annenberg media ♪ by: narrador: bienvenidos a destinos: an introduction to spanish. primero vamos a ver algunas escenas de este episodio. no ha sufrido más que unas pocas magulladuras. ¿entonces? entonces, ya puede dejar esta cama

para alguien que la necesita de veras. con permiso. hola, manuel. sí, regresé hace poco. me alegro, porque quiero hablar contigo sobre algunas cosas. cuando quieran, nos vamos. yo necesito cambiar dinero. yo también. bueno, sobrino, ¿qué te pareces si nos tomamos un café? vamos. las esperamos en la cafetería. bien. también vamos a aprender vocabulario y expresiones relacionados con el turismo. ¿a cuánto está el dólar? a dos mil novecientos pesos. angela: ¿cuánto cuesta cada timbre? es de unas ruinas indígenas. a mí me gustan las postales que tienen vista panorámica. mira, como ésta. sí, es muy linda. necesito enviar unas postales a puerto rico. ¿cuánto cuesta cada timbre?

mil quinientos pesos. este es un teatro de y para adultos y no pienso cambiar nada de la obra y voy a seguir ensayando con los actores. lo esperan en la clínica de guadalajara esta tarde. ¿esta tarde? i¿hoy mismo?! no hay tiempo que perder. cuanto antes tenga los resultados de los exámenes será mejor. ( sirena ) captioning of this program is made possible by the annenberg/cpb project and the geraldine r. dodge foundation. ahorita necesito tu carro, por favor. en el episodio previo, carlos le dijo a ramón

que gloria había desaparecido y después salió muy tarde por la noche a buscarla. al día siguiente, roberto se despertó. se sentía bien, y escuchó atentamente mientras angela le contaba todo lo que había sucedido desde que conoció a raquel en san juan. no, el abuelo está muy enfermo y lo han llevado a un hospital. pero sí he conocido al tío arturo que ha venido desde la argentina. es muy simpático. y más tarde, roberto conoció a su tío. ...que él es nuestro tío arturo. ies increíble! ¿increíble? ¿qué cosa? tenés la misma sonrisa de tu padre, angel. de veras, ila misma sonrisa! carlos regresó a casa de ramón, pero gloria no estaba con él.

ya les daré una explicación a todos. es hora de que sepan la verdad. ( suspira ) doctora: muy bien... no ha sufrido más que unas pocas magulladuras. ¿entonces? entonces, ya puede dejar esta cama para alguien que la necesita de veras. con permiso. bueno, entonces podemos ir a conocer al abuelo. ¿dónde está mi ropa? iay!, la ropa, es verdad. se quedó en el pueblo. y la que traías no está en muy buenas condiciones iy menos para presentarte al abuelo! bueno, bueno, no es ningún problema. podemos ir de compras y después ir a conocer al abuelo. ¿qué les parece? me parece muy bien.

pati: vamos a ensayar la escena que comienza... en la página noventa y dos. perfecto. ¿sí? pati, veo que ha regresado. hola, manuel. sí, regresé hace poco. me alegro, porque quiero hablar contigo sobre algunas cosas. no quiero ser brusca, pero... en este momento me gustaría ensayar con los actores.

me parece... pati, es urgente. me gustaría hablar contigo ahora. bueno, si es tan urgente que no puede esperar... guillermo, ¿quieres ayudarles a ensayar la primera parte de la escena? sí, ¿cómo no? gracias. vamos a comenzar entonces en la página noventa y dos. ¿qué querías? ¿sabes que esta obra me parece un poco controversial? si me lo recuerdo me has dicho que es muy controversial. pues, sí. hasta creo que ni siquiera la vamos a poder estrenar. i¿cómo?! no te enojes. los patrocinadores me han dicho que no están dispuestos a seguir apoyando la obra a menos que cambies unas de las escenas más controversiales. manuel, no entiendo. hemos discutido esto diez veces y te he dicho que no, que no pienso cambiar absolutamente nada. pati, mira. o cambias las escenas

o cancelamos la producción. iasí es! ilisto! cuando quieran, nos vamos. yo necesito cambiar dinero. yo también. bueno, sobrino, ¿qué te pareces si nos tomamos un café? vamos. las esperamos en la cafetería. bien. quisiera cambiar unos dólares, por favor. ¿cómo no? ¿cuántos? ¿a cuánto está el dólar? a dos mil novecientos pesos. bueno. quiero cambiar cien dólares entonces. muy bien. quisiera cambiar unos dólares, por favor. ¿cómo no? ¿a cuánto está el dólar?

