6. Uncertainty and Information

1. 6. Uncertainty and Information • Many strategic situations involve the players having different information. In this section we shall 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.

2. Yogi on Uncertainty and Information "You can observe a lot just by watching.“- Yogi Berra "I didn't really say everything I said." - Yogi Berra and Groucho on the Same Subject “Quote me as saying I was misquoted.”- Groucho Marx Games People Play.

3. Games People Play.

4. Uncertainty and Information • 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? Games People Play.

5. Uncertainty and Information • 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: Information and how it is solicited matters. Games People Play.

6. Yogi Berra on Navigation "If you come to a fork in the road, take it.“– Yogi Berra "You've got to be very careful if you don't know where you're going, because you might not get there.“– Yogi Berra Games People Play.

7. Strategies to Manipulate Information • To manipulate information there are two options • Signal – convey information to others. • Signal jamming – prevent the conveyance of information. • To influence the unobservable behavior of others an incentive scheme is required • Links rewards or penalties to an observable outcome in a way that effects the unobservable. Games People Play.

8. Strategies to Manipulate Information Games People Play.

9. Strategies to Manipulate Information • Typically information is asymmetric – one player knows more than another. • The informed individual may want to • Conceal information. • Reveal misleading information. • Reveal selected information truthfully. • The uninformed individual may want to. • Elicit information. • Filter truth from falsehood. • Remain ignorant – remember strategic moves. Games People Play.

10. Strategies to Manipulate Information Games People Play.

11. Screening and Signaling • 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.

12. Screening and 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.

13. Pooling and Separating • Both signaling and screening are costly. • What they achieve is a separation of types. • There are obviously gains from knowing a players type. • The gains may of may not exceed the costs. • When the costs exceed the gains there is typically no attempt to discover a players type. The lazy workers act like the hard working ones who do not over-exert themselves. In this case we have pooling. • When the gains exceed the costs we get separating behavior. Games People Play.

14. Incentive 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. Games People Play.