I'm going to talk about the strategizing brain. We're going to use an unusual combination of tools from game theory and neuroscience to understand how people interact socially when value is on the line.
我要說說大腦決策 我們要用一些不尋常組合的工具 從賽局理論到神經科學 以瞭解利益糾葛時大眾的互動
So game theory is a branch of, originally, applied mathematics, used mostly in economics and political science, a little bit in biology, that gives us a mathematical taxonomy of social life, and it predicts what people are likely to do and believe others will do in cases where everyone's actions affect everyone else. That's a lot of things: competition, cooperation, bargaining, games like hide-and-seek and poker.
賽局理論源自應用數學 主要用在經濟和政治學 很少被應用在生物學上 它提供了關於社會行為的數學模型 當人的行為會互相影響時 它可以用來預測 當人類行為會互相影響時 人可能會採取的行動 這包含很多事:競爭、合作、議價 一些像是捉迷藏和撲克牌的遊戲
Here's a simple game to get us started. Everyone chooses a number from zero to 100. We're going to compute the average of those numbers, and whoever's closest to two-thirds of the average wins a fixed prize. So you want to be a little bit below the average number but not too far below, and everyone else wants to be a little bit below the average number as well. Think about what you might pick. As you're thinking, this is a toy model of something like selling in the stock market during a rising market: You don't want to sell too early, because you miss out on profits, but you don't want to wait too late, to when everyone else sells, triggering a crash. You want to be a little bit ahead of the competition, but not too far ahead.
我們用一個簡單的遊戲開始吧 每個人從 0 到 100 間選一個數字 我們會計算這些數值的平均 選擇最接近平均值 2/3 數值的人贏 所以你會需要比平均值低一點的數值 但又不要太低 而且每個人都會想要 選比平均值低一些的數值 想想你會選什麼 你可能會想: 這就像是股價上揚時 賣股票時機選擇的簡單模型 你不想太早賣 因為你會減少獲利 但又不想太晚賣 因為大家都賣完後股價會崩盤 所以你會想超前大家一步,但別過頭 好,對於大家的想法有兩種可能
OK, here's two theories about how people might think about this, then we'll see some data. Some of these will sound familiar because you probably are thinking that way. I'm using my brain theory to see. A lot of people say, "I really don't know what people are going to pick, so I think the average will be 50" -- they're not being strategic at all -- and "I'll pick two-thirds of 50, that's 33." That's a start. Other people, who are a little more sophisticated, using more working memory, say, "I think people will pick 33, because they're going to pick a response to 50, and so I'll pick 22, which is two-thirds of 33." They're doing one extra step of thinking, two steps. That's better. Of course, in principle, you could do three, four or more, but it starts to get very difficult. Just like in language and other domains, we know that it's hard for people to parse very complex sentences with a recursive structure. This is called the cognitive hierarchy theory, something I've worked on and a few other people, and it indicates a kind of hierarchy, along with some assumptions about how many people stop at different steps and how the steps of thinking are affected by lots of interesting variables and variant people, as we'll see in a minute.
然後我們看看數據 有些聽起來可能會很熟悉 因為你就是這麼想 因為我是用大腦理論分析出來 許多人會說: 「我不知道大家會怎麼選, 但我知道平均值是 50。」 這其中沒有策略思考成份 「我會選 50 的 2/3 ,也就是 33 。」這是個開始 其他人比較世故一些 消耗大腦多一點運算能力 說:「別人會因 50 而選 33 , 所以我就選 22 , 也就是 33 的 2/3 。」 他們多想了一步,也就是兩步 這更好,當然理論上 你可以多想三步、四步或更多 但是想越多越困難 就像在語言或其他領域 要組織層疊的句子結構很困難 順帶一題,這稱為認知層級理論 這是我和一些人研究的東西 這研究用來驗證 思考深度存在階層關係的假設 和哪些有趣變因會影響思考深度 這部份我們等下就會看到 另一個不同的理論 也是較為早期、為人熟知的
A very different theory, a much more popular one and an older one, due largely to John Nash of "A Beautiful Mind" fame, is what's called "equilibrium analysis." So if you've ever taken a game theory course at any level, you'll have learned a bit about this. An equilibrium is a mathematical state in which everybody has figured out exactly what everyone else will do. It is a very useful concept, but behaviorally, it may not exactly explain what people do the first time they play these types of economic games or in situations in the outside world. In this case, the equilibrium makes a very bold prediction, which is: everyone wants to be below everyone else, therefore, they'll play zero.
