Signaling and Screening in Incomplete Information Games

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– 1 – UNIVERSITY OF PIRAEUS Department of International and European Studies Signaling and Screening in Incomplete Information Games John A. Paravantis Associate Professor May 2021

Transcript of Signaling and Screening in Incomplete Information Games

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UNIVERSITY OF PIRAEUS Department of International and European Studies

Signaling and Screening in Incomplete Information Games

John A. Paravantis Associate Professor

May 2021

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Games of incomplete information Hunt for Red October contains dynamic games with incomplete information In such games, there is a lot of signaling (σινιάλο ή σηματοδότηση) and screening (κόσκινο ή κρησάρα). Throughout this presentation, I rely heavily on Dixit and Nalebuff (2008).

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Tiffany wants to get married… Tiffany is in love with a successful business executive. He is smart, single and straight. She is … 37 years old and wants to have kids. His kids from a previous marriage are not ready for him to remarry. Tiffany wants a credible signal that he is serious about her. So she demands that he get a tattoo!

The guy refused and failed Tiffany’s screening device. Tiffany got married – he is still on the runway, on permanent ground delay…

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Some thoughts A credible signal is the cousin of a commitment device. Τhere are strategies that guarantee that a player will carry out what was promised. Signaling and screening looks for something weaker.

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How about telling the truth? Why can’t we rely on others to tell the true? Because it might be against their interests! Sometimes, people’s interests and communications are aligned. For instance, when you order a steak medium rare, the waiter can safely assume that you really want your steak medium rare. But if you ask the waiter for a recommendation, he may try to steer you to a more expensive item! C.P. Snow, attributing strategic insight to the mathematician G.H. Hardy:

If the Archbishop of Canterbury says he believes in God, that

is all in the way of business, but if he says he doesn’t, one can

take it he means what he says.”

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So, what should we do? The greater the conflict, the less the message may be trusted. Suppose that, right before taking a penalty shot, a striker shouts «I am going right». Should the goalkeeper believe him? In fact, the kicker might be trying even a second level deception – lying by telling the truth! The only rational reaction to an assertion (such as a promise or a threat) made by another player whose interests are totally opposed to yours is to ignore it completely. Don’t assume it to be true and don’t assume its opposite to be true either – just thing about the equilibrium of the actual game.

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King Solomon’s dilemma

1 Kings (3), The Oxford Annotated Bible (1962).

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Building a reputation

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Was King Solomon wise or lucky? The second woman made a strategic blunder. She should have simply repeated whatever the first woman said. King Solomon was both wise and lucky: his strategy worked because of the second woman’s error. A true game theory king could have set up a bidding game, designed so that the false claimant would give up the child for fear of paying a large fine (that the true mother would have paid gladly).

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Manipulating information The kind of problems faced by Tiffany and Solomon arise in many strategic interactions. Some players know more than others about something that affects all payoffs. Some who possess extra information are keen to conceal it (like the false claimant in Solomon’s story). Others are keen to reveal the truth (like the true mother). Players with less information (like King Solomon) typically want to elicit it truth from those who know it.

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Actions speak louder than words General principle governing such situations: actions speak louder than words! Players should watch what another player does not what he says. In «The Love Song of J. Alfred Prufrock», T.S. Eliot (1888–1965) writes that one should constantly

prepare a face to meet the faces that you meet

recognizing that our «face» is our actions that are being interpreted in certain ways by other people. So we should not behave in ways that work to our disadvantage.

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Signaling, signal jamming and screening Players in strategic games who possess special information will try to conceal it if may hurt their interests when it becomes known. On the other hand, they will take actions that, when properly interpreted, reveal information that works favorably for them. Actions that promote favorable leakage are called signaling. Actions that reduce or eliminate unfavorable leakage are called signal jamming. If you want to elicit information from someone else, you may set up a situation that the other party takes action depending on the nature of the information it possesses. This is called screening. For instance, Tiffany’s request for a tattoo was her screening test.

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Signaling the quality of a used car A warranty is, in effect, an implied statement by the seller of a used car

I know the quality of this car to be sufficiently good that I can

afford to offer the warranty.

Would you rely on the mere statement

I know this car to be of excellent quality.

With the warranty, the seller if putting his money where his mouth is! Offering a warranty separates the sellers who merely «talk the talk» from those who can «walk the walk».

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Screening for a used car of good quality The seller can take the initiative and signal the quality of a used car by offering a warranty. A buyer may take the initiative and screen the seller by asking for a warranty! These two strategies work in similar ways to reveal private information. How would you interpret a seller’s offer to let you get a car inspected by a mechanic?

