Games People Play.Games People Play.

6. Uncertainty and Information6. Uncertainty and Information

Many strategic situations involve the players Many strategic situations involve the players having different information. In this section we having different information. In this section we shall learnshall learn

How to find out what your opponent knows.

How to credibly transmit information to your opponent that you want them to know.

How to prevent your opponent finding out what you know.

How to make individuals act as you wish even when you cannot directly observe their behavior.

Games People Play.Games People Play.

Yogi on Uncertainty and Yogi on Uncertainty and InformationInformation

"You can observe a lot just by watching.“- "You can observe a lot just by watching.“- Yogi BerraYogi Berra

"I didn't really say everything I said." - "I didn't really say everything I said." - Yogi BerraYogi Berra

and Groucho on the Same Subjectand Groucho on the Same Subject

““Quote me as saying I was misquoted.”Quote me as saying I was misquoted.” - Groucho Marx- Groucho Marx

Games People Play.Games People Play.

Games People Play.Games People Play.

Uncertainty and InformationUncertainty and Information

Puzzle: The “Literal Liar” problem.Puzzle: The “Literal Liar” problem.You are traveling along a road and reach a fork. One

branch lead to the village of the liars the other to the village of the truth tellers. A villager, who may be from either village, sits at the roadside. You may ask him one question to find out which branch leads to which village.

What is your question?What is your question?

Games People Play.Games People Play.

Uncertainty and InformationUncertainty and Information

Answers to the Literal Liar Problem.Answers to the Literal Liar Problem.“If you were a member of the other village, how would you answer the question, ’does the left branch lead to the village of the truth tellers?’”“Which is the road to your village?”

Message:Message: Information and how it is solicited matters. Information and how it is solicited matters.

Truth isTruth is

YesYes NoNo

Local isLocal isTruthfulTruthful NoNo YesYes

LiarLiar NoNo YesYes

Games People Play.Games People Play.

Yogi Berra on NavigationYogi Berra on Navigation

"If you come to a fork in the road, take it.“"If you come to a fork in the road, take it.“ – Yogi Berra– Yogi Berra

"You've got to be very careful if you don't know where "You've got to be very careful if you don't know where you're going, because you might not get thereyou're going, because you might not get there.“– Yogi .“– Yogi BerraBerra

Games People Play.Games People Play.

Strategies to Manipulate Strategies to Manipulate InformationInformation

To manipulate information there are To manipulate information there are two optionstwo options

Signal – convey information to others.

Signal jamming – prevent the conveyance of information.

To influence the unobservable To influence the unobservable behavior of others an incentive behavior of others an incentive scheme is requiredscheme is required

Links rewards or penalties to an observable outcome in a way that effects the unobservable.

Games People Play.Games People Play.

Strategies to Manipulate Strategies to Manipulate InformationInformation

Games People Play.Games People Play.

Strategies to Manipulate Strategies to Manipulate InformationInformation

Typically information is asymmetric – one Typically information is asymmetric – one player knows more than another.player knows more than another.The informed individual may want toThe informed individual may want to

Conceal information.Reveal misleading information.Reveal selected information truthfully.

The uninformed individual may want to.The uninformed individual may want to.Elicit information.Filter truth from falsehood.Remain ignorant – remember strategic moves.

Games People Play.Games People Play.

Strategies to Manipulate Strategies to Manipulate InformationInformation

Games People Play.Games People Play.

Screening and SignalingScreening and Signaling

Screening.Screening.Suppose you wish to discover a players type. There are

hard workers and lazy ones. Hard workers are also more able to obtain good grades in college. The cost to a hard worker of raising her grades from C’s to an A’s is $1,000, whereas for a lazy worker the cost is $5,000.

Now offer a payment of $2,000 to all workers who have A’s from college. The hard workers find the investment worthwhile while the lazy ones do not. The scheme therefore acts a screen, to separates hard from lazy workers.

Games People Play.Games People Play.

Screening and SignalingScreening and Signaling

Signaling.Signaling.Signaling is similar to screening in many respects.

The key differences is that the players themselves take actions to reveal their type. Hard workers may choose to get good grades in college so as to signal their worth to potential employers. They choose to get A’s because they know lazy workers will choose not to copy them.

Note that the hard workers might otherwise have been happy with B grades, but have to exert the extra effort to get A’s because the lazy workers are also willing to make the effort of getting B’s if it hides their type.

Games People Play.Games People Play.

Games People Play.Games People Play.

Manipulating InformationManipulating InformationPuzzle:Puzzle: Suppose that instead of two types of workers there are three; High, Medium and Suppose that instead of two types of workers there are three; High, Medium and

Low.Low.

All else equal no type wishes to work for a higher grade (A,B or C) than necessary.

Highs and Mediums can get any grade they wish.

Lows can only get B’s or C’s.

Highs can be confused with Mediums who in turn can be confused with Lows.

Highs cannot under any circumstances be confused with Lows.

No type wishes to be confused with a lower type.

How do high types reveal their qualities to prospective employers?How do high types reveal their qualities to prospective employers?

Games People Play.Games People Play.

Manipulating InformationManipulating Information

Answer to puzzleAnswer to puzzleHighs get C’sHighs get C’s

Mediums get A’sMediums get A’s

Lows get C’sLows get C’s

Mediums cannot choose B’s or C’s because Lows will copy them.Mediums cannot choose B’s or C’s because Lows will copy them.

Highs cannot choose A’s or B’s because Mediums will copy them.Highs cannot choose A’s or B’s because Mediums will copy them.

Lows will not choose B’s because it gains them nothing.Lows will not choose B’s because it gains them nothing.

Games People Play.Games People Play.

Pooling and SeparatingPooling and Separating

Both signaling and screening are costly. Both signaling and screening are costly.

What they achieve is a separation of typesWhat they achieve is a separation of types..There are obviously gains from knowing a players type.There are obviously gains from knowing a players type.

The gains may of may not exceed the costs.The gains may of may not exceed the costs.

When the costs exceed the gains there is typically no When the costs exceed the gains there is typically no attempt to discover a players type. The lazy workers act attempt to discover a players type. The lazy workers act like the hard working ones who do not over-exert like the hard working ones who do not over-exert themselves. In this case we have pooling.themselves. In this case we have pooling.

When the gains exceed the costs we get separating When the gains exceed the costs we get separating behavior.behavior.

Games People Play.Games People Play.

Incentive SchemesIncentive Schemes

Often used to induce effort when it is unobservable.

Consider a manager faced with choosing among several projects. If he gives the normal level of effort in assessing them the probability of success is 60%. If he gives extra effort the probability of success rises to 80%. But the extra effort is costly to the manager and he will not make it unless given the correct incentives.

The solution is to pay the manager a bonus if the project is successful.

But how much more?

Extra effort raises the probability of success by 20%, so 20% times the bonus must be at least as large as the cost of effort to the manager.