大部份歸因於約翰.納許的《美麗境界》 稱為均衡分析 如果你曾修過賽局理論的課 你可能都學過一些 「均衡」是對每個人都知道 其他人會怎麼做的數學狀態 這是一個有用的概念 但是首次應用在經濟領域 或是其他現實世界的問題時 它卻無法確切解釋人的行為 在這狀況下 「均衡」是一個大膽的假設: 每個人都會想比 其他人選的數值低 所以他們都會選 0
Let's see what happens. This experiment's been done many, many times. Some of the earliest ones were done in the '90s by me and Rosemarie Nagel and others. This is a beautiful data set of 9,000 people who wrote in to three newspapers and magazines that had a contest. The contest said, send in your numbers, and whoever is close to two-thirds of the average will win a big prize. As you can see, there's so much data here, you can see the spikes very visibly. There's a spike at 33 -- those are people doing one step. There is another spike visible at 22. Notice, by the way, most people pick numbers right around there; they don't necessarily pick exactly 33 and 22. There's something a bit noisy around it. But you can see those spikes on that end. There's another group of people who seem to have a firm grip on equilibrium analysis, because they're picking zero or one. But they lose, right? Because picking a number that low is actually a bad choice if other people aren't doing equilibrium analysis as well. So they're smart, but poor.
讓我們來看結果 這是一個被重複多次的實驗 我、羅斯瑪麗.納格爾及其它人 在 90 年代進行的早期實驗 這是由 9 千人參加 公佈在 3 家報紙和雜誌的競賽後 所蒐集到的資料 競賽問題說: 「回傳你所選的數字, 而任何最接近 2/3 平均值的人獲獎」 如你所見,因為資料龐大 你可以清楚的看到一些高峰 在 33 有一個高峰 這是只思考一步的人 另外一個高峰是在 22 順帶一題 多數人選擇 33 和 22 附近的數值 他們不一定只選 33 或 22 所以在附近會有一些雜訊 但是你可以看到這些高峰確實存在 另外一些人 對均衡理論有深入的瞭解 因為他們選擇 0 或 1 但是他們輸了,對吧? 因為如果其他人不懂均衡理論 選擇低數值就不是個好策略 所以他們聰明卻也貧窮
(Laughter)
(笑聲)
Where are these things happening in the brain? One study by Coricelli and Nagel gives a really sharp, interesting answer. They had people play this game while they were being scanned in an fMRI, and two conditions: in some trials, they're told, "You're playing another person who's playing right now. We'll match up your behavior at the end and pay you if you win." In other trials, they're told, "You're playing a computer, they're just choosing randomly." So what you see here is a subtraction of areas in which there's more brain activity when you're playing people compared to playing the computer. And you see activity in some regions we've seen today, medial prefrontal cortex, dorsomedial, up here, ventromedial prefrontal cortex, anterior cingulate, an area that's involved in lots of types of conflict resolution, like if you're playing "Simon Says," and also the right and left temporoparietal junction. And these are all areas which are fairly reliably known to be part of what's called a "theory of mind" circuit or "mentalizing circuit." That is, it's a circuit that's used to imagine what other people might do. These were some of the first studies to see this tied in to game theory.