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Words are cheap If the mechanic finds a serious flaw and you walk away, the seller is no worse off, regardless of the condition of the car!

So, such an offer is not a credible signal. In a similar fashion, a warranty given by a private seller is of significantly smaller utility to a prospective buyer.

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Hyundai takes on America In the late 1990s, Hyundai raised the quality of their cars. This was not recognized by the US consumers. To get its claims across, in 1999 Hyundai signaled its quality by offering an unprecedented 10-year/100,000 mile warranty on the power train.

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Groucho Marx’s self deprecation Groucho Marx famously said that he didn’t care to belong to any club that would accept him at a member!

This relates to information asymmetries.

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The plight of insurance companies Insurance policies selectively attract the worst risks. For example, a life insurance policy with a premium of 5% will be especially attractive to people whose mortality rate is greater than 5%! Many people with lower mortality will buy such policies but those with greater risk will be overrepresented. Raising prices can make matters worse because the good risks will find the policies too expensive leaving behind the worse cases! So we come back to the Groucho Marx effect: anyone willing to buy insurance at those prices is not someone you would want to insure! This is the famous adverse selection problem, where bad types are attracted to a transaction.

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Credit card debts Let’s consider credit card loans.

Some banks offer cards with a transfer of balance option, to steal customers from other banks. Who do you think find this option attractive?

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Maxpayers, revolvers and deadbeats Roughly, there are three types of credit card customers: maxpayers, revolvers and deadbeats. Maxpayers pay their bill in full each month. They have no intention to switch. Revolvers borrow money on the card but pay it back over time. Given the high interest rates on credit cards, these are the most profitable customers. Deadbeats are also borrowers but, unlike revolvers, they are going to default on the loan and have no interest in switching. So, while a bank is not able to identify who the profitable customers are, the nature of transfer of balance offers ends up attracting just the profitable customers!

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The best vs the worst There are good and bad job candidates out there, in the market. Bad candidates lack the talent for a top job but hope to get such a job and make a good salary until they found out. In Greece, (untalented) candidates may pull strings to gain entrance.

What about good candidates? How can they compete?

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The signaling value of education… Education carries out signaling value! A good degree from a top university acts as a signal of ability. A graduate is in effect saying

If I were less able, would I have graduated from Princeton with

honors?

In addition, a good MBA costs $200,000 to get (when you take into account both tuition and foregone salary) and is quite difficult to graduate from (at least abroad). If anyone can be accepted into an MBA and get the degree easily (for instance, by cheating), the MBA pool is contaminated by the untalented and does not serve as a screening device any more.

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…that turns into a rat race! Unfortunately, education signaling may turn into a rat race. If the more able get more education, the less able may find it profitable to do likewise, be mistaken for the more able and be given better jobs and wages. Then the truly able get even more education to distinguish themselves. Pretty soon, clerical jobs require Master’s degrees! Incidentally, Dixit and Nalebuff (2008) assert that nothing can be done about this wasteful completion: a public policy is needed!

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Accident or cheating? The US maintains a health insurance system called Worker’s Compensation that covers work-related injuries or illness. By the nature of this system, workers, doctors and lawyers have severe temptations to overstate the problems and collect larger sums than warranted. According to the CEO of Oregon’s state-owned Worker’s Compensation insurer

If you run a system where you give money to everyone who

asks, you are going to get a lot of people asking for money.

What would you do to address this issue?

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Signaling via Bureaucracy Although people often thing of bureaucratic delays and inconveniences as proof of government inefficiency, these may sometimes be valuable strategies to cope with such informational problems! (Not in Greece, for sure!) Benefits in kind may also be useful in the context of asymmetric information, for example giving a wheelchair instead of money!

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Inaction may speak the loudest of all! Sometimes, it is inaction that reveals the most! For example, in «Silver Blaze» Sir Arthur Conan Doyle creates one of the most famous scenes of Sherlock Holmes:

Gregory (Scotland Yard detective): Is there any other point to

which you would wish to draw my attention?

Holmes: To the curious incident of the dog in the night-time.

Gregory: The dog did nothing in the night-time.

Holmes: That was the curious incident.

What conclusion would you draw?

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Why did the dog not bark? Clearly, the dog didn’t bark because the intruder was familiar!

That was a very clear signal – at least to Sherlock Holmes!

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Countersignaling Some of the people most able to signal may refrain from doing so! Minor officials prove their status with petty displays of authority

while the truly powerful show their strength through gestures of magnanimity.

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More countersignaling Mediocre students answer a teacher’s easy questions; the best students are embarrassed to prove their knowledge of trivial points. Also, people of moderate ability seek formal credentials to impress employers and society; the truly talented often downplay their credentials even if they have invested a lot of effort to obtain them. Finally a person of average reputation defensively refutes accusations against his character, while a highly respected person finds it demeaning to dignify accusations with an answer.