a dos mil novecientos pesos. aquí tiene su recibo, señorita. gracias. ¿sabes si roberto tiene dinero? sí. también cambié para él. yo también quisiera cambiar unos dólares. ¿cómo no? ¿cuántos? mmm... unos... doscientos. muy bien. pues, ¿qué piensas de roberto? es muy simpático. me cae muy bien. hablamos un poco anoche pero me gustaría hablar más con él a solas. tome, señorita. quinientos ochenta mil pesos, y su recibo. necesito comprar sellos. angela, aquí no se dice "sellos". se dice "timbres". yo guardé unos de antes.

mira. gracias, raquel pero yo tengo que mandar muchas postales a mi familia. ¿venden sellos... ay, digo timbres, aquí? normalmente, sí, señorita pero ahora no tenemos. tendrá que ir al correo. ¿está muy lejos el correo? no, está aquí cerquita. a la vuelta nada más. gracias. voy a comprar unas postales aquí al lado. ¿quieres ir conmigo? sí, vamos. arturo y roberto pueden esperarnos. vamos. ¿cómo es posible que la opinión de unos cuantos señores sea causa para la cancelación de esta obra? bien sabes que "la opinión de unos cuantos señores" cuenta siempre. cuenta en la televisión, cuenta en el cine cuenta aquí en el teatro universitario. y no solamente aquí en este teatro sino en todos los teatros universitarios de este país. y la verdad es que esta obra tiene partes que son ofensivas para ciertas personas.

pues, me importa un comino su opinión. diles a esos señores que vayan a apoyar las películas de walt disney. este es un teatro de y para adultos y no pienso cambiar nada de la obra y voy a seguir ensayando con los actores. pati, piensa bien en esto: puedes arruinar las futuras oportunidades que tienes para dirigir. mira, aquí hay tarjetas postales. iay, es muy linda! es de unas ruinas indígenas. a mí me gustan las postales que tienen vista panorámica. mira, como ésta. sí, es muy linda. me gustaría poder visitar algunos lugares mientras estemos aquí. pues, no hay razón para no hacerlo. mis padres llegan, y creo... ¿tus padres llegan? sí. ¿por qué te sorprendes? bueno, porque te conozco ya hace un tiempito y todavía no sé nada de tu familia.

itú ya lo sabes todo acerca de la mía! es verdad. ya vas a conocer a mis padres. me gustaría eso. ¿tu mamá es como tú? bueno... espera mejor a que la conozcas. son muy unidas, ¿no? claro que sí. pero a veces mi mamá me cansa. ¿por qué? hablaremos de eso más tarde. bueno. me voy a comprar estas postales y nos vamos al correo para comprar timbres ¿de acuerdo? podemos hablar mientras caminamos. y una vez mi mamá fue a mi oficina. y allí, delante de todos, se puso a decir "esta es mi hija, la licenciada rodríguez".

a mí me dio tanta verguenza. empleado: señorita, por favor. ah, sí. necesito enviar unas postales a puerto rico. ¿cuánto cuesta cada timbre? mil quinientos pesos. deme seis, por favor. ¿y cuánto cuesta a mandar una carta a puerto rico? ¿por correo aéreo? sí, señor. mil quinientos pesos también. deme también timbre para dos cartas, por favor. es por si le envíe una carta a jorge. son doce mil pesos. gracias. necesito enviar unas postales a puerto rico. ¿por correo aéreo?

así que mi mamá es un poco mandona, ¿entiendes? ¿pero te llevas bien con ella? bueno, lo intento. lo que pasa es que ella a veces no se da cuenta de cómo sus acciones afectan a los demás. ¿y tu papá? ah, él es totalmente diferente... medido, tranquilo, mesurado. con él se puede hablar muy fácilmente. eres la niña mimada de tu papá. bueno. doctor, ¿ocurre algo malo? es mejor que hablemos a solas. adelante, pase por aquí.

gracias. ilupe! ¿mande? ramón: lupita, por favor sírvenos un cafecito. sí, señor. pati: cinco minutos de descanso. ¿un poco de café? iay! gracias. bueno... dime, ¿qué pasa? nada. estoy haciendo unos cambios en el diálogo de elena. hay una parte de la escena que no funciona bien.