那大腦中發生了什麼事呢? 柯里切利和納格爾 的一項研究給了明顯、有趣的答案 他們讓一些人玩這遊戲時 同時接受功能型核磁共振(fMRI) 包含兩種狀況:在其中一組 受試者被告知他們是 和遊戲中的人玩 而我們最後會比較你們的作為 如果你贏了,就會得到獎勵 另外一組受試者 被告知他們是在電腦玩 受試者隨機分組 所以你們可以看到 當和對電腦玩的人比較時 對手是人的受試者 腦部活化程度較高 從圖上你可以看到 一些我們已知的區域 內側額葉皮層,事實上 在這裡的是背內側額葉皮層 腹內前側額葉皮層 和像是你在玩「老師說」遊戲時 處理大量衝突解決的前扣帶皮層 以及左右邊的躡頂葉交界區 而這皆我們所熟知的區域 被納入一個名為「心靈原理」迴路 或稱為「心靈迴路」的一部份 這迴路是用來想像別人可能的行動 所以這部份早期的研究 和賽局理論有關
What happens with these one- and two-step types? So, we classify people by what they picked, and then we look at the difference between playing humans versus computers, which brain areas are differentially active. On the top, you see the one-step players. There's almost no difference. The reason is, they're treating other people like a computer, and the brain is too. The bottom players, you see all the activity in dorsomedial PFC. So we know the two-step players are doing something differently.
但那些「想一步」和 「想兩步」的玩家又是如何呢? 所以我們將受試者依其選擇區分 然後我們再看看 對手是人或電腦 在腦部活化區域層面的不同 上方你可以看到「想一步」的玩家 它們幾乎沒有不同 原因是他們將人視為電腦, 所以大腦也就如此反應 你可從下方玩家中 看到背內側額葉皮層的活動 所以我們知道這些 「想兩步」的玩家有些不同 你可能會停下來想想 「我們從這些資訊中得到什麼?」
Now, what can we do with this information? You might be able to look at brain activity and say, "This person will be a good poker player," or "This person's socially naive." We might also be able to study things like development of adolescent brains once we have an idea of where this circuitry exists.
你可能從大腦活動中判斷 「這人會成為撲克牌高手」 或「這人是交際新手」 既然我們知道這個迴路的存在 我們也可以研究一些 像是青少年腦部的發育
OK. Get ready. I'm saving you some brain activity, because you don't need to use your hair detector cells. You should use those cells to think carefully about this game. This is a bargaining game. Two players who are being scanned using EEG electrodes are going to bargain over one to six dollars. If they can do it in 10 seconds, they'll earn that money. If 10 seconds go by and they haven't made a deal, they get nothing. That's kind of a mistake together. The twist is that one player, on the left, is informed about how much on each trial there is. They play lots of trials with different amounts each time. In this case, they know there's four dollars. The uninformed player doesn't know, but they know the informed player knows. So the uninformed player's challenge is to say, "Is this guy being fair, or are they giving me a very low offer in order to get me to think there's only one or two dollars available to split?" in which case they might reject it and not come to a deal. So there's some tension here between trying to get the most money but trying to goad the other player into giving you more. And the way they bargain is to point on a number line that goes from zero to six dollars. They're bargaining over how much the uninformed player gets, and the informed player will get the rest. So this is like a management-labor negotiation in which the workers don't know how much profits the privately held company has, and they want to maybe hold out for more money, but the company might want to create the impression that there's very little to split: "I'm giving the most I can."
準備好囉 我為你們準備了些腦力激盪 你們不用擔心想太多會掉頭髮 你們應該專注思考這個遊戲 這是個協商遊戲 兩位被接上腦電波圖(EEG) 電極的玩家 正在進行一項由 1 到 6 元的協商 如果在 10 秒內完成, 最後就會得到這份金錢 如果未在 10 秒內完成協商,就得不到錢 這是種兩人一起造成的錯誤 不同的地方在於左邊玩家 確實知道每場協商的底價 而他們會重複多次、 所包含的金額不同的協商 在這個例子中,他們知道是 4 元 而一邊玩家不知道底價 只知到他們的對手知道 所以不知道底價的玩家會質疑 「對方真的很公平 或是他只給我很低的金額 讓我以為我們真的 只有 1、2 塊錢可以分 ?」 如此他們可能會拒絕對方, 而讓協議流產 所以這包含「想要的到最多的錢」 和「如何促使對手給你更多錢」的衝突 他們議價方式是 是從 0 到 6 這條線上指出一點 他們是在協商「不知情玩家」該得多少 而「知情玩家」會得到剩下的 這就好像顧主和勞工的協商 勞工不知道 公司獲利經額的資訊 他們想要得到更多的錢 但是公司會想營造一個假象 就是營收很少而且 「我已將能給的部份都給出去了」
First, some behavior: a bunch of the subject pairs play face-to-face. We have other data where they play across computers. That's an interesting difference, as you might imagine. But a bunch of the face-to-face pairs agree to divide the money evenly every single time. Boring. It's just not interesting neurally. It's good for them -- they make a lot of money. But we're interested in: Can we say something about when disagreements occur versus don't occur?
