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ya verás las sorpresas que te esperan cuando despiertes, roberto. primero, conoceremos a nuestro abuelo. narrador: bienvenidos a destinos: an introduction to spanish. primero vamos a ver algunas escenas de este episodio. ¿cómo era rosario? bueno, mi madre... era una mujer llena de vida, afectuosa. a veces tenía momentos de tristeza y yo no entendía por qué. tú eres el esposo de raquel, ¿verdad? no, carlitos, yo soy soltera. entonces ¿son novios? carlos: mi hijito, ¿por qué preguntas esas cosas, eh? en este episodio, vamos a aprender el vocabulario relacionado con el dinero y los asuntos financieros.

y aquí está la lista entera de gastos. muy bien. ¿y los recibos? están en este sobre. tuve que cargar mucho a mi tarjeta de crédito para no gastar todo mi efectivo. muy bien. ay, luis, ¿cómo estás? bien. quería decirles que ya he comprado mi pasaje para méxico. raquel se pondrá muy contenta de verte. ¿sabe ella que voy por allá? no, no, no, no. será una completa sorpresa. hasta luego. captioning of this program is made possible by the annenberg/cpb project and the geraldine r. dodge foundation.

ramón: bueno, arturo nos gustaría saber algo sobre tu mamá. consuelo: sí. tenemos mucha curiosidad por saber de ella. sí. comprendo perfectamente. ¿cómo era rosario? bueno, mi madre... era una mujer llena de vida, afectuouosa. a veces tenía momentos de tristeza y yo no entendía por qué. desde niño, me di cuenta que trataba angel... irosario! irosario!

ya verás las sorpresas que te esperan cuando despiertes, roberto. primero, conoceremos a nuestro abuelo, el padre de papá. ¿recuerdas que él creía que su padre había muerto? pues, iestá vivo! y vive aquí en méxico. dicen que es un rico y que tiene una gran hacienda. ( suspira ) angela: hablando de dinero... tengo que ver cómo está mi situación económica. en mi cuenta de ahorros en san juan, no tengo casi nada.

¿cómo es posible que en mi cuenta de ahorros tenga solamente diez dólares? ¿en qué he gastado todo mi dinero? el banco también me ha mandado esta cuenta. iah...! ahora recuerdo. saqué trescientos dólares con mi tarjeta de crédito. ¿cómo voy a pagar esta cuenta si no tengo dinero en mi cuenta de ahorros? tengo que admitirlo: manejo muy mal el dinero. mamá y papá tenían razón. yo soy un poco... impráctica. pero tú... el hijo inteligente... el hijo responsable. me imagino que tienes todo muy bien organizado, ¿no?

roberto, siento mucho la pelea que tuvimos.

¿me vas a perdonar? arturo: y desde que mi madre murió nunca supe más nada de angel. iqué triste! pero gracias a raquel he podido conocer a mis sobrinos los hijos de angel. consuelo: ahora tendrán tiempo para conocerse mejor, espero. sí, por supuesto. ¿y es la primera vez que vienes a méxico? sí, es la primera vez. y tengo muchas ganas de conocer el país. debes regresar para las fiestas patrias. pronto vamos a celebrar la fiesta de independencia. ¿contra españa? bueno, en méxico celebramos varias fechas: la independencia, revolución y algunas batallas importantes. sabes, arturo, como en todos los países de américa latina

también nosotros celebramos el aniversario de la independencia de españa. el dieciséis de septiembre se dio el grito de independencia. en ese día, en el pueblo de dolores el padre miguel hidalgo supo que los españoles habían descubierto los planes de independencia del grupo de patriotas. el padre miguel hidalgo era uno de estos patriotas. entonces, en la madrugada de ese día el padre tocó las campanas de la iglesia llamando a todos los habitantes del pueblo. cuando llegaron hidalgo les habló otra vez de la igualdad entre los hombres. les habló de cómo los indígenas, mestizos y criollos deberían tener los mismos derechos que los españoles que gobernaban las colonias. dijo que era el momento de ser una nación independiente. y así empezó la lucha por la independencia.

por ese motivo, cada dieciséis de septiembre hay grandes celebraciones en todo el país. como dice ramón, debes regresar para celebrar estas fiestas con nosotros. ime gustaría! consuelo: pero, mercedes no has dicho nada del cinco de mayo. tienes razón. otra lucha importante que celebramos es contra los franceses. como ya sabrás, arturo, en mil ochocientos sesenta y uno los franceses invadieron méxico. napoleón tercero siempre había soñado con poseer territorios en américa. en esa época, benito juárez era presidente de méxico. pero nuestro país estaba dividido. había un gran conflicto entre los conservadores y los liberales. llegaron las tropas francesas y con la ayuda de los conservadores napoleón pudo instalar a maximiliano de austria como emperador de méxico. pero el imperio de maximiliano no duró mucho.

