My girlfriend watched a documentary about John Nash and how he overcame his schizophrenia. I tried telling her about the Nash Equilibrium (NE) concept and she didn't understand...so either I did a poor job explaining or she wasn't focusing on my explanation or a bit of both. I'm going to attempt to define NE and give an example in layman's terms below.
NE is a game theory concept, so it applies to games. Economists use the word game a bit differently than other people, so you can think of a game as a scenario where more than one player interact with each other and the payoffs (perhaps who wins and who loses and by how much) are determined by the decisions of all the players. A simple game is played on The Price is Right. The winner is the player who guesses the number closest to the value of the item without going over. All four players make a guess and therefore whether or not one player is a winner depends on the value of the item and the guesses of the other three players. Likewise, paper-rock-scissors is a game. If you throw rock, your payoff depends on what your opponent throws.
In a NE, no player can increase his own payoff by deviating if everyone else keeps their move the same. Think about letting just one player (at a time) have a do-over...if they change their move, then we say they have deviated. Another aspect of NE that hurts brains is that there can be multiple NE in one game. I am going to describe a two player game for simplicity.
THE GAME:
You and I get to pick an integer between 1 and 9 inclusive. We do not get to communicate with each other about what we will pick. Say that you pick a number by writing it down and giving the paper to a person organizing the game. The payoffs are as follows: if we pick the same number, then we each get paid that number of dollars (by the person who is organizing the game). If we pick different numbers then we each have to pay the same number of dollars as the number we picked (to the person organizing the game).
Example 1 payoff:
I pick 5 and you pick 7. Now I have to pay 5 and you have to pay 7.
Example 2 payoff:
We both pick 4. Now we both get paid $4.
What about the NE?:
The moves we made in example 1 are not a NE. If I were allowed to deviate, I would change my pick to 7 and we would both get paid $7. If you were allowed to deviate then you'd pick 5 and we'd both get $5. It only takes one of us wanting to deviate to make the scenario a non-NE. The moves we made in example 2 are a NE. If either of us were given the chance to deviate (given that the other player cannot change their move) then neither of us would want to because we'd go from getting $4 to paying something which does not make us better off.
Here's the tricky thing...
First of all, you have to get past the idea that this is a simultaneous move game and you will not know what your opponent has chosen until after you have made your move. Second of all, you might have deduced that any time we both pick the same number in the game above leads to a NE. That is correct. There are 9 NEs for that game. We could settle on any one of them and it would be a NE. All other choices where we pick different numbers are not NEs because one of us would like to deviate if we knew that the other person would not be able to change his answer.
I hope that helps. I can answer any questions in the comments.
Note: I've only discussed pure strategy NE because mixed strategy will blow your mind...and I can't say much about it to the lay person except that it would be bad for a player to commit to a strategy such as "always choose paper in paper-rock-scissors" because the opponent would then crush you by always choosing scissors.
Sunday, November 11, 2012
Saturday, November 10, 2012
Greg Mankiw on Health Insurance
I was at the Cengage Learning annual teaching conference on Friday and had a great time. Gail Hoyt gave a seminar for grad students about the top 5 tips for effective teaching & top 5 tips for the job market. That was really good and followed by N. Gregory Mankiw's keynote address at lunch. What Mankiw said really resonated with me. I had no idea that he was so light-hearted and funny...I feel like he could give Yoram Bauman (the stand-up economist) a run for his money if he tried.
Mankiw's speech was about the fiscal challenge ahead. I really liked what Mankiw had to say about gas taxes (there should be a ~$2.00/gallon tax on gas to help correct the negative externalities generated by driving) and getting rid of the mortgage interest deduction on taxes (even though I own a house, I realize that this is a terribly inequitable tax and costs our government lots of revenues). What really resonated with me was his take on medical insurance. I've actually had much the same conversation with my girlfriend and it was super duper neat-o to hear Dr. Mankiw express my views from his mouth to a room full of people/webcast full of viewers. Here's the upshot of the problems with medical insurance:
People are using medical insurance as non-insurance. Insurance should be for unexpected events, not regular medicine or treatments. Since medical insurance compensation is tax deductible, people have too much of it. To see why, consider what would happen if your auto insurance was tax deductible. You would tell your employer that you're willing to take a pay cut if he pays for your auto insurance policy. You would want better coverage than you currently have (as long as insurance is a normal good, which it's hard to argue otherwise). Normal auto insurance now covers incidental things like accidents but it does not cover regular maintenance items like new tires, burned out headlights, oil changes, and filter replacement. If you had the tax deductible setup, then you'd want as much of your car expenses to be covered by insurance (with a more expensive policy). We would probably see clauses allowing insurance to cover filter replacement and oil changes. People might even want to go as far as to have their policy cover gasoline fill-ups.
If this sounds ridiculous to you, consider someone with a monthly prescription that is covered by their insurance. That might be too much insurance coverage. I think that there are ways around "insuring" monthly prescriptions. One reason why it's attractive to have insurance coverage for monthly prescriptions is the difference in cost between paying out-of-pocket vs. paying through insurance. Part of the reason for the price difference is the market power of the insurance company compared to that of an individual consumer. The insurance company can negotiate lower rates. Another reason is that healthy people are subsidizing pill takers. That setup might make sense for temporary prescriptions but not regular recurring prescriptions (which is like auto insurance covering gasoline).