首先看看行為, 一部份玩家座在長桌上、面對面協商 我們也有一些 他們透過電腦協商的數據 你可以想像 兩者的差距十分有趣 長桌上面對面的協商 會同意每次都均分金錢 無聊死了! 平均分配並不有趣 這對他們很好,因為他們拿到很多錢 我們感興趣的是 如何解釋歧見是否發生
So this is the other group of subjects, who often disagree. They bicker and disagree and end up with less money. They might be eligible to be on "Real Housewives," the TV show.
這是通常都達不成協議的一組 他們有機會因歧見而爭執 最後得到很少錢 他們協商情景 甚至可以改編成實境秀
(Laughter)
你看左側
You see on the left, when the amount to divide is one, two or three dollars, they disagree about half the time; when it's four, five, six, they agree quite often. This turns out to be something that's predicted by a very complicated type of game theory you should come to graduate school at CalTech and learn about. It's a little too complicated to explain right now, but the theory tells you that this shape should occur. Your intuition might tell you that, too.
當配額為 1 到 3 元時 他們約有 50% 會拒絕 而當配額為 4 到 6 元則會接受 這就是我們所預期的 非常複雜的賽局理論 你應該到加州理工的研究所來學學 現在要解釋這太困難了 但這理論預期會出現這種趨勢 而你的直覺或許也是這樣告訴你 現在我要給你們 看腦電波圖(EEG)的紀錄
Now I'm going to show you the results from the EEG recording. Very complicated. The right brain schematic is the uninformed person, and the left is the informed. Remember that we scanned both brains at the same time, so we can ask about time-synced activity in similar or different areas simultaneously, just like if you wanted to study a conversation, and you were scanning two people talking to each other. You'd expect common activity in language regions when they're listening and communicating. So the arrows connect regions that are active at the same time. The direction of the arrows flows from the region that's active first in time, and the arrowhead goes to the region that's active later. So in this case, if you look carefully, most of the arrows flow from right to left. That is, it looks as if the uninformed brain activity is happening first, and then it's followed by activity in the informed brain. And by the way, these are trials where their deals were made. This is from the first two seconds. We haven't finished analyzing this data, so we're still peeking in, but the hope is that we can say something in the first couple of seconds about whether they'll make a deal or not, which could be very useful in thinking about avoiding litigation and ugly divorces and things like that. Those are all cases in which a lot of value is lost by delay and strikes.
這非常複雜 右邊的腦部模型 是代表「不知情玩家」 而左邊則是「知情玩家」 記得我們是同時監控兩個大腦 所以我們可以探討 在相同或相異大腦區域中 在一段時間內的活化狀況 就像你想研究一段對話 你就同時掃描兩個人的腦部活動 而你會預期當他們正在對話時 共同活化的是語言區 所以這個箭頭連接了同時活化的區域 而箭號方向從 最先活化的區位指出去 箭頭部份表示較後期活化的區域 在這個例子中,如果你仔細看 大部份的箭號是由右而左 看起來「不知情玩家」的 腦部較先活化 接著才是「知情玩家」 順帶一提, 這是在達成協議的測試中出現的 這是最初兩秒鐘所得到的數據 我們還沒完成這部份的分析 所以這只是大概觀察到的狀況 但我們希望從前 1、2 秒鐘 就可以判斷他們是否能達成協議 這可以用在避免 協商破裂,而走向進訴訟程序 例如:最後以不愉快的離婚收場 在很多案例中 是因為延誤和罷工而減損的價值
Here's the case where the disagreements occur. You can see it looks different than the one before. There's a lot more arrows. That means that the brains are synced up more closely in terms of simultaneous activity, and the arrows flow clearly from left to right. That is, the informed brain seems to be deciding, "We're probably not going to make a deal here." And then later, there's activity in the uninformed brain.
