The slow leak of information
I’m preparing to purchase a new computer. I know that this probably makes me a bad person, and that with the $2000 I’ll likely drop on the computer that I could have saved literally about 5000 living, breathing people from things that would otherwise kill them in terrible ways. There are times when I wish that I could come up with some way to get around that argument that I mentioned in my last post. Then I could act like everyone else does and buy things for myself every once in a while without a tremendous surge of guilt. Then I could engage in my day-to-day routines without the knowledge hanging over my head that I’m a bad person.
In preparation to buy a new machine to replace the one I’m currently using, I was going through some of my saved documents. In keeping with my pack-rat nature, I tend to keep documents long past when I need them, and have a folder where I dump old essays, photographs, and assignments. I decided that I should go through some of these documents and see whether I should delete them, and sort them into documents I wanted to keep and documents that it is safe for me to delete. As I was opening random documents, I came across an essay for one of my classes in my undergraduate career. Pols 608: Social Choice and Game Theory... I recall it being a really fun class where we learned about mathematical modeling of individual behaviour and how we could, using a minimum of assumptions, predict human behaviours and how to manipulate groups of people into making choices that we wanted them to make.
Here is a sample of what was in one of my essays from that class:
"Scenario: A citizen, congressional representative, and bureaucrat are engaged in a game represented by the extended form game represented on the attached sheet labeled "Pre-tweak Extended Form Game." The constituent has the decision to make whether to telephone the Congressional member about a problem that she thinks is an important issue. Even if she doesn’t call the Congressman, there is a chance that he’ll take action on the issue anyway, and the call takes some time that she otherwise might have spent on things that she finds enjoyable. The Congressperson, regardless of the choice of the constituent, can take action on the issue, or ignore the issue. If he takes action, he will be seen as a pioneer in the fight against the problem, but nobody will notice if he does nothing about the issue, since he is simply one of hundreds who did nothing on the issue. To see the representation of the scenario as an extended game, see "Figure 1" which is attached.
"The extensive form game has been described, and the equilibria are given here:
Nash Equilibria: {(L, A1A2), (L, D1A2)}
Subgame Perfect Equilibria: {(L, A1A2), (L, D1A2)}
"In this game, we find that the addition of a criterion for subgame perfect behavior does not alter the equilibrium points that we find through a Nash analysis. Indeed, the Nash analysis is simply a comparison of dominated strategies in an attempt to find the points where it is clear that nobody would choose a different path, given the same choice of strategy by other people.
"The scenario as given above can be changed to alter the outcome of the game. In this scenario, when the legislation is handed over to the bureaucracy for implementation, a petty bureaucrat finds a way to embezzle all of the funds from the new program and flee the country. Thus, the scenario is more like the following:
"Scenario: A citizen, congressional representative, and bureaucrat are engaged in a game represented by the extended form game represented on the attached sheet Figure 2." The constituent has the decision to make whether to telephone the Congressional member about a problem that she thinks is an important issue. Even if she doesn’t call the Congressman, there is a chance that he’ll take action on the issue anyway, and the call takes some time that she otherwise might have spent on things that she finds enjoyable. The Congressperson, regardless of the choice of the constituent, can take action on the issue, or ignore the issue. If he takes action, he will be seen as a pioneer in the fight against the problem, but nobody will notice if he does nothing about the issue, since he is simply one of hundreds who did nothing on the issue. If the legislation is passed, a bureaucrat is handed the job of carrying out the will of the legislature, but he discovers that he has the opportunity to embezzle some large amount of money away from the funding for the new program designed to address the problem that the legislation was trying to combat.
"The extensive form game has been described, and the equilibria are given here:
Nash Equilibria: {(C, A1D2, E1E2), (C, A1D2, E1N2), (L, D1A2, N1E2), (L, D1A2, E1E2), (L, A1A2, E1E2)}
Subgame Perfect Equilibria: {(L, D1A2, E1E2)}
"By using the subgame perfect criteria for the equilibria, we discover that many of the Nash equilibrium points are not the final resting place for the game, and that a certain outcome is more likely when the game is played with the utility outputs given.
"This is just one of many examples which could be constructed to show the differences between games with only the addition of small changes to the overall structure of the game. Simple alterations to the payoff structure, additions of nodes, players, or information sets all will likely change the result of the game in different ways. For this reason, when constructing a decision tree or extended form game, great care must be taken to ensure that the representation adequately matches the factors you wish to model in reality."
Now, here’s the problem: At one point in the not too distant past (less than 3 years), I knew what that all meant. And knew it so well that I got 50 points of 50 points possible on the paper. I no longer understand what most of the material in this paper is about. What in God’s name is a Nash Analysis? What is a Subgame Perfect Equilibrium Point?
Nothing makes a man feel smaller than realizing that he’s slowly losing information that he once held onto with ease. This must be what it feels like for an elderly person who forgets the name of a grandchild, or who has forgotten the name of a brother that died back in ‘the war.’ It’s disheartening. I’m a little less intelligent today than I was a few years ago. Sometime over the holiday break, I’m going to break out my old textbook for that class and try to recapture some of what I’ve lost. I know that I’m always full of cliche sounding comments, but I’m not going to go gently into that good night.