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Countersignaling among academic faculty Zipporah (Fagi) Levinson, widow to Norman Levinson of the MIT math department, said on John Nash:

For Nash to deviate from convention is not as shocking as you

might think. They were all prima donnas. If a mathematician

was mediocre he had to toe the line and be conventional. If he

was good, anything went.

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Further countersignaling in academia Fewer than 4% of economists at universities with a PhD program, used a title in their voicemail message, compared to 27% of their colleagues at universities without a doctoral program. You may want to compare TEI and AEI in Greece. Or you may was to compare the «faces» of your least and most favorite teachers in your undergraduate and graduate education. Does it …signal accurately?

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Signal jamming If you are buying a used car from the previous owner, you may think that if the car is washed and polished, its interior is clean and carpets are vacuumed, it is likely that the car has been well looked after. However, these are signals that even careless owners can mimic when they offer the car for sale! Therefore, this signal does not serve to distinguish among the two types of car. It all depends on the proportion of the two types in the population! When all types take the same action that is, therefore, fully uninformative, we have a pooling equilibrium of the signaling game. By contrast, when one type signals and the other does not, we have a separating equilibrium. Conveniently enough, this is a nice lead to the world of evolutionary games.

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Bodyguard of lies At the 1943 Tehran Conference, Churchill famously said to Stalin:

In wartime, truth is so precious that she should always be

attended by a bodyguard of lies.

Two rival business men meat in the Warsaw train station.

Where are you going, says the first

To Minsk, replied the other.

To Minsk, eh? What a nerve you have! I know that you are

telling me that you are going to Minsk because you want me to

believe that you are going to Pinsk. But it so happens that I

know that you really are going to Minsk. So why are you lying to

me?

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Speaking the truth in order not to be believed On June 27, 2007, Ashraf Marwan (son-in-law of Egyptian president Abdel Nasser) died in London, falling from the balcony of this fourth story flat in Mayfair.

Thus ended the life of a man who was either the best-connected Israeli spy or a brilliant Egyptian double agent.

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Cry wolf? In 1973, Marwan sent the code «Radish», that meant imminent war, to Israel. As a result, Israel called up thousands of reservists and wasted tens of millions on what turned out to be a false alarm. Six months later, on October 5, Marwan signaled «Radish» again. This time, Marwan’s alarm was not trusted. At 2:00 pm on the next day, the Yom Kippur holiday, Egypt and Syria attacked and almost overran the Israeli army. Ganeral Zeira, Israel’s intelligence head, lost his job over the fiasco. Whether Marwan was a spy for Israel or a double agent remained uncertain. And if his death wasn’t an accident, we don’t know if it was the Israelis of the Egyptians who are to blame.

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Price discrimination by screening We close with the application of the concept of screening that most impinges on our lives: price discrimination. To differentiate among different customers, sellers commonly create different versions of the same good and price these versions differently. This strategy implicitly reveals the customer’s private information, namely their willingness to pay (WTP). The sellers are screening the buyers! As an example, publishers take advantage of the inverse relationship between willingness to pay and willingness to wait by publishing the book initially in hardcover at a higher price and a year or so later in paperback at a lower price. Similarly, computer software makers often offer a «lite» or student version that has fewer features and sells at a lower price. Occasionally, they produce the lite version by taking the full version and disabling some features – this costs more!

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More price discrimination IBM offered two versions of a laser printer: the E version printed at 5 pages a minute while for $200 more you could the fast version that printed at 10 pages a minute. The only difference between the two was that IBM actually added a chip in the firmware of the E version that slowed printing down! The Sharp DVE611 DVD player and their DV740U unit were both made in the same Shanghai plant. The key difference was that the DVE611 lacked the ability to play DVDs formatted to the PAL European standard on TV sets that use the NTSC American standard. However, the functionality was there all along, just hidden from the customer! Some ingenious users figured out how to play with the remote control faceplate and some system switches so that the functionality was restored. You could restore full functionality simply by punching a hole in the faceplate at the appropriate spot - this was shared on the web!

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Using signaling and screening to your advantage All in all, as you become more experienced in using game theory to your advantage in your personal and professional life, you will ⚫ start seeing signals everywhere ⚫ scrutinize your own actions for their signal content.

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References Dixit, A. and B.J. Nalebuff (2008): The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life, W.W. Norton and Company. May, H. and B.M. Metzer, editors (1962): The Oxford Annotated Bible, Revised Standard Version, Oxford University Press, New York.