If my gasoline were subsidized, you can bet that I'd drive more than I do now. So would everyone else. It's a tragedy of the commons type problem. The monetary outlays on gasoline would increase and people would be concerned about the rising costs of auto insurance...but they wouldn't want to remove the moral hazard (speaking just about the gas and not about reckless driving) associated with purchasing that insurance.
Speaking of the rising cost of medical insurance, Mankiw does not think this is a bad thing. One reason why the cost has increased is that the productivity of medical capital has increased. We are also able to do amazing things with medical technology that we couldn't in the past. When I broke my wrists, I was able to regain a near full range of motion. I was informed by my surgeon that I would have about half the range of motion in each plane had this accident occurred only 5 years earlier. Mankiw offers a thought experiment: would you agree to pay the rate on medical treatment paid by your grandfather (in his 40s) in exchange for only getting the care that he could have received all those years ago. Mankiw's personal answer is no. My answer is no. What about yours? Consider the drugs that have been invented since then. The MRI technology, laser surgery, etc. Those things are more expensive than the older alternatives, but they're also more effective. Mankiw further points out that we do not seem to experience diminishing marginal utility in years of life like we do for consuming other goods. Nobody says "I've made it to 74 and it's all downhill from here...I don't care if I live another year." We do say "I've had 47 slices of apple pie...I would hate to eat a 48th." Given that a goal of medical care is to prolong life (or to improve the quality) then he thinks that we'd be willing to spend plenty more on it. Perhaps with everything else getting cheaper we have more money to spend on medical care. He would like to see medical care keep increasing in cost to keep up with the technological improvements.
I think another reason medical costs have risen is the shift in demand for medical services caused by insured people. I'll admit that I've gone to the clinic at school for a sore throat because the visit was free. I would not have driven to the doctor's office and paid $100 for a similar visit. Driving down the cost of medical care will require: 1) aligning doctors' incentives to provide cheaper medical care, 2) driving down demand for medical services...perhaps by a preference shift toward healthier lifestyles or sudden death inducing activities and/or 3) a bigger increase in the supply of medical inputs.
I hope I've done some justice to his talk. I've added some of my own thoughts along the way, so don't get mad at Greg if you disagree with anything above unless directly attributed to him.
Mankiw's speech was about the fiscal challenge ahead. I really liked what Mankiw had to say about gas taxes (there should be a ~$2.00/gallon tax on gas to help correct the negative externalities generated by driving) and getting rid of the mortgage interest deduction on taxes (even though I own a house, I realize that this is a terribly inequitable tax and costs our government lots of revenues). What really resonated with me was his take on medical insurance. I've actually had much the same conversation with my girlfriend and it was super duper neat-o to hear Dr. Mankiw express my views from his mouth to a room full of people/webcast full of viewers. Here's the upshot of the problems with medical insurance:
People are using medical insurance as non-insurance. Insurance should be for unexpected events, not regular medicine or treatments. Since medical insurance compensation is tax deductible, people have too much of it. To see why, consider what would happen if your auto insurance was tax deductible. You would tell your employer that you're willing to take a pay cut if he pays for your auto insurance policy. You would want better coverage than you currently have (as long as insurance is a normal good, which it's hard to argue otherwise). Normal auto insurance now covers incidental things like accidents but it does not cover regular maintenance items like new tires, burned out headlights, oil changes, and filter replacement. If you had the tax deductible setup, then you'd want as much of your car expenses to be covered by insurance (with a more expensive policy). We would probably see clauses allowing insurance to cover filter replacement and oil changes. People might even want to go as far as to have their policy cover gasoline fill-ups.
If this sounds ridiculous to you, consider someone with a monthly prescription that is covered by their insurance. That might be too much insurance coverage. I think that there are ways around "insuring" monthly prescriptions. One reason why it's attractive to have insurance coverage for monthly prescriptions is the difference in cost between paying out-of-pocket vs. paying through insurance. Part of the reason for the price difference is the market power of the insurance company compared to that of an individual consumer. The insurance company can negotiate lower rates. Another reason is that healthy people are subsidizing pill takers. That setup might make sense for temporary prescriptions but not regular recurring prescriptions (which is like auto insurance covering gasoline).
If my gasoline were subsidized, you can bet that I'd drive more than I do now. So would everyone else. It's a tragedy of the commons type problem. The monetary outlays on gasoline would increase and people would be concerned about the rising costs of auto insurance...but they wouldn't want to remove the moral hazard (speaking just about the gas and not about reckless driving) associated with purchasing that insurance.