pues, las batallas con juárez continuaban. en mil ochocientos sesenta y siete maximiliano fue capturado y fusilado. benito juárez asumió su autoridad una vez más. una de las batallas más importantes ocurrió el cinco de mayo de mil ochocientos sesenta y dos en la ciudad de puebla. allí el general zaragoza venció a las tropas francesas. aunque la lucha contra los franceses duró varios años más la batalla de puebla representa el espíritu y la valentía con que los mexicanos luchaban. cada año celebramos el cinco de mayo como un ontecimiento muy importante. también en muchas partes de california se celebra el cinco de mayo. para nosotros es una fiesta tan importante como el cuatro de julio. incluso en muchas escuelas públicas de los angeles

se celebra el cinco de mayo. yo no sabía eso. bueno, claro, en miami no hay mucha gente con ascendencia mexicana. el cinco de mayo no es muy importante allí. carlos: si tienes tiempo, arturo debes de visitar el museo de las intervenciones en esta ciudad. somos el único país que tiene un museo de este tipo. es verdad, méxico ha sido invadido varias veces. es algo de lo que estamos muy conscientes. arturo, ¿sabrás algo sobre nuestra revolución de mil novecientos diez? sí, un poco. sé quién es pancho villa... arturo, nuestra revolución de mil novecientos diez fue mucho más que pancho villa. tienes que entender que entonces el país pasaba por una época muy difícil. porfirio díaz era el presidente y muchos lo acusaban de proteger sólo a los ricos. el iniciador de la revolución fue francisco madero.

madero convocó al pueblo mexicano a la lucha contra porfirio díaz y así en mil novecientos diez comenzó la revolución. además de pancho villa también emiliano zapata fue muy importante. el era un campesino que luchaba contra los ricos en el sur del país. la revolución duró diez años desde mil novecientos diez hasta mil novecientos veinte. murieron más de un millón de mexicanos y el país tardó muchos años en recuperarse social, política y económicamente. es verdad. por eso, muchos mexicanos se establecieron en los estados unidos. mis abuelos, por ejemplo, se fueron a vivir al sur de california en mil novecientos doce. muy comprensible, eso. ah... ¿y cómo está don fernando? pues, débil. sin embargo, él quiere regresar a la gavia.

tal vez eso le haría muy bien. es cierto. y con él allí podríamos tener una gran reunión con toda la familia. pedro: naturalmente. raquel también debería estar presente. por supuesto. espero que no pienses regresar a los angeles todavía. no, no, voy a pasar unos días más en méxico. mis padres vienen de visita. carlitos: ipapá! ipapá! carlos: perdón. con permiso. sí. hijito, ¿qué te ocurre? ¿tuviste una pesadilla? sí. bueno, pues quédate con nosotros y verás como se te pasa. sí. ya se siente mucho mejor. ¿verdad? sí. iqué rápido se ha recuperado, carlitos! es que estuvo enfermito, con gripe. pero ahora se le ve muy bien. tú eres el esposo de raquel, ¿verdad? no, carlitos, yo soy soltera.

entonces ¿son novios? carlos: mi hijito, ¿por qué preguntas esas cosas, eh? porque sólo los novios o los esposos se besan en el jardín ¿no es cierto? ( consuelo ríe ) ( suspira ) hombre: pero, maría... ¿y si raquel se enoja? ¿no es mejor preguntarle si desea ver a luis? ihace años que ya no son novios! ay mira, tú ve a ver tu televisión, como haces siempre y déjame a mis asuntos. yo conozco a mi hija. iyo también conozco a mi hija! pero yo creo que... ( teléfono suena ) hello? iay, luis! ¿cómo estás? bien. quería decirles que ya he comprado mi pasaje para méxico. justamente estábamos hablando de eso. ¿cuándo sales? mañana. tengo solo unos días de vacaciones más

y quiero aprovecharlos. raquel se pondrá muy contenta de verte. ¿sabe ella que voy para allá? no, no, no, no. será una completa sorpresa. tengo tantas ganas de verla. yo creo que a ella también le gustará verte a ti. bien. entonces, nos veremos en méxico. sí, sí, está bien. nos vemos. ibuen viaje! gracias. también para uds. hasta luego. anda, viejo. vete a sentar allí. tengo que terminar de pagar estas cuentas. mujer: bueno, la última cuenta. ihíjole! todo está tan caro. icaramba! pagué cinco cuentas y ya no me queda nada en la cuenta corriente.

tengo que transferir dinero de la cuenta de ahorros a la cuenta corriente. narrador: como muchas personas mayores de la clase trabajadora maría rodríguez se preocupa por el dinero. como todo el mundo, los mayores tienen sus gastos: la casa... el teléfono... el agua... y el gas. pero a diferencia de los jóvenes sus ingresos son fijos. los ingresos son el dinero que entra en una casa. es lo que gana una familia. los gastos son el dinero que sale.