In preparation to buy a new machine to replace the one I’m currently using, I was going through some of my saved documents. In keeping with my pack-rat nature, I tend to keep documents long past when I need them, and have a folder where I dump old essays, photographs, and assignments. I decided that I should go through some of these documents and see whether I should delete them, and sort them into documents I wanted to keep and documents that it is safe for me to delete. As I was opening random documents, I came across an essay for one of my classes in my undergraduate career. Pols 608: Social Choice and Game Theory... I recall it being a really fun class where we learned about mathematical modeling of individual behaviour and how we could, using a minimum of assumptions, predict human behaviours and how to manipulate groups of people into making choices that we wanted them to make.
Here is a sample of what was in one of my essays from that class:
"Scenario: A citizen, congressional representative, and bureaucrat are engaged in a game represented by the extended form game represented on the attached sheet labeled "Pre-tweak Extended Form Game." The constituent has the decision to make whether to telephone the Congressional member about a problem that she thinks is an important issue. Even if she doesn’t call the Congressman, there is a chance that he’ll take action on the issue anyway, and the call takes some time that she otherwise might have spent on things that she finds enjoyable. The Congressperson, regardless of the choice of the constituent, can take action on the issue, or ignore the issue. If he takes action, he will be seen as a pioneer in the fight against the problem, but nobody will notice if he does nothing about the issue, since he is simply one of hundreds who did nothing on the issue. To see the representation of the scenario as an extended game, see "Figure 1" which is attached.
"The extensive form game has been described, and the equilibria are given here:
Nash Equilibria: {(L, A1A2), (L, D1A2)}
Subgame Perfect Equilibria: {(L, A1A2), (L, D1A2)}
"In this game, we find that the addition of a criterion for subgame perfect behavior does not alter the equilibrium points that we find through a Nash analysis. Indeed, the Nash analysis is simply a comparison of dominated strategies in an attempt to find the points where it is clear that nobody would choose a different path, given the same choice of strategy by other people.
"The scenario as given above can be changed to alter the outcome of the game. In this scenario, when the legislation is handed over to the bureaucracy for implementation, a petty bureaucrat finds a way to embezzle all of the funds from the new program and flee the country. Thus, the scenario is more like the following:
"Scenario: A citizen, congressional representative, and bureaucrat are engaged in a game represented by the extended form game represented on the attached sheet Figure 2." The constituent has the decision to make whether to telephone the Congressional member about a problem that she thinks is an important issue. Even if she doesn’t call the Congressman, there is a chance that he’ll take action on the issue anyway, and the call takes some time that she otherwise might have spent on things that she finds enjoyable. The Congressperson, regardless of the choice of the constituent, can take action on the issue, or ignore the issue. If he takes action, he will be seen as a pioneer in the fight against the problem, but nobody will notice if he does nothing about the issue, since he is simply one of hundreds who did nothing on the issue. If the legislation is passed, a bureaucrat is handed the job of carrying out the will of the legislature, but he discovers that he has the opportunity to embezzle some large amount of money away from the funding for the new program designed to address the problem that the legislation was trying to combat.
"The extensive form game has been described, and the equilibria are given here:
Nash Equilibria: {(C, A1D2, E1E2), (C, A1D2, E1N2), (L, D1A2, N1E2), (L, D1A2, E1E2), (L, A1A2, E1E2)}
Subgame Perfect Equilibria: {(L, D1A2, E1E2)}
"By using the subgame perfect criteria for the equilibria, we discover that many of the Nash equilibrium points are not the final resting place for the game, and that a certain outcome is more likely when the game is played with the utility outputs given.
"This is just one of many examples which could be constructed to show the differences between games with only the addition of small changes to the overall structure of the game. Simple alterations to the payoff structure, additions of nodes, players, or information sets all will likely change the result of the game in different ways. For this reason, when constructing a decision tree or extended form game, great care must be taken to ensure that the representation adequately matches the factors you wish to model in reality."
Now, here’s the problem: At one point in the not too distant past (less than 3 years), I knew what that all meant. And knew it so well that I got 50 points of 50 points possible on the paper. I no longer understand what most of the material in this paper is about. What in God’s name is a Nash Analysis? What is a Subgame Perfect Equilibrium Point?
Nothing makes a man feel smaller than realizing that he’s slowly losing information that he once held onto with ease. This must be what it feels like for an elderly person who forgets the name of a grandchild, or who has forgotten the name of a brother that died back in ‘the war.’ It’s disheartening. I’m a little less intelligent today than I was a few years ago. Sometime over the holiday break, I’m going to break out my old textbook for that class and try to recapture some of what I’ve lost. I know that I’m always full of cliche sounding comments, but I’m not going to go gently into that good night.
posted by The Academian | 2:37 PM
0 Comments:
Post a Comment
<< Home