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Following up on Sandeep’s post about Alex Rodriguez’s alleged pitch-tipping, a game theorist is naturally led to ask a few questions. How is a tipping ring sustainable? If it is sustainable what is the efficient pitch-tipping scheme? Finally, how would we spot it in the data?
A cooperative pitch-tipping arrangement would be difficult, but not impossible to support. Just as with price-fixing and bid-rigging schemes, maintaining the collusive arrangement benefits the insiders as a group, but each individual member has an incentive to cheat on the deal if he can get away with it. Ensuring compliance involves the implicit understanding that cheaters will be excluded from future benefits, or maybe even punished.
What would make this hard to enforce in the case of pitch-tipping is that it would be hard to detail exactly what compliance means and therefore hard to reach any firm understanding of what behavior would and would not be tolerated. For example, if the game is not close but its still early innings is the deal on? What if the star pitcher is on the mound, maybe a friend of one of the colluders? Sometimes the shortstop might not be able to see the sign or he is not privy to an on-the-fly change in signs between the pitcher and catcher. If he tips the wrong pitch by mistake, will he be punished? If not, then he has an excuse to cheat on the deal.
These issues limit the scope of any pitch-tipping ring. There must be clearly identifiable circumstances under which the deal is on. Provided the colluders can reach an understanding of these bright-lines, they can enforce compliance.
There is not much to gain from pitch-tipping when the deal becomes active only in highly imbalanced games. But the most efficient ring will make the most of it. A deal between just two shortstops will benefit each only when their two teams meet. A rare occurrence. Each member of the group benefits if a shortstop from a heretofore unrepresented team is allowed in on the deal. Increasing the value of the deal has the added benefit of making exclusion more costly and so helps enforcement. So the most efficient ring will include the shortstop from every team. Another advantage of including a player from every team in the league is that it would make it harder to detect the pitch-tipping scheme in the data. If instead some team was excluded then it would be possible to see in the data that A-Rod hit worse on average against that team, controlling for other factors.
But it should stop there. There is no benefit to having a second player, say the second-baseman, from the same team on the deal. While the second-baseman would benefit, he would add nothing new to the rest of the ring and would be one more potential cheater that would have to be monitored.
How could a ring be detected in data? One test I already mentioned, but a sophisticated ring would avoid detection in that way. Another test would be to compare the performance of the shortstops with the left-fielders. But there is one smoking gun of any collusive deal: the punishments. As discussed above, when monitoring is not perfect, there will be times when it appears that a ring member has cheated and he will have to be punished. In the data this will show up as a downgrade in that player’s performance in those scenarios where the ring is active. And to distinguish this from a run-of-the-mill slump, one would look for downgrades in performance in the pitch-tipping scenarios (big lead by some team) which are not accompanied by downgrades in performance in the rest of the game (when it is close.)
The data are available.
I’m almost beginning to feel sorry for Alex Rodriguez. Everyone is picking on him. The latest strike against him is that he is being accused of collusion. He has an enviable batting record but now it seems the figures may be inflated. Alex is accused of pitch-tipping. Pitch-tipping involves somehow signaling the oncoming pitch to the hitter of the opposing team. According to an op-ed in NYT:
So, according to the latest story, Alex is connected to some pitch-tipping scheme in which he relayed signs to the opposing hitter (if he was a friend) or for someone who would return the favor when he was hitting. This was supposedly done in one-sided games where, in theory, one team had no chance of catching up. Alex was said to be in cahoots with a lot of middle infielders. Allegedly, there was some sign he would relay to the hitter — a movement with his glove or his feet — to let the hitter know what type of pitch was coming and where.
That is, there was “I scratch your back and you scratch mine” equilibrium. No contract is in place to enforce this so it would have to be enforced implicitly over multiple rounds as a repeated game equilibrium. It’s pretty cunning and companies have been known to do it. Alex didn’t need a M.B.A. to be taught it. He learned it in the game of hard strikes.