hay gastos para mantener la casa la salud y comprar la comida. en fin, hay muchos gastos en la vida diaria. los ingresos de los mayores son fijos porque ya no trabajan. dependen de la seguridad social o de otro sistema. pero las cuentas y los precios no son fijos a causa de la inflación. y mientras los ingresos de otras personas suben los ingresos de los jubilados no cambian.

pancho... parece que vamos a méxico. y aquí está la lista entera de gastos. muy bien. ¿y los recibos? están en este sobre. tuve que cargar mucho a mi tarjeta de crédito para no gastar todo mi efectivo. muy bien. mañana le daré tus recibos a mi secretaria y le diré que te haga un cheque. eso sería muy conveniente. tengo que hacer cuentas en mi oficina de los angeles. si puedo regresar con un cheque, tanto mejor. tenemos una secretaria que siempre grita "ihay muchos gastos y pocos ingresos! ¿cómo me van a pagar a mí?" tu secretaria no tiene de qué preocuparse ni tú tampoco. mañana tendrás tu cheque también. gracias, pedro. quiero que me des cuanto antes

los documentos que tienes de rosario y angel. tendremos que mostrárselos a fernando. por supuesto. en el hotel tengo fotos de angel un certificado de nacimiento y mañana estarán reveladas las fotos que tomé durante mi viaje. ¿fotos de qué? de la tumba de rosario, también de la de angel. tengo fotos de las casas donde vivieron. muy bien. esos papeles son muy importantes para fernando... y para nosotros también. bueno, tendremos que regresar a la sala. los otros nos estarán esperando. arturo, ya estoy lista. ¿nos vamos? arturo: cuando quieras. los llevo al hotel. ah, gracias, ramón, pero no es necesario que te molestes. no es molestia. de veras. tenemos carro. entonces podemos aprovechar para hablar de nuestros asuntos

esta misma noche, si no estás muy cansado. de acuerdo, tío pedro. ¿mañana vendrán a ver a fernando? bueno, a primera hora tenemos que ir a ver a roberto. si le den el alta podemos ir todos juntos a ver a don fernando. ojalá así sea. estoy segura que sí. uds. tienen que preparar a don fernando para la visita. claro, será una emoción muy fuerte pero se pondrá muy feliz. bueno. ha sido un placer conocerlos a todos. raquel, encantado. adiós. todos: adiós. hasta luego. trescientos siete, por favor.

con gusto. ¿estás muy cansada para una copa? no. la verdad, yo también estaba pensando lo mismo. bien. entonces, tengo una pequeña sorpresa para vos. vuelvo en seguida. bueno, aquí estoy, esperando a arturo. acabamos de llegar de la casa de pedro. iqué bien lo pasamos con la familia! creo que tuvimos un buen encuentro. la familia le pidió a arturo que hablara de alguien. ¿de quién querían que hablara?

¿cómo era rosario? bueno, mi madre... era una mujer llena de vida, afectuosa. la familia quería que arturo hablara de rosario. después, seguimos conversando y la familia le dijo a arturo que debería regresar a méxico. ¿por qué le decían que regresara a méxico? como dice ramón, debes regresar

para celebrar estas fiestas con nosotros. me gustaría. querían que arturo regresara para conocer más el país. como arturo no conoce méxico muy bien la familia empezó a hablar de las fiestas nacionales y algo de la historia de méxico. después seguimos conversando y carlitos, el hijo de carlos y gloria, bajó. había tenido una pesadilla. pero carlitos también dijo algo que a arturo y a mí nos dio mucha verguenza. ¿recuerdan qué dijo carlitos? carlitos dijo que nos vio a arturo y a mí besándonos en el jardín. iqué verguenza!

¿qué pensará la familia de mí? ( suspira ) después revisé las cuentas con pedro. le di los recibos de todos los gastos de mi viaje. el prometió darme un cheque por los gastos y otro por mis servicios. entonces, pedro me pidió algo. el quería que yo le diera algo importante. ¿qué quería pedro que yo le diera? quiero que me des cuanto antes los documentos que tienes de rosario y angel.

tendremos que mostrárselos a fernando. pedro quería que yo le diera unos papeles muy importantes de rosario y angel. estos papeles pueden ser importantes para comprobar que angela y roberto son los nietos verdaderos de don fernando. es un poco tarde pero tengo ganas de seguir conversando con arturo. esta noche en el jardín... ( suspira ) no sé. el va a bajar en cualquier momento con una sorpresa para mí. ¿qué puede ser? la trescientos dieciocho, por favor. con gusto.

hay un mensaje para ud. gracias. ¿te acordás? ipor supuesto que sí! iay arturo, qué bonito marco le has puesto! iah, no tan linda como la modelo! ¿qué es? un mensaje? sí, a ver. ies de pedro! dice que lo llame en cuanto llegue al hotel. pero, isi acabamos de llegar de su casa! ¿será un mensaje atrasado? no, mira la hora. llamó hace unos minutos. ¿le habrá pasado algo a don fernando? captioned by the caption center wgbh educational foundation

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>> 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 scenario of modern game theo, which came intits 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 in any 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 eir 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.

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