Birds do it, Bees do it, Humans do it.
Being the social animals that we are, sex is a normal part of everyday human existance. But why is "the Talk" stereotyped to the point where parents are unwilling to say a thing? The extent of a talk I got was, almost verbatim: "Don't be stupid. Use a condom."
There must be some sort of game going on here.
PLAYERS: Parents we will refer to as one player, for simplicity's sake. Child will be another player. We will assume that the child is around 11 years old because most schools start their sex-ed courses then. Peers will be another player, because as the stereotype goes, kids learn more from their friends about sex than their parents.
ACTIONS: Parents have a continuum of actions, reprsenting the amount of information to provide. This info will be represented with the letter i, and will belong to the closed interval [0,1], i=0 means the parents tell nothing, i=1 means they tell everything(anyone have a doctor as a mother/father?).
Peers will likewise have a continuum of actions, but kids can be a font of very unreliable info. Their info will be represented by the letter p, and will belong to the closed interval [-1/2, 1/2]. p=0 again represents no info. p=-1/2 means REALLY bad info, p=1/2 means decent info.
Now for the Child. They will have an choice of being sexually active or not, with the outcome/utility of that being a random number dependent on the info available, and their choice dependent on the info they have. Due to sex-ed, we will assume that the Child has an initial info of 1/4.
GAME: There is a cost for the Parents associated with giving the talk, possibly representing embarrassment or awkwardness. We will say that the cost is equal to the info given. Parents will also have a cost if the Child becomes sexually active and becomes pregnant(or gets someone pregnant) or gets an STI, which we will say is -10. Parents will have a benefit associated with their child becoming sexually active and having a healthy relationship(though this may be unrealistic, it helps ensure that the parents can have positive utility), which we will say is 2.
The Peers get a benefit for any p=/=0(bragging) that is equal to |p|(It doesn't matter how good the info is, but how much you have). They likewise, however, get a cost associated with their friend getting pregnant/STI that we will say is -5(not as bad as parents, but still sucks).
Now for the interesting part, the Child. We will assume that, like many kids, that they don't listen much to what their parents say, so i is only worth 1/2 of its value. We will also assume that, like many kids, they trust their friends. Hence, p is worth its absolute value. Total info, T, is therefore equal to 1/4 + |p| + (1/2)i. We are, unfortunately, assuming that all of this info is independent, which is not terribly accurate, but it makes the math much easier.
So, the Child will always become active if T > 1. They have lots of info and are just waiting to try it out.
The Child for sure will not become active if T < 3/4. They just aren't sure and need more info.
If T is in [3/4, 1], then they will pecome active with probability T.
The outcome for the Child of all this is
Not Active: 0. No change.
Active, but problems arise(pregnancies/STIs/whatever): -5
Active, but no problems arise: 2. Sex is fun, I ain't gonna lie.
Active, no problems, healthy relationship: 5. Sex is even better with love.(oh man, do I sound sappy)
Now, for some PROBABILITIES.
Problems: 1/4 + p + i. If you're well informed, problems are unlikely. If this total is <0, then treat it as 0, can never be more than .99 as there is always the possibility for a problem. "Failing" this probability roll means a problem arose.
Healthy relationship: 1/4 + i. As much as kids may not realise it, the parents probably know a fair bit about relationships. This total is never treated as greater than .95 because, again, some people are just unlucky.
This is a pretty big pill to swallow, but is a decent starting point. In the next part, I'll talk strategies.
2007-05-16
2007-05-08
The Chore Rotation
Live with anyone, anywhere, and you will run into this sort of situation. Things need to get done to help keep wherever you're living in reasonable/clean/respectable/whatever condition, and you want everyone to be a part of it, at least in theory.
I personally had to deal with some of this recently, so this was the first topic that came to mind. I was also discussing this with my girlfriend, so I figured it deserved mentioning.
For ease of analysis, I will look at the case where the chore in question is cleaning, though it extends easily to more general chores. I will also consider the two player case, though, again, the multi-player case is a pretty natural extension.
I guess I need to state my ASSUMPTIONS, and these will likely be the same for any situation I describe: Players are rational(in rough non-technical terms, can do a lot of computations really fast), self interested(will always act to increase their own utility), and are informed(know all the rules, alternatives and outcomes of the game).
Rational is an okay assumption in games where there are not many outcomes, so not many problems there.
Self-interested is a pretty good assumption considering how most people act in real life.
