazon reviewer Marc Schenker in Vancouver has become a Web-ratings vigilante. For the past several years, he has left nothing but one-star reviews for products. He has called men’s magazine Maxim a “bacchanalia of hedonism,” and described “The Diary of Anne Frank” as “very, very, very disappointing.”
I have noticed that Amazon reviewers are highly polarized with 5 stars being the most common with 1 star reiews coming in second. And in fact it makes a lot of sense. Say you think that a product is over-rated at 4.3 stars and you think that 4 stars is more appropriate. If there are more than just a few ratings, then to bring the average down to 4 you would have to give the lowest possible rating.
Once enough ratings have already been counted, subsequent raters will be effectively engaging in a tug of war. Those that want to raise the average will give 5 stars and those that want to reduce it will give 1.
Many Senators who support health care reform have made public commitments not to vote for any bill without a public option. Such pronouncements are not cheap talk. The pledge can be broken of course but constituents and fellow legislators will hold to account a Senator who breaks it.
And they can be relevant. A commitment not to vote for the Baucus bill raises the costs of proposing that bill because the pledged Senator would have to be compensated for breaking his pledge if he is going to be brought on board. In a simple bargaining game, the pledge will be made if and only if the cost of breaking the pledge is higher than the proposer is willing to pay. In this case the Baucus bill would not be proposed.
But legislative bargaining is not so simple. Each Senator has only one vote. A Senator who commits not to vote for the Baucus bill effectively moves the median voter (for that bill) one Senator to the right. This changes things in three ways by comparison to simple bargaining.
- The committed Senator will not be the median voter and so he will not be part of the bargaining.
- There is presumably a relatively small gap between the old median and the new so the costs imposed by the pre-commitment are much smaller.
- In the event that the gambit fails and the Baucus bill is proposed, it will be a worse bill from the perspective of the gambiteer (it will be farther to the right.)
This means that the commitment is a much less attractive strategy in the legislative setting and it loses much of its relevance. That is, those who are making this commitment would probably not have been willing to vote for the Baucus bill even without any pledge.
Wired reports that the Soviet Union actually had a doomsday device and kept it a secret.
“The whole point of the doomsday machine is lost if you keep it a secret!” cries Dr. Strangelove. “Why didn’t you tell the world?” After all, such a device works as a deterrent only if the enemy is aware of its existence. In the movie, the Soviet ambassador can only lamely respond, “It was to be announced at the party congress on Monday.”
So why was the US not informed about Perimeter? Kremlinologists have long noted the Soviet military’s extreme penchant for secrecy, but surely that couldn’t fully explain what appears to be a self-defeating strategic error of extraordinary magnitude.
The silence can be attributed partly to fears that the US would figure out how to disable the system. But the principal reason is more complicated and surprising. According to both Yarynich and Zheleznyakov, Perimeter was never meant as a traditional doomsday machine. The Soviets had taken game theory one step further than Kubrick, Szilard, and everyone else: They built a system to deter themselves.
By guaranteeing that Moscow could hit back, Perimeter was actually designed to keep an overeager Soviet military or civilian leader from launching prematurely during a crisis. The point, Zheleznyakov says, was “to cool down all these hotheads and extremists. No matter what was going to happen, there still would be revenge. Those who attack us will be punished.”
The logic is a tad fishy. But it is not obvious that you should reveal a doomsday device if you have one. It is impossible to prove that you have one so if it really had a deterrent effect you would announce you have one even if you don’t. So it can’t have a deterrent effect. And therefore you will always turn it off.
What you should worry about is announcing you have a doomsday device to an enemy who previously was not aware that there was such a thing. It still won’t have any deterrent effect but it will surely escalate the conflict. (via free exchange via Mallesh Pai.)
We talked a lot before about designing a scoring system for sports like tennis. There is some non-fanciful economics based on such questions. Suppose you have two candidates for promotion and you want to promote the candidate who is most talented. You can observe their output but output is a noisy signal that depends not just on talent, but also effort both of which you cannot observe directly. (Think of them as associates in a law firm. You see how much they bill but you cannot disentangle hard work from talent. You must promote one to partner where hard work matters less and talent matters more.)
How do you decide whom to promote? The question is the same as how to design a scoring system in tennis to maximize the probability that the winner is the one who is most talented.
One aspect of the optimal contest seems clear. You should let them set the rules. If a candidate knows he has high ability he should be given the option to offer a handicap to his rival. Only a truly talented candidate would be willing to offer a handicap. So if you see that candidate A is willing to offer a higher handicap than candidate B, then you should reward A.
The rub is that you have to reward A, but give B a handicap. Is it possible to do both?
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