este... no me refiero a la obra, sino a ti. ¿qué te pasa a ti? ya sabes, manuel y sus patrocinadores quieren cancelar la obra. pati, yo te conozco ya hace mucho tiempo y desde que regresaste de méxico has estado distinta. ¿te sucede algo más? es juan. se ha enojado conmigo a causa de esta obra. ¿cómo? no entiendo. sí... cuando le dije que tenía que regresar a nueva york se enojó conmigo. el quería que yo me quedara en méxico con su familia. bueno, eso se puede entender pero tu presencia aquí era muy necesaria. mira, eso lo entendemos tú y yo pero él no lo entiende tan fácilmente. no sé qué hacer. a veces me siento como si estuviera entre la espada y la pared.

pati, ¿se te ha ocurrido alguna vez que juan tiene celos, de ti? ¿celos? de mí? bueno, mejor dicho envidia... de tu carrera. mira, yo los conozco muy bien a los dos y tú eres una persona de muchísimo talento y has tenido mucho éxito en la carrera. ¿y tú crees que él no puede aguantar eso? bueno. es difícil para cualquier persona pero tienes que tomar en cuenta de que juan es un hombre un poco machista, y como el menor de su familia se acostumbró a ser centro de atención. nunca había pensado en eso. pues... guillermo ¿podrías venir un momento, por favor? sí, ahorita voy. o.k. gracias. bueno. voy a ver qué desastre nos espera, ¿eh?

mercedes: doctor si le he entendido bien debemos llevar a papá urgentemente a guadalajara para que le hagan los exámenes. exactamente. el doctor salazar, que normalmente atiende aquí a sus pacientes se encuentra en guadalajara, como uds. saben. y se niega a regresar aquí para atender a sólo un paciente pero está dispuesto a examinarlo allá. me parece un poco raro. pues, este doctor es el mejor en este campo y la escuela de medicina de guadalajara le pidió que consultara con sus médicos. así es, señora, no hay más remedio. ¿y? qué tal? ya está, me llevo el traje también. muy bien. ¿llamaste a la clínica donde está el abuelo? sí, pero no encontré a mercedes.

la recepcionista me dijo que estaba en el hospital pero debe haber salido por un momento. bueno, podemos ir a almorzar y después, vamos para allá, ¿qué les parece? vamos. te esperamos en la caja, ¿está bien? ¿y no hay otro doctor aquí? esta es una gran ciudad. como le dije, el doctor salazar es el mejor. y si se preocupa por el viaje, no tiene por qué. su papá viajará bien a guadalajara en avión. lo hacemos con frecuencia. ¿y es tan urgente? sí. me tomé la libertad de hacer los arreglos. lo esperan en la clínica de guadalajara esta tarde. ¿esta tarde? i¿hoy mismo?! no hay tiempo que perder. cuanto antes tenga los resultados de los exámenes será mejor. pero, no hay tiempo de prepararlo avisar a la familia... el tiempo puede ser nuestro peor enemigo.

señora, ¿ud. puede preparar todo rápidamente para el viaje? pues... no sé... si es necesario... es una buena oferta. lo platicaremos con el resto de la familia. la gavia inn... suena bien, ¿verdad? bueno, es un poco prematuro para hablar de nombres. ya verá. esto puede llegar a ser un paraíso. esto ya es un paraíso. tiene razón. bien... no le quito más su tiempo. hasta pronto. muchas gracias por su visita. ilupe! ilupita! iven, apresúrate, por favor! ¿qué ocurre? ¿quién llamó? era mercedes. dice que el médico quiere que llevemos a papá a guadalajara para unos exámenes. iy quiere que sea hoy mismo! ¿puedes preparar alguna ropa para mercedes y papá? tenemos que llevarla luego. ¿cómo no, señor? por favor, la llave

de la habitación trescientos cinco. gracias. bueno... voy a la habitación a cambiarme. regreso como en diez minutos. te espero aquí. aprovecho para escribir unas postales y enviarlas. bien. si me permiten subo un momento a mi habitación. sí. qué bueno que dejaron que roberto saliera del hospital, ¿verdad? pero roberto no tenía nada de ropa. había dejado su ropa en el pueblo donde estaba la excavación. antes de ver a don fernando, teníamos que ir de compras. aquí tiene su recibo, señorita. gracias. raquel: pero antes de ir de compras, angela y yo cambiamos dinero. yo también quisiera cambiar unos dólares. ¿cómo no? ¿cuántos? mmm... unos... doscientos. es de unas ruinas indígenas.