Speaking of the rising cost of medical insurance, Mankiw does not think this is a bad thing. One reason why the cost has increased is that the productivity of medical capital has increased. We are also able to do amazing things with medical technology that we couldn't in the past. When I broke my wrists, I was able to regain a near full range of motion. I was informed by my surgeon that I would have about half the range of motion in each plane had this accident occurred only 5 years earlier. Mankiw offers a thought experiment: would you agree to pay the rate on medical treatment paid by your grandfather (in his 40s) in exchange for only getting the care that he could have received all those years ago. Mankiw's personal answer is no. My answer is no. What about yours? Consider the drugs that have been invented since then. The MRI technology, laser surgery, etc. Those things are more expensive than the older alternatives, but they're also more effective. Mankiw further points out that we do not seem to experience diminishing marginal utility in years of life like we do for consuming other goods. Nobody says "I've made it to 74 and it's all downhill from here...I don't care if I live another year." We do say "I've had 47 slices of apple pie...I would hate to eat a 48th." Given that a goal of medical care is to prolong life (or to improve the quality) then he thinks that we'd be willing to spend plenty more on it. Perhaps with everything else getting cheaper we have more money to spend on medical care. He would like to see medical care keep increasing in cost to keep up with the technological improvements.
I think another reason medical costs have risen is the shift in demand for medical services caused by insured people. I'll admit that I've gone to the clinic at school for a sore throat because the visit was free. I would not have driven to the doctor's office and paid $100 for a similar visit. Driving down the cost of medical care will require: 1) aligning doctors' incentives to provide cheaper medical care, 2) driving down demand for medical services...perhaps by a preference shift toward healthier lifestyles or sudden death inducing activities and/or 3) a bigger increase in the supply of medical inputs.
I hope I've done some justice to his talk. I've added some of my own thoughts along the way, so don't get mad at Greg if you disagree with anything above unless directly attributed to him.
Friday, November 9, 2012
Thursday, November 8, 2012
Chromebook Update: External Monitor
W00t! My chromebook now recognizes my external monitor at its native resolution! I can mirror monitors, but I cannot run dual monitors. It's steps in the right direction. The improvements keep coming every 6 weeks.
Wednesday, November 7, 2012
Obama FTW
I am amazed at the numbers from the election. The popular vote went 50% Obama, 48% Romney, but Obama's electoral votes outnumbered Romney's 303 to 203. That's some good campaigning and maybe a little bit of luck.
I had been thinking about Obama's lame duck presidency as a bad thing. Now, I wonder if he will get some really great stuff done in that time. I think that he has good intentions, but you know what they say about good intentions (if you don't know, it's either "the highway to hell is paved with good intentions" or "good intentions don't guarantee good outcomes).
I really hope that fiscal sanity can be restored. By some measures, Obama's done a great job (see here) and by others he's done poorly (see here). Unfortunately, I couldn't vote for either of the major candidates yesterday. I cast a throw-away vote for Gary Johnson. Funny enough, it was Romney's own propaganda that made me decide that I could not vote for him. Not that my vote would have made a difference anyway (although at this time Florida still has not been officially called, the vote difference is near 46,000 votes).
I had been thinking about Obama's lame duck presidency as a bad thing. Now, I wonder if he will get some really great stuff done in that time. I think that he has good intentions, but you know what they say about good intentions (if you don't know, it's either "the highway to hell is paved with good intentions" or "good intentions don't guarantee good outcomes).
I really hope that fiscal sanity can be restored. By some measures, Obama's done a great job (see here) and by others he's done poorly (see here). Unfortunately, I couldn't vote for either of the major candidates yesterday. I cast a throw-away vote for Gary Johnson. Funny enough, it was Romney's own propaganda that made me decide that I could not vote for him. Not that my vote would have made a difference anyway (although at this time Florida still has not been officially called, the vote difference is near 46,000 votes).
Saturday, November 3, 2012
VO2 Max Update
I went to do my second VO2 max session for Emery's study on Thursday. There was slight improvement because I got 65mgO2/kg weight/minute, up from 64 a couple weeks ago. I still got stuck at the same part of the test (running up an 8% grade at 9.5mph aka 6:19 per mile)...but this time I lasted about 15-20 seconds longer than last time.
We determined that my speed for the downhill run (DHR) portion of the test will be 9.4mph. That's pretty cool because the farthest I've ever run in an hour is 9.32 miles (well, I ran a 15k in 59:52). I'll be running down a 5% grade for that entire hour. I think it'll start to hurt after 40 minutes. I guess the whole goal of the study is to make sure that I'm extremely sore. There are moments when I wonder exactly what would make me sign up for something like this...but then I think it's cool again.
We determined that my speed for the downhill run (DHR) portion of the test will be 9.4mph. That's pretty cool because the farthest I've ever run in an hour is 9.32 miles (well, I ran a 15k in 59:52). I'll be running down a 5% grade for that entire hour. I think it'll start to hurt after 40 minutes. I guess the whole goal of the study is to make sure that I'm extremely sore. There are moments when I wonder exactly what would make me sign up for something like this...but then I think it's cool again.
Friday, November 2, 2012
Pick #319
Japandroids - "I Quit Girls" from Post-Nothing
edit 11-7: I saw Daniel Tosh wearing a Japandroids shirt on his 11-6 broadcast of Tosh.0! I wonder if he saw this post before making a wardrobe decision.
edit 11-7: I saw Daniel Tosh wearing a Japandroids shirt on his 11-6 broadcast of Tosh.0! I wonder if he saw this post before making a wardrobe decision.
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