Informed is tricky. For small games with few alternatives it's reasonable, but it's still tricky. I'll try to avoid it when I can.
SETUP: Each player has two choices: clean(A) or don't clean(B). There is a benefit associated with having a clean house, we'll call it H, which is >0. However, there is a cost associated with cleaning. We'll call this C. The benefit to a dirty house is 0.
GAME1: House is cleaned each week. Each player is in charge of cleaning half the house, and the part of the house that is cleaned rotates between each player each week. There is a "gentleman's agreement" that cleaning will get done that both players agree to, ie, they are going against the self-interested assumption. This agreement also includes that when cleaning gets done, the whole house must be cleaned in a given week.(This is a fairly common agreemen among housemates)
The utility for both players in this case is H - C. We will assume that H>C so that there is net positive utility to a clean house.
Things are going along swimingly. However, one week Player 1(p1) is unable to clean for whatever reason. They have only option D, and so have to do it. Player 2(p2) decides that this week, she will do the cleaning.
p1 utility = H, p2 utility = H -2C. H - 2C could be <0, but this is only for one week.
The next week, however, p1 is able to clean, but the agreement before is nulled since she couldn't clean before. She is now self interested once again. Her utility from the last week is H which is > H - C, so she has no incentive to start cleaning again.(perhaps she is lying to the other player, continuing her story from the week prior)
p2 is now in a difficult position. If H - 2C > 0, then she will likely still clean, since if she doesn't clean, her utility is 0. This is stll unfair, as H > H -2C, so p2 is still getting a raw deal.
If H - 2C < 0, then she won't clean either, since her utility will increase from a number less than 0 to 0.
At this point the players are in a Nash equilibrium. There is no incentive to single-handedly start cleaning again until H - 2C > 0.
At that point people get angry and start yelling at each other to clean.
GAME2: Similar to above, each player is in charge of half the house, but it does not rotate. The benefit to half a clean house is obviously (1/2)H. The agreement this time is that each person cleans only the half of the house they are responsible for.(Another common agreement)
The utility for both players adhering to the agreement is once again H - C which is > 0.
Let's say a similar thing happens here, that p1 can't clean for one week for whatever reason. p2 then cleans her half, and gets a utility of (1/2)H - C. This could be less than, equal to, or greater than 0, as before. If we multiply these expressions by 2, we get H - 2C is greater than, less than, or equal to 0, depending. We are in the same situation as before.
Thus, we get into situations where once the agreement/system breaks, the players end up in a Nash Equilibrium where no one is willing to start the system back up.
The philosphy I follow with regards to cleaning is thus: Clean up after yourself. Not only does this keep your own personal space clean, it helps keep public spaces clean, and shifts blame of dirtiness to the other players. It puts you on what I call the "high horse", where a player is in a position to incentivize(read: guilt) other players into action.
Any other cleaning strategies out there?
I personally had to deal with some of this recently, so this was the first topic that came to mind. I was also discussing this with my girlfriend, so I figured it deserved mentioning.
For ease of analysis, I will look at the case where the chore in question is cleaning, though it extends easily to more general chores. I will also consider the two player case, though, again, the multi-player case is a pretty natural extension.
I guess I need to state my ASSUMPTIONS, and these will likely be the same for any situation I describe: Players are rational(in rough non-technical terms, can do a lot of computations really fast), self interested(will always act to increase their own utility), and are informed(know all the rules, alternatives and outcomes of the game).
Rational is an okay assumption in games where there are not many outcomes, so not many problems there.
Self-interested is a pretty good assumption considering how most people act in real life.
Informed is tricky. For small games with few alternatives it's reasonable, but it's still tricky. I'll try to avoid it when I can.
SETUP: Each player has two choices: clean(A) or don't clean(B). There is a benefit associated with having a clean house, we'll call it H, which is >0. However, there is a cost associated with cleaning. We'll call this C. The benefit to a dirty house is 0.
GAME1: House is cleaned each week. Each player is in charge of cleaning half the house, and the part of the house that is cleaned rotates between each player each week. There is a "gentleman's agreement" that cleaning will get done that both players agree to, ie, they are going against the self-interested assumption. This agreement also includes that when cleaning gets done, the whole house must be cleaned in a given week.(This is a fairly common agreemen among housemates)
The utility for both players in this case is H - C. We will assume that H>C so that there is net positive utility to a clean house.