raquel: compramos unas postales... a mí me gustan las postales que tienen vista panorámica. mira, como ésta. sí, es muy linda. raquel: y también unos timbres. necesito enviar unas postales a puerto rico. ¿cuánto cuesta cada timbre? mil quinientos pesos. mientras mirábamos las postales angela y yo hablábamos de mis padres. angela quería saber algo de mi mamá. angela quería saber si ella es como yo. ¿recuerdan lo que le dije? ya vas a conocer a mis padres. me gustaría eso. ¿tu mamá es como tú? bueno... espera mejor a que la conozcas. yo le dije a angela que pronto conocería a mi mamá. y entonces ella misma podría decir si es como yo.

mi mamá y yo nos llevamos bien pero no creo que tengamos la misma personalidad. bueno, por fin fuimos de compras y roberto se compró unos pantalones y un traje. me llevo el traje también. muy bien. luego, volvimos aquí al hotel y almorzamos. ahora estoy esperando a roberto y arturo. ojalá vuelvan pronto. mientras raquel espera a roberto y arturo vamos a repasar lo que ha ocurrido en la familia castillo. hola, manuel. sí, regresé hace poco. me alegro, porque quiero hablar contigo... en nueva york, pati habló con manuel, el productor. ¿qué recuerdan uds. de la conversación?

los patrocinadores me han dicho que no están dispuestos a seguir apoyando la obra a menos que cambies unas de las escenas más controversiales. manuel, no entiendo. pati: y te he dicho que no pienso cambiar absolutamente nada. pero pati le dijo que no quería hacer esos cambios. entonces, ¿qué le dijo manuel? o cambias las escenas o cancelamos la producción. así es. manuel le dijo que él cancelaría el estreno de la obra. pues, me importa un comino... pero pati se mantuvo firme.

ella le dijo a manuel que ella no tenía miedo. mientras tanto, en el hospital en méxico el doctor le dijo algo muy importante a mercedes. ¿qué le dijo? su papá viajará bien a guadalajara en avión. lo hacemos con frecuencia. ¿y es tan urgente? sí. me tomé la libertad de hacer los arreglos. lo esperan en la clínica de guadalajara esta tarde. el doctor le dijo a mercedes que...

pero raquel y los demás no saben nada de lo que está pasando con don fernando. en unos minutos, vamos a ir a ver a don fernando. angela está escribiendo unas postales y yo estoy esperando a roberto y arturo. me pregunto, ¿cómo va a reaccionar don fernando cuando por fin conozca a roberto y a angela? ¿qué le va a preguntar a arturo sobre rosario?

está bien, carlos. ahora puedes explicarme, ¿qué pasa con gloria? hay much cosas que platicarte, pedro. ¿te parece si lo hacemos en tu casa? está bien. ( sirena ) captioned by the caption center wgbh educational foundation

annenberg media ♪ for information about this and other annenberg media programs call 1-800-learner and visit us at www.learner.org.

mujme casé, trabajé, unacrié tres hijos.ena. trabajé mucho y lo planeamos todo. todo menos la degeneración macular de los ojos. me ha robado mi vista y mi independencia. y esta enfermedad de los ojos será una epidemia para cuando mis hijos alcancen mi edad. llame al 1-800-437-2423 para información gratis de la organización de investigaciones de la degeneración macular.

>> we've all heard it said that life is like a game. most games, whether we work in teams or work alone, have well-defined rules, with clear benefits for winning and costs for losing. and that makes them something we can think about logically and mathematically. but what about life? can mathematics tell us anything about the competitions and collaborations that happen every day between individuals, groups,

nations, even between animals or microbes? from the social sciences to biology, robotics and beyond, the answer is yes. welcome to game theory. [ overlapping conversation ] >> so, mr. blue, we got you dead to rights. picked you and mr. white up not a half a block from the scene of the robbery. >> we were out buying groceries. >> we were out buying groceries. >> is that where you got this little item? >> that? that doesn't prove a thing. >> doesn't prove anything. >> really? now, what do you think your friend blue will say about that? >> he won't talk. he better not. >> look, i'm going to lay it out for you: you talk, we let you go. >> both: no jail time? >> nada. zip. >> what happens to white? >> what happens to blue? >> he gets 90 days. >> what if he talks and i don't? >> well, then he walks and you