(Hat tip: Pablo Montagnes, PhD student).
A game-theorists’ term derived from the commonplace admonishment “Talk is Cheap.” To say that “talk is cheap” is to suggest that words have no meaning because they don’t raise the stakes. “Actions speak louder than words.” Or, to quote the game theorist Yogi Berra “A verbal contract isn’t worth the paper it’s written on.” Our casual understanding that the meaning of words derives solely from their ultimate consequences demonstrates that we have deep game-theoretic instincts.
But game theory is useful because with careful study we arrive at insights one or more steps beyond our instincts. And indeed, upon further reflection, just because talk is cheap does not imply by itself that words have no meaning. In fact “cheap talk” can and often does matter because it enables credible exchange of information provided such communication is consistent with self-interested motives. Even though talk is cheap, when upon landing at O’Hare, I phone my taxi dispatcher and tell him I am ready to be picked up at the curbside, he believes me and sends a cab.
Moreover, cheap talk is credible even when there is substantial conflict of interest between the talker and the listener. Despite my claims to the contrary, the dispatcher knows that I am actually calling from inside the airplane and I am not at the curbside yet and he delays the dispatch long enough so that the driver arrives at the curbside after me and not before.
Suprisingly, talk can be credible sometimes only because it is cheap. If instead of me, it is an uninterested third-party who calls the dispatcher to send a cab, the dispatcher knows that she has no reason to say anything other than the truth, and the dispatcher sends the cab immediately.
A final digression on the genesis of the phrase “cheap talk” as a term of art in game theory. It is tempting to suppose that the popularity of the phrase derives from the irony that the logic of incentive-compatible communication turns the idea that “talk is cheap” on its head. But the origin of the phrase is something of a mystery. The first game theorists to demonstrate the role of communication in strategic interactions were Vince Crawford and Joel Sobel in their hugely important paper “Strategic Information Transmission” Interestingly, a quick search through the text of that paper reveals that neither “cheap” nor “talk” appears anywhere in the paper.
(dinner conversation with Dilip, Tomek, Stephen and Sylvain acknowledged.)
The chef Bobby Flay is ubiquitous on the Food Network. I usually see him in two shows, Iron Chef America and Throwdown with Bobby Flay. Both are competitive shows. Flay usually loses on Throwdown and wins on Iron Chef.
On Throwdown, Bobby Flay makes one dish and competes with an expert . For example, recently there was a show where he made a deep dish pizza against Chicago native Lou Malnati. The two dishes are judged by two experts side by side with a partisan local audience watching. Flay lost.
On Iron Chef America, the format is different. There is a secret ingredient (though I bet both contestants have a fair idea of what it will be!). In this format, Flay and his fellow Iron Chefs are matched against a gourmet chef. Last week the secret ingredient was butter. The entrant was Koren Grieveson of avec in Chicago. Koren picked Cat Cora to compete against. And the competition was tied. As I said, this is a rare event in Iron Chef because the incumbent usually wins. Why?
I think it’s all in the judging. On Iron Chef, the chefs get to present their dishes to the judges so there is no anonymity. On Throwdown, they do not identify who cooked which dish.
I wish they would adopt the same format for Iron Chef. The judges are biased towards the incumbent. For example, while Cat Cora’s food looked good, she won more points in the category of “originality”. One of her dishes was bread and butter, another was gnocchi in a butter sage sauce. These are original only if one adopts an ironic definition of the word “original”. But then everything is original and the category makes no sense! Frankly, I went to avec last night and I just find it hard to believe Cat Cora’s food is better. Maybe I am expressing the bias manifested on Throwdown: the bias of the local audience towards the local contestant. This can also be fixed by making the judges judge in a different room. Similarly, on Iron Chef, a third party, say Alton Brown, could present the dishes. If the judges have questions, the show can set up speakers in a separate room where the chef is standing nervously. S/he can answer the questions into an earpiece worn by Alton Brown. He can relay the answers to the judges. This can be done in a theatrical way to add more drama and tension.
