哈佛大学：《中级微观经济学》（英文版）Lecture 7 More on Uncertainty

Economics 2010a Fa|2003 Edward L. Glaeser Lecture 7

Economics 2010a Fall 2003 Edward L. Glaeser Lecture 7

7. More on Uncertainty Prospect Theory, LoSS Aversion b. Subjective Utility and Common Knowledge Risk Aversion d. First and Second Order stochastic Dominance Asset demand and risk Aversion

7. More on Uncertainty a. Prospect Theory, Loss Aversion b. Subjective Utility and Common Knowledge c. Risk Aversion d. First and Second Order Stochastic Dominance e. Asset Demand and Risk Aversion

f. State Dependent Preferences g. Application The Draft

f. State Dependent Preferences g. Application: The Draft

a great deal of attention has been recently paid to ideas like prospect theory and loss aversion(Kahneman and Tversky) Point #f 1 of these studies-people are very sensitive to framing and current position Rabin-people are risk averse over small bets-this is actually incompatible with standard measured levels of risk aversion Point #2 people are concave in the win domain(classically riskaverse), but convex in the loss domain

A great deal of attention has been recently paid to ideas like prospect theory and loss aversion (Kahneman and Tversky). Point # 1 of these studies– people are very sensitive to framing and current position. Rabin – people are risk averse over small bets– this is actually incompatible with standard measured levels of risk aversion. Point # 2: people are concave in the win domain (classically riskaverse), but convex in the loss domain

Subjective Probabilities and common Knowledge Agreeing to disagree-the lemon juice out of your ear problem Assume for a second that people were risk neutral-utility is always just cash Some people say that you can get betting because of differences of opinion about probabilities In other words consider the situation where someone comes up to you and bets you 10 dollars that lemon juice is going to squirt out of your ear so you win if lemon juice doesn't squirt out of your ear

Subjective Probabilities and Common Knowledge Agreeing to disagree–the lemon juice out of your ear problem. Assume for a second that people were risk neutral–utility is always just cash. Some people say that you can get betting because of differences of opinion about probabilities. In other words, consider the situation where someone comes up to you and bets you 10 dollars that lemon juice is going to squirt out of your ear so you win if lemon juice doesn’t squirt out of your ear

You initially place probability p0

You initially place probability p.5, on this occuring. Certainly one might think that your expected gain from this bet is (1-p)10-p10 or (1-2p)100

Your opponent would offer the bet only if (2p-1)10>0, so if p>5>p, it seems like you should have a horse race But this can't actually happen To see this let's put some structure on learning Remeber bayes Rule P(B|4)=P(B∩AP(A) This is always the key to understanding belief formations So more information structure The unconditional probability of a lemon squirting is p If the lemon is squirting, then every person receives a positive signal with probability Z If the lemon is not squirting then every person recieves a positive signal with

Your opponent would offer the bet only if (2p’-1)100, so if p’.5p, it seems like you should have a horse race. But this can’t actually happen. To see this, let’s put some structure on learning. Remeber Bayes’ Rule PB|A  PB  A/PA This is always the key to understanding belief formations. So more information structure. The unconditional probability of a lemon squirting is p. If the lemon is squirting, then every person receives a positive signal with probability z. If the lemon is not squirting then every person recieves a positive signal with

probability 1-z The probability of lemon squirting conditional upon recieving a positive signal is zp/(zp+(1-z(1-p)) There are actually four possible states of the world Signal, Lemon Signal, No Lemon No Signal, lemon No signal, no lemon (1) signal, no lemon, (2)signal, lemon, (3)no signal, no lemon, 4)no signal, lemon The probabilties of each of these states are(1)(1-z)(1-p),(2)Zp,(③3)z(1-p),(4) (1-z)p

probability 1-z. The probability of lemon squirting conditional upon recieving a positive signal is zp/(zp(1-z)(1-p)). There are actually four possible states of the world: Signal, Lemon Signal, No Lemon No Signal, Lemon No Signal, No Lemon (1) signal, no lemon, (2) signal, lemon, (3) no signal, no lemon, (4) no signal, lemon. The probabilties of each of these states are (1) (1-z)(1-p), (2) zp, (3) z(1-p), (4) (1-z)p

If you havent received a signal-your probability assessment is(1-z)p/ (z+p-2pz If you have recieved a signal, your probability assessment is zp/(1-z-p+2pz) If there are two people, the situation is even harder- there are actually eight states of the world based on the signal that each person has recieved

If you haven’t received a signal– your probability assessment is (1-z)p/(zp-2pz). If you have recieved a signal, your probability assessment is zp/(1-z-p2pz). If there are two people, the situation is even harder– there are actually eight states of the world based on the signal that each person has recieved

In this gambling example we need to deal with two people So we have the following states of the world 2(1-p)(1-z)2 pz(1-2)(1-p)z(1-z) pz(1-)(1-p)z(1-z) p(1-2)2(1-p) If the other person has bet- what should you assume? So conditional upon you not getting a

In this gambling example we need to deal with two people: So we have the following states of the world: pz2 1  p1  z2 pz1  z 1  pz1  z pz1  z 1  pz1  z p1  z2 1  pz2 If the other person has bet– what should you assume? So conditional upon you not getting a