get 90 days. >> what if he rats on me and i rat him? >> you both get 60 days. >> both: what if neither one of us talks? >> then it's a light sentence: you both do 30 days. but you need to ask yourself: how much do you trust your buddy? >> both: okay, he did it. [ laughing ] >> now, that wasn't such a good strategy. or was it? both mr. blue and mr. white end up in jail. but with the right combination, one or the other could have been free. then again, if they had cooperated with each other and kept quiet, they'd still go to jail, but with an easier sentence. so, what's their best strategy? or is there one? our two criminals are, in fact, caught in what's called "the prisoner's dilemma," a classic scenio of modern game theo, which came into its own as a part of mathematics in the 20th century. you see, the point is that

interactions are strategic, say, cooperative or competitive, and how well we do iany given strategy almost always depends on the actions of others. the value of an interaction can be expressed in terms of a cost and a benefit, as in the loss or capture of piece in a chess game. the great surprise of game theory is that it not only applies to "games" but interactions in the real world, like the dilemma facing mr. blue and mr. white. to do that, let's take a look at the game these kids are playing. >> one, two, three. even. one, two, three. >> it's called odd-even, sort of a simple version of rock-paper-scissors. one kid takes odd and the other takes even. for each round, the kids choose to reveal either one finger or two. when they add up the number of fingers, if that number's odd, the kid who chose odd wins all the points. if it turns up even, the kid who chose even gets all the points.

in every round, one kid wins and one kid loses. pretty simple, and it doesn't seem like there's much strategy going on. but let's look further. the best way to understand what the odd-even game looks like in terms of who wins and who loses is to build a grid and look at how each single round, or game, could go. let's put odd on the left and even on top. so if the first, odd, chooses 1 and even chooses 1, even gets the two points, and we can say, theoretically, that odd loses two points. we write it like this, starting with odd's score being -2 and even's score being 2, even's payoff. the second time, maybe odd chooses 1 again and even chooses 2. now we've got 3, an odd number, so odd gets the points. odd's payoff is 3, even's cost is -3. third time, odd chooses 2, even

chooses 1. odd wins again. and again odd's payoff is 3, even's cost is -3. fourth time, they choose 2 and 2, and so on. even wins. now, if we're trying to decide on a best strategy, we actually have to do a little algebra and figure out the probability of each solution turning up. now, here's where we see the magic of math. it turns out that if odd plays 1 7/12ths of the time, odd will actually accumulate more points over time, winning the game. this is an example of a "mixed strategy" because odd has to mix up what he does. in fact, if you do only one thing all the time, your odds of winning aren't going to increase. just the opposite in the long run, because your opponent's going to figure out pretty quickly what you're doing. this kind of payoff matrix does help us see that our instinct for not making the same choice all the time is also a

mathematically sound one. odd-even is an example of what we call a zero-sum game: "i win, you lose." a player benefits only at the expense of others. if you add the payoff and benefit for each hand, they add up to 0. but most games are non-zero-sum: a gain by one player doesn't necessarily mean a loss by another player, as in blue and white's prisoner dilemma. let's take a look at their payoff matrix to see if there's a best strategy for their non-zero-sum game. "c" stands for "cooperate," the choice to keep quiet. "d" stands for "defect," the choice to rat the other person out. it's pretty obvious that mutual defecting gets the biggest jail time and cooperating gets the lightest, at least when we're talking about both people. but if we're looking for the best strategy for one individual, what we're really looking for are ways to maximize that person's benefits while minimizing their maximum cost. for example, let's pick mr.

blue. if he cooperates with white, he gets a reward of a light sentence. >> i don't know anything. >> thirty days! >> but if blue succumbs to the temptation to defect and white cooperates, blue goes free and white gets the worst punishment, the sucker's payoff. >> white did it. >> ninety days for white. blue is free to go. >> and if both blue and white defect, it's the harshest punishment for both of them. >> white did it! >> blue did it! >> sixty days, the both of you. >> so what's a prisoner to do? if i'm a prisoner, the potential payoffs really define the game. they're ranked in this order: "t," temptation to defect, is greater than "r," the reward, which is greater than "p," the punishment, which is greater than "s," the sucker's payoff. and if we plug in values, the payoff matrix clearly shows the stakes and the dilemma, because