A basketball game where one team is vastly superior to the other is boring to watch. By leveling the playing field, Food Network can add more uncertainty to the competition and get more viewers.
Writing and studying for an exam is a game played between Professor and student. In this game the Professor has to pick which questions to ask and the student has to pick which topics to study. The game has the flavor of rock-scissors-paper in that the Professor would like to be unpredictable. That way the students will have to devote studying time to all topics rather than focus on just one that they know the Professor will ask about.
But the Professor might not want the students to spend too much time memorizing concepts from the book. Instead he may want them to spend their time thinking about how to apply those concepts to new problems. How can the Professor be unpredictable and still deter the students from trying to memorize the book? The solution is to use an open book exam. This way the Professor is committing not to ask rote questions which would turn the exam into nothing more than a contest to see which students are the fastest to search through the book and find the topic.
With an open-book exam, the students can predict that the Professor will not ask such questions and they will not bother studying for them. They bring their books to the exam and never have to open them. And they still cannot predict which questions (apart from the mundane ones) the Professor will ask.
Keep in mind that this means students should dislike open-book exams. Many students don’t understand this and are always asking for open-book.
Also, the worst possible format is the common practice of allowing students to write out crib notes on one sheet of paper. This turns studying into pure rent-seeking. All students will predict which are the essential concepts from the book and will write them down and, predicting this, the Professor will not ask questions about those topics. In the end the outcome is just like open-book except the poor students lose valuable studying time while they squeeze the book onto a sheet of paper.
(To my PhD students and undergrads taking exams today: aren’t you glad the exams are closed book? Oh and good luck!)
William J. Fell, the parking meter repairman in Alexandria VA, skimmed $170,000 worth of coins from parking meters over the course of one year.
The 61-year-old city employee did it, police say, by going to work at 3 a.m., well before his shift started. He would jump in his city truck and, under the cover of darkness, empty into bags the contents of coin canisters from parking meters all over Old Town, according to court documents.
Done carefully, taking a constant percentage, this would be hard to detect based purely on tracking total revenue. However, at some point the city raised the parking rate to $1 per hour. How do you adjust your skimming rate to avoid detection?
Last year, the city took in just over $1 million in revenue from its 1,040 parking meters, officials said. But they realized something was amiss. They had raised the rates to $1 an hour but weren’t getting as much money as they expected.
Oops. If Mr. Fell thinks that the city knows the correct elasticity of demand, then he should keep the same skim rate as before. That way the city sees exactly the percentage change in revenue they were expecting. Apparently Mr. Fell thought that the city had overestimated demand elasticity and therefore was expecting a smaller increase in revenue than they were actually getting so he raised his skim rate to compensate.
Of course, alternative explanation is that Mr. Fell is not motivated by standard economic incentives:
That much money in quarters, dimes and nickels would weigh at least four tons. If it was all in nickels, it would weigh nearly 19 tons.
Police were perplexed after they subpoenaed Fell’s bank accounts but did not see any of the money there. That was when they decided that it might be in his home and executed a search warrant April 15 — tax day.
Police say Fell, who lives alone, did not appear to use the money for anything specific and mostly just kept it in his home.
Smart classroom + YouTube + Golden Balls.
Golden balls indeed.
For the game theorists in the room, the difference must boil down to whether we have random matching across populations (case 1) or within a single population (case 2.)
Scrabble point revaluation in the works?
“Za,” “qi” and “zzz” were added recently to the game’s official word list for its original English-language edition. Because Z’s and Q’s each have the game’s highest point value of 10, those monosyllabic words can rack up big scores for relatively little effort. So now that those high-scoring letters are more versatile, some Scrabble aficionados would like to see the rules changed — which would be the only change since Alfred Butts popularized the game in 1948.
