an update on the battle.
i couldn't really find an old picture of my cup. since i don't usually take pictures of my cups. but i have this one and you can see some stains. just multiply that around the entire rim and on the bottom of the cup. now it is completely clean. so cool.
game theory of the day is centipede game. two people. there is two uneven pots of money in front of person a. person a can choose to take the pot with more money and leave the smaller pot for the other person (and game ends) or he can pass both pots to the other person. if the pots are passed over, both pots accumulate money. when person b gets the pot, he can choose to end the game by taking the larger pot or send it back to have it accumulate more money. so basically, it is a balance between how much you want the pot to accumulate money and risking the other guy taking it. kind of a game of chicken.
the standard strategy is to take the money at your first chance, which means the games ends right when it starts. similar to iterated prisoner's dilemma and unexpected hanging paradox, there is an end when someone will take the money, so should take the money before, and before, and before, and this leads to the first possible chance. but apparently in real life (and not on processed trees), people often don't follow this strategy. usually they will let it run a few rounds before taking the money. it depends on how altruistic the other player is. if he is altruistic, it would be good to let it run a few times then take advantage of him and take the money. or people like to take risks and stuff.
but being altruistic is good for both players (hence, the descriptive word "altruistic"). by pushing the pot back every turn, the money accumulates more than what would have been collected by taking it. so by helping the other person you also help yourself. only the idea that one must have more than the other leads one to take the money. so i guess it is good to be altruistic. but then you would be second place (and in this case, last place). who could be satisfied with that!?
so i have this mug that is really stained from tea. (i drink tea basically every morning. yes, like an old man). i've tried many things (soap, vinegar, baking soda, etc) to get the stain off but it has stayed stained for almost 3 years. today i drank a hot chocolate from the mug, and the stains disappeared. interesting chemistry. must investigate.
so i've moved on from marriage into imprisonment (can argue that's not changing anything at all, but whatever). i think this game theory should be named prisoners' dilemma, with the apostrophe moved over, since there are two prisoners. unless only one thinks. but both have a dilemma. prisoners' dilemmas? huh. anyway, two suspects are caught. each one is told they can sell out the other guy and they can go free and the other guy will get 10 years. if they both sell each other out, they both get 5 years. if both don't say anything, they just get 6 months. so the obvious answer is to sell the other guy out.
but being in jail once isn't fun enough, so they made an iterated prisoner's dilemma, which means this game is played n times (n being some number. i guess it should be a positive integer). according to john nash, the nash equilibrium is... sell the other guy out! the game eventually has to end (unless n is positive infinite. would it still be an integer?) and the prisoners know this. a prisoner would have to sell out on the other guy on the last turn, because there's no more chances to be punished by the other guy. since they are all going to sell each other out on the last turn, they should sell each other out the turn before. and the turn before. and the turn before. all the way to the beginning. (kind of reminds me of unexpected hanging paradox, which is a king tells some guy they are going to be hanged unexpectedly on some day this week. guy believes he won't die because if he's not killed by thursday, he'll know he will die on friday. which means he can't die on thursday, or he'll know by wednesday, etc. in the end, he's still hanged unexpectedly [because he came to the conclusion that he isn't].)
then there's some guy that made some "superrationality" approach to the iterated dilemma. a superrational prisoner will know when he's against another superrational prisoner and they'll act the same, because they can think of what is in each others' minds or something. so in this way, they will agree to be quiet sometimes. too bad we can't read other people's minds. and a superrational prisoner will know the other person is thinking of cooperating and then cheat him and win. and the other prisoner might think this and try to cheat back. and then in the end, they both are selling each other out again. maybe. i don't quite understand super things.
the some brilliant anatol rapoport guy wrote (well, typed) four lines of BASIC code and apparently it is the best results for some contest. and he won. basically his thing, called "tit for tat," is cooperate and then copy what the other person does the previous round. so there's lots of cooperation. and that is good. but the prisoner must have four traits: nice, retaliating, forgiving, and non-envious. nice being optimistic and cooperative. retaliating if the other person starts to retaliate. forgiving, which is to cooperate again if the person doesn't retaliate against the retaliation (so it doesn't cycle). non-envious is not trying to beat the other guy. some problems with this one is that sometimes it might go into an endless spiral of selling each other out. oh well, too bad. and too bad most people probably don't have all four traits. it's interesting though because it shows that the best strategy is to cooperate. this idea is kind of modeled after reciprocal altruism in biology (or did the idea of reciprocal altruism come after?). well, if this is the best strategy, should be applied to more of life, but i guess this is a long-run thing and in the long run we're all dead. so since we know there is an end, we should cheat at the very end. and this propagates forward, like nash equilibrium. too bad we must always win. i will win. short run is the best. leads to doom, but it's okay. like global warming, no one wants to lose their technological process by stopping.
i can't sleep because someone decided to say "stable marriage problem" and then my mind suddenly became so invested in this game theory and i stopped studying and now i can't sleep. so here it is: there are a group of males and a group of females. same number of people in each. each female has a preference of males in a list. and each male has a preference of females in a list. during round one, all the males propose to their first choice. if a female has more than one male proposing, she says "yes (it's more like a maybe)" to male that's highest on her list and rejects the rest. if a female has just one guy, she says "yes (maybe)".
round 2 begins and the males that don't have a yes female go on and ask their second choice, even if the female said yes to some other male. if a female that's already in a "yes" relationship gets asked by a male that is higher on her list than the guy she yes-ed to, she can dump her first guy (crycry, suicide) and move higher up the list. this keeps repeating and eventually, everyone is paired up. apparently, by this method, all the marriages are stable and there are no relationships that have people that would like to be with another person and have the other person want to be with them. so everything is stable.
but the results are kind of weird. it turns out that the coupling is optimal for males and pessimal (what an odd word, but wikipedia uses it) for females. this means males get their higher choices and females are usually not getting their highest choice. yet, females are the ones that are rejecting and moving higher. so it seems odd. but the popular girls that have a lot of guys can be choosy and get choices near the top. so that sucks for the girls that don't get proposed to very much, because they are stuck with their lame few choices. so i guess those females can be more optimal if they are asking. (but that is against societal norms!)
but this assumes that everyone is in a room and knows all their options. which isn't likely, and people come in and out of life, so this cross-section of time is not good. and there's not always equal numbers of males and females (like in china!) and blahblabhabh. lists of preference change. variables everywhere.
anyway, i thought about the if there was an extra male. it would just end up in a loop, i think. always one leftover guy, just going down his list. and i guess... nevermind. just kidding. he would just be left out. poor guy. there would be some sorting around, but eventually no one would want that guy. well, extra girl is easy, because she's just the girl that no guy wants. the fat ugly one. poor her.
also, it's weird that if all the guys have a different girl as their first choice, then in one round, everyone is in a stable marriage. that is odd. doesn't even consider the females. but as long as everything is stable. stable state. lowest energy state. boring. no excitation. oh, that's dirty.
in conclusion, the results were determined to support the hypothesis of yes +/- no.
time is the only independent variable. everything is dependent on it. except, maybe the perception of time, (which might be dependent on perception, [which might be dependent on activity and perception in general, {which might be dependent on life}]), but what units with those be? just drudge along at the speed of time. good enough for me.
inspire, expire, inspiration, expiration. a repetitive cycle. takes energy to inspire, gravity will expire for you. no work at all. just let it fall. unless you really need to expire fast. good thing there's more airflow resistance in expiration than during inspiration.