it seems like choosing to defect is always the best strategy. in mathematical terms, p is what we call the minimax solution, a choice that minimizes the maximum loss. hungarian-american mathematician john von neumann described the minimax solution in 1928 and effectively established the field of game theory. using functional calculus and topology and chess, von neumann proved it possible to work out the best strategy in zero-sum games that would maximize potential gains or minimize potential losses. von neumann quickly recognized that his ideas could be applied to the game of business, so in 1944, he teamed up with economist oskar morgenstern and wrote theory of games and economic behavior. the book revolutionized the field of economics. at that time, economists focused on how each individual responds to the market and not how individuals interact with each

other. von neumann and morgenstern argued that game theory provides a tool to measure how each player's actions influence their rivals. with the minimax solution, there was at last some mathematical way to help figure out the best strategy in a zero-sum game. but the problem remained: is there a best strategy for a non-zero-sum game like the prisoner's dilemma? the complexities of non-zero-sum games were of great interest to the mathematician john nash. in a series of articles published between 1950 and 1953, nash produced some amazing insights into these kinds of situations. while still a student at princeton, nash realized that in any finite game, and not just a zero-sum game, there is always a way for players to choose their strategies so that none will wish they had done something else. for the prisoner's dilemma, the best strategy is always to defect. that is, a pure d strategy. the minimax theorem had already

showed why in terms of costs and benefits, but nash's insight was about behavior: if i play my strategy against your strategy, is there a point where changing my strategy won't help me? the answer is yes. knowing that and searching for that point creates what nash called a strategic equilibrium in the system. and the strategy that creates that equilibrium is now, quite naturally, called the nash equilibrium. however, this didn't necessarily mean that the payoffs to each individual are desirable, so it still looked like selfish interest was the rule in game theory. but as we said, people aren't numbers, and they do seem to cooperate, to trust each other, at least sometimes. >> you ratted me out. >> you ratted me out. >> so, what you reading? >> book on mathematics.

>> you got a plan for when we get out? >> maybe. >> what about that drugstore? you know, the one on broadway? >> didn't we already do that one? >> seems like it's ripe. >> i guess. third time's the charm. >> both: one, two, three. one, two, three. one, two, three. >> rock-paper-scissors is a game played by children, adults, even prison guards all over the world. but while it's just a game, it's also an interesting mathematical object, and it's the next step in our investigation of game theory. i'm here with david krakauer. david is a research professor at the santa fe institute whose work lies at the interface of evolutionary biology, mathematics, and computer science. so, david, rock-paper-scissors, just a game for prison guards? >> well, no. i mean, what makes this game inresting is there's no best pure strategy solution. if you take rock-paper-scissor -- well, let's play it. let's say i play stone while you play paper.

well, so paper seems to be better than stone, so i'll play paper. well, now you play scissor. well, scissor seems to be the best of all because it's better than the previous move, which is better than the previous move, so it must be the best, but now you play scissor and i play stone, and i win, so you've lost. so there's this peculiar property called non-transitivity of the payoff, and that leads to a strange solution where there is no best pure strategy. >> there's no best thing for me to do absolutely every time. >> all the time, exactly. unconditionally. and so in this game, it turns out the best thing you can do is just play completely randomly. you play each strategy with a probability of one-third. >> so i have to randomize. so that randomization is an example of a mixed strategy, is that right? >> mixed strategy simply refers to the probability of playing any one of the pure strategies. and in this case, the pure strategies would be paper, scissor, or rock. and the mixed strategy specifies the probability associated with each pure strategy, so a third, a third, and a third. >> right, and if i deviated from that in any way, then you could

exploit that in some fashion. >> yeah, if i saw that, dan, you liked particularly playing rock, i'd pick up on that cue and i'd just start playing paper, and then i'd get overall a larger score than you. >> right. >> and so we have lots of thoughts in our heads and intuitions about things, and we're not quite sure which is right, what's superfluous, and what's real. and so mathematics can help to amplify the weak intellectual signal. and so a good example is, you know, what are our intuitions about cooperation? when should we be nice, when should we not cooperate? and using mathematics and computational modeling, axelrod, at university of michigan, a political scientist, in 1978 staged a tournament of computer programs competing in a virtual world over the prisoner's dilemma game. >> so you have a whole collection of people, and everybody's competing, trying to stay out of jail for the longest amount of time. >> so what you have is a large number of computer programs all competing so as to maximize their payoff. and so in the first tournament that was held, 14 computer