Let’s kill two birds with one stone. Eliminate the role of chance in scrabble by having players buy their letters rather than draw them at random. Whenever a player needs to replenish his tiles, a tile is turned over and put up for auction. Players bid for the tile with points. A player who already has seven tiles who wins the auction selects one of his tiles to replace and puts that tile up for auction. This continues until all players have seven tiles.
This removes chance from the game and also eliminates the need to revalue the tiles because that will be taken care of endogenously by competitive bidding.
Update: Free Exchange at http://www.economist.com makes fun of me.
Tyler Cowen asks why do people lose originality as they gain influence? There are two observationally equivalent ways to explain it.
- Since nobody really knows anything more than anybody else, opinion-rendering boils down to a game where everybody makes a random guess. The outcome of this game is that one person says something unconventional that turns out to be right. (by pure luck.) He gets noticed for that. Influence is the reward for being noticed. (We don’t have to assume that the public is unaware that he is just as ignorant as everyone else. The public is just trying to coordinate on whom to listen to. Winning the random-guessing game makes him a focal point.) Having influence is nice and in order not to jeopardize that he goes on saying the same thing as before which turned out to be right and is now conventional wisdom.
- Since nobody really knows anything more than anybody else, opinion-rendering boils down to a game where everybody makes a random guess. And people go on making random guesses over and over. People whose guesses are right get noticed and get influence, the more unconventional the guess the more you get noticed. Its very rare that something really unconventional is correct, so the people who repeatedly make unconventional guesses eventually lose influence. It follows that those that survive this game for a long time are those whose random guesses were unconventional once and conventional the remainder of the time. We forget about all of the others.
Tyler asked for case studies. But given the nature of the question what he really wants is a theory that generates a forecast that we can test against future data. So as you guessed from the title, my case study is Noriel Roubini. In 10 years he will either continue to be a regular talking head who no longer says anything unconventional (theory 1) or he will continue to make unconventional guesses and will have lost influence and be forgotten (theory 2).
Suppose you are going to say something that is literally true but you know in advance that your listener will misinterpret you and be led to believe something false. If you say it anyway, are you lying?
Conversely, is it a lie to say a falseshood if you know that, because you will be misinterpreted, this is the only way to get your listener to believe in what is actually true?
Naming a blog is like naming a baby. * Those of us who have gone thorugh the baby-naming process recognize some subtle strategic issues that arise. Each spouse searches for names in books, online, in the garden, etc. and when a good idea comes up suggests it to the other spouse. Then there is some discussion and possibly the name is put on the shortlist and the process continues. At some point a name has to be chosen.
Here is where the strategy comes in. Suppose there is a name you really like and you think your spouse might find acceptable, let’s say Hercules. You put Hercules on the shortlist. But now suppose you come up with another name that you know your spouse likes better than the first one but which boders on unacceptable for you. Let’s say “Brad.” Do you suggest Brad?
At first glance it seems obvious you should hide Brad in the drawer, lock it tight and throw away the key. But its not always clear. By suggesting Brad you might convince your spouse that you are playing ball and you might get points for that and it might even improve the chances of a baby Hercules.
In fact, I think something like this would be a property of an efficient mechanism. In economics we think about situations like this and how to design the rules of the game to deliver an acceptable outcome, in this case a baby whose name will not scar him for life. The unusual feature of this particular problem is that the alternatives, i.e. the possible names, are not given in advance but have to be suggested in order to be considered. If I keep “Brad” a secret, chances are my spouse won’t think of it and I won’t have to worry about it.
So the key issue in designing the rules of this game is to give each spouse enough incentive to reveal the names that they might otherwise try to keep secret. After all, taking into account both spouses preferences, Brad might actually be the best name if say my spouse really likes it much better than Hercules. And in that event we want to give it a chance to be selected.
How would we design the rules to give that incentive? The only way to do this is to “pay” a spouse who offers an additional name by increasing the chance of that spouse getting his preferred choice. And in practice the goodwill your spouse feels when you suggested Brad has exactly this effect.
*In answer to your question, Sandeep is the Mommy.
Cheap Talk 