Things are going along swimingly. However, one week Player 1(p1) is unable to clean for whatever reason. They have only option D, and so have to do it. Player 2(p2) decides that this week, she will do the cleaning.
p1 utility = H, p2 utility = H -2C. H - 2C could be <0, but this is only for one week.
The next week, however, p1 is able to clean, but the agreement before is nulled since she couldn't clean before. She is now self interested once again. Her utility from the last week is H which is > H - C, so she has no incentive to start cleaning again.(perhaps she is lying to the other player, continuing her story from the week prior)
p2 is now in a difficult position. If H - 2C > 0, then she will likely still clean, since if she doesn't clean, her utility is 0. This is stll unfair, as H > H -2C, so p2 is still getting a raw deal.
If H - 2C < 0, then she won't clean either, since her utility will increase from a number less than 0 to 0.
At this point the players are in a Nash equilibrium. There is no incentive to single-handedly start cleaning again until H - 2C > 0.
At that point people get angry and start yelling at each other to clean.
GAME2: Similar to above, each player is in charge of half the house, but it does not rotate. The benefit to half a clean house is obviously (1/2)H. The agreement this time is that each person cleans only the half of the house they are responsible for.(Another common agreement)
The utility for both players adhering to the agreement is once again H - C which is > 0.
Let's say a similar thing happens here, that p1 can't clean for one week for whatever reason. p2 then cleans her half, and gets a utility of (1/2)H - C. This could be less than, equal to, or greater than 0, as before. If we multiply these expressions by 2, we get H - 2C is greater than, less than, or equal to 0, depending. We are in the same situation as before.
Thus, we get into situations where once the agreement/system breaks, the players end up in a Nash Equilibrium where no one is willing to start the system back up.
The philosphy I follow with regards to cleaning is thus: Clean up after yourself. Not only does this keep your own personal space clean, it helps keep public spaces clean, and shifts blame of dirtiness to the other players. It puts you on what I call the "high horse", where a player is in a position to incentivize(read: guilt) other players into action.
Any other cleaning strategies out there?
In the beginning...
There was darkness, chaos and ignorance.
One day, there came the light, and the light was understanding, and the understanding was light. Chuck "Orcus" McPhail had come.
Okay, enough pretention. It just had to be done, sorry.
As a recent graduate of the University of Waterloo's prestgious Faculty of Mathematics, I like to think I have a handle on things. Specifically math.
My final year at UW, I took two courses in particular that opened up my eyes to some interesting possibilities: a course in Game Theory, and a course that dealt a lot with Mechanism Design(algorithmic Game Theory).
Take players, alternatives, outcomes, preferences and some assumptions about interaction and you're ready to do some analysis. I fell in love with this topic and it is easily my favourite branch of mathematics, a lot of my final year of study being related to how these things work within Graph Theory.
But more to the point, once I learned all that, I started seeing all sorts of everyday situations that can be modelled in Game Theoretic terms. And so, we come to the point.
Here, I will do some analysis of everyday/political/economical/stupid/amusing situations that I come up with as if they were strategic games. Sometimes I hope to be insightful, most of the time I will just be thinking on-screen.(Someone needs to find a better computer equivalent to "thinking out-loud")
Cheers.
One day, there came the light, and the light was understanding, and the understanding was light. Chuck "Orcus" McPhail had come.
Okay, enough pretention. It just had to be done, sorry.
As a recent graduate of the University of Waterloo's prestgious Faculty of Mathematics, I like to think I have a handle on things. Specifically math.
My final year at UW, I took two courses in particular that opened up my eyes to some interesting possibilities: a course in Game Theory, and a course that dealt a lot with Mechanism Design(algorithmic Game Theory).
Take players, alternatives, outcomes, preferences and some assumptions about interaction and you're ready to do some analysis. I fell in love with this topic and it is easily my favourite branch of mathematics, a lot of my final year of study being related to how these things work within Graph Theory.
But more to the point, once I learned all that, I started seeing all sorts of everyday situations that can be modelled in Game Theoretic terms. And so, we come to the point.
Here, I will do some analysis of everyday/political/economical/stupid/amusing situations that I come up with as if they were strategic games. Sometimes I hope to be insightful, most of the time I will just be thinking on-screen.(Someone needs to find a better computer equivalent to "thinking out-loud")
Cheers.
Subscribe to:
Posts (Atom)