programs were contributed. and there was one clear winner. and the one that won was "tit for tat." and tit for tat just says, "do unto others what they do unto you." and so i just copy your move in the last game. >> so if i cooperated last time -- so i'm playing you, and if you cooperated last time, then in the next game, i'm going to cooperate. if you defected last time, in the next game i'm going to defect when i play you. >> exactly. so here's this hugely complex problem, the problem of cooperation. somehow you capture the essence of the problem in the prisoner's dilemma matrix, which is this trivial little 2 x 2 matrix that somehow gets to the heart of the problem. and then you find that the way to do this, to win that game when it's repeated several times, is to play tit for tat and nothing more complex. >> it wasn't him. >> it wasn't him. >> wasn't him. >> was not him. >> was not him. >> so tit for tat is interesting, but it does seem to have limitations because ultimately, it could also be in one of these anti-cooperative death spirals, if you like: i defect, you defect, i defect.

>> he did it. >> he did it. >> he did it. >> he did it. >> he did it. >> he did it. >> that kind of idiotic solution where you simply copy what the guy did in the last round, it leads to that perpetual defection. and it turns out that when there's some noise or uncertainty, then tit for tat is not the best strategy. so when axelrod had that tournament, it was working inside a computer. errors were never made. the only uncertainty was what your opponent was going to play. but you always knew exactly what they played once they played it. but let's say that you forgot what they played. so i play you, dan, and let's say you cooperated, and i think, "did dan cooperate or defect? i think he defected." so i defect and then you defect. now, it turns out there's an alternative strategy that does better when the world is uncertain, and that strategy -- >> which is closer to life. >> which is much closer to life, and that strategy is called pavlov. named after pavlov, who did work on conditioning, and specifically on the notion of reinforcement, that if you do something good that's rewarded,

you'll do it again. and if you do something bad that's punished, you're less likely to do it again. and so there's a strategy called pavlov which plays by the so-called "win, stay, lose, shift" rule. and that rule can error-correct. >> so it can take care of this uncertainty. >> and the intuition there is that if you defect against me, i've lost, so i should shift. and so i shift back to "cooperate." and then you see cooperation in the last round, and you cooperate again. and then since -- and then you're winning, you stay on that strategy. >> so you essentially want to learn from your mistakes. >> exactly. >> so nash was actually solving this as a pure math problem, but in fact it has an evolutionary context, is that right? >> that's right. so in 1973, an english evolutionary biologist, john maynard smith, rediscovered the nash equilibrium and called it an evolutionary stable strategy. and he was particularly interested in what limits aggression. and it turns out that if you write down a simple game, you can show why it's often the case

that more passive, restrained strategies evolve. and the game that he wrote down was called the hawk-dove game. >> imagine we have two populations, one aggressive and one passive. hawks will always fight over a resource and doves will not fight under any circumstances. when a dove meets a hawk, the dove always backs down and gives up the resource to the hawk. and when a hawk fights a hawk over a resource, the conflict is brutal and the winner takes all. and the loser, well, he ends up injured. the winner gets the reward for this interaction, but because he's suffered a cost in the process, it diminishes the value of that benefit. we can write this out mathematically like this: the benefit of winning the resource, which is b, minus the cost of the fight to get it, which is c. since a hawk would win about half the time, the net payoff is...

but when a dove meets a dove, they share equally with no injury. in other words, they get the benefit half the time but never pay a cost of conflict. as long as the benefit to be gained from each interaction outweighs the cost of fighting, there's a clear best strategy: be a hawk. but when the cost of fighting is higher than the benefit to be gained, the logic changes and doves can succeed. under these circumstances, the stable population will be a mix of both hawks and doves. and do we actually see this in the world in any particular species patterns and things like that? >> this is an interesting question, and it relates to how you map highly abstract mathematics of the sort that we're talking about to real-world empirical observations. and i would claim that this kind of mathematics conforms to that model of an intuition amplifier rather than a strategy

calculator because it doesn't -- it's so simplified and so abstracted, it tells you why not everyone is mean and aggressive, but it can't tell you precisely how many will be aggressive or non-aggressive. >> so this is amazing. so now we have a mathematics that is really beginning to get at the way we think. and that's what we see now in the sort of game theory applied to real economics with uncertain payoffs. for example, game theory of evolution, where you really need inheritance and things like that. so there's still a big world out there for game theory to move into and to change for. so thanks for coming. it's been fascinating. >> thank you. >> game theory can help us understand why animals evolve over time. but it can also help us understand social behavior. before the 1960s, some scientists thought that the natural selection motto of "survival of the fittest" as applied to behavior would favor the dominance of aggressive behavior, the strong over the weak. maynard smith showed that the

most evolutionarily stable society is one in which both hawks and doves have a role, which is why natural selection actually works to maintain a balance of different characteristics in a population. >> i'm interested in discovering why animals behave the way they do, and the only way to do it really is mathematically. my name's craig packer. i'm a professor in the department of ecology, evolution, and behavior at the university of minnesota. much of my research has been informed by game theory. we're at wildlife safari in winston, oregon, and we've come to see some lions and see if any of their behaviors illustrate some of these principles of game theory. so the two males are still intact? >> yes, they are. >> i started studying lions in the late 1970s on a population of lions that had already been

studied for 12 years. lions are one of the most militantly social species of all mammals: they work together to raise their babies, they often work together to hunt. our current study area in the serengeti is 2,000 square kilometers, and we're keeping tabs on 24 different prides of lions. it's actually the most extensive study of any carnivore anywhere in the world. i think evolutionary game theory is a very powerful tool for understanding animal behavior. with animals, you have the very simplifying situation that you never can ask them what they're thinking. all you can do is rely on the outcomes. looks like you've got a fairly relaxed group. when is the rut? >> it happened about three weeks

ago. >> that's what it's all about. i mean, the only point of being a male and being so splendid and everything is to get those splendid genes in the next generation. one of our big questions in studying lions for the last few decades has been to approach the problem of why it is that lions are the only social cat. and so we're now using a game theoretical approach. what we're finding is that sociality is much more likely to evolve in a situation where the animals live on very high-quality habitat: they have water, they have food, they have places to hide so you can reach out and grab your prey. what you get then are these singletons now becoming groups, defending those territories against anybody else, and that becomes the new e.s.s., the new evolutionarily stable strategy. when i first started studying lions in the 1970s, there was

always a bias in people that it was a mistake ever to imbue an animal with a complex repertory of behaviors. maynard smith with game theory comes along and says, "if i'm a lion, i live in a world filled with other lions, and so what i get depends on what the other lions are doing." he brought genetics into the whole story. people were convinced that lions were social because they had to work together, to cooperate, to catch their prey. and when we did our own research on that subject, we found that not only did they not cooperate, but if you thought about it for a few minutes, why should they cooperate? because every individual in every group, no matter how unified the group may appear at first appearance, everybody has their own self-interests. and as it happens in a situation like hunting, it often is better off if you just notice that, "ah, my companion or my sister

or my mother or whoever is halfway to catching that zebra. looks good. if i just sit still, i get a free lunch!" more and more data are showing that animals seem incapable of solving a prisoner's dilemma. they go for the instant gratification. if there's a mutualistic benefit, they always cooperate. if it's not immediately mutualistic, then they don't do it. i study problems. and i love the problems the lions present because they have such a complex social system and they play such a complex role in ecosystems that understanding their behavior is incredibly important. and so always it's the problem that we haven't really addressed yet that's the most exciting. >> so just like with tit for tat and pavlov, the evolutionary stable strategy provides us with

a model that, in a sense, buttresses our own intuition about how the world works. now if we can just keep learning the lessons of game theory. >> hey, mr. blue, i thought you just got out! >> what do you make of it, huh? >> get over here. you guys must be the worst robbers in the city. two days out of jail, and you're back again? what's your story this time? >> both: i don't know nothing. >> thirty days. >> going to be good. >> game theory forces us to think about choices, strategies, and payoffs. not in a way that reduces us to easily predictable individuals caught in a grid, but in relation to the activity of others. in the iterated prisoner's dilemma, it would be great if everybody played a pure cooperate strategy, since this is what would give the greatest payoff. but the temptation to cheat, to

buck the system, is there. maybe that's the point, that math goes beyond our instincts. our instincts are often wrong, and mathematics, carefully considered, can be a guide beyond the gut. with mathematics, we can show that a common behavior that we might consider foolish can in fact make considerable sense. sometimes these "odd" strategies are informally encoded in cultural norms, like the golden rule. at its heart, that's perhaps really what game theory is about: the evolution of these rules and norms or institutions that make the best of the difficult situation of living in our world. captions by lns captioning portland, oregon www.lnscaptioning.com

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