而這都是因為歧見 你會看到這和前一個例子不同 上面有很箭號 這表示大腦正在同步運作 更確切的說是同時間的活動 而箭號由左指向右 這好像是「知情玩家」的大腦開使思考 「這個可能是失敗的協商」的訊號 後來這個活化模式也出現在「不知情玩家」
Next, I'm going to introduce you to some relatives. They're hairy, smelly, fast and strong. You might be thinking back to your last Thanksgiving.
接著讓我來介紹我們的近親 牠們多毛、體味重、迅捷和強壯 你可能會想到你上個感恩節的裝扮
(Laughter)
如果你帶了知黑猩猩的話
Maybe, if you had a chimpanzee with you. Charles Darwin and I and you broke off from the family tree from chimpanzees about five million years ago. They're still our closest genetic kin. We share 98.8 percent of the genes. We share more genes with them than zebras do with horses. And we're also their closest cousin. They have more genetic relation to us than to gorillas. So, how humans and chimpanzees behave differently might tell us a lot about brain evolution.
查理.達爾文、你和我在 50 萬年前 從演化樹上和黑猩猩分開 遺傳上,是牠們仍是最接近我們的親戚 我們之間有 98.8 % 相同的基因 我們之間的共同基因 比斑馬和野馬間多的多 我們也是牠們最接近的親戚 牠們和我們的基因相似度 比和大猩猩更接近 所以人類和黑猩猩行為的不同 可能提供我們瞭解腦部演化的線索
This is an amazing memory test from [Kyoto], Japan, the Primate Research Institute, where they've done a lot of this research. This goes back a ways. They're interested in working memory. The chimp will see, watch carefully, they'll see 200 milliseconds' exposure -- that's fast, eight movie frames -- of numbers one, two, three, four, five. Then they disappear and are replaced by squares, and they have to press the squares that correspond to the numbers from low to high to get an apple reward. Let's see how they can do it.
這是日本名古屋靈長類研究中心 一個令人驚歎的記憶測試 他們在那裡做了很多類似的研究 這已經是早期的研究, 他們對記憶形成很有興趣 猩猩會有 200 毫秒的時間 仔細去看 —— 這是很快的 8 個字卡 —— 數字從 1 到 5 當字卡消失後會出現方塊 牠們必須依據數字大小順序 按壓方塊 正確就能得到蘋果 讓我們看看牠們表現如何
This is a young chimp. The young ones are better than the old ones, just like humans.
這是隻年輕的黑猩猩 像人類一樣 年輕的表現比年老的好
(Laughter)
而且牠們已經做了幾千次了
And they're highly experienced, they've done this thousands of times. Obviously there's a big training effect, as you can imagine.
可以說是駕輕就熟 你可以想像有很大一部份歸於訓練 (笑聲)
(Laughter)
你可以看到牠們 已經呈現玩膩時倦怠
You can see they're very blasé and effortless. Not only can they do it very well, they do it in a sort of lazy way.
他們不只做的很好 而且是用一種慵懶的方式完成
(Laughter)
對嗎?誰認為自己可以打敗這些猩猩呢?
Who thinks you could beat the chimps?
(Laughter)
錯了 (笑聲)
Wrong. (Laughter)
我們可以嘗試 或許我們真的會試試
We can try. We'll try. Maybe we'll try.
好的,這研究的另一部份
OK, so the next part of the study I'm going to go quickly through is based on an idea of Tetsuro Matsuzawa. He had a bold idea he called the "cognitive trade-off hypothesis." We know chimps are faster and stronger; they're also obsessed with status. His thought was, maybe they've preserved brain activities and practice them in development that are really, really important to them to negotiate status and to win, which is something like strategic thinking during competition. So we're going to check that out by having the chimps actually play a game by touching two touch screens.
我會很快的帶過 這是基於松澤綱野的想法 他有一個想法 稱為認知妥協假說 我們知道猩猩迅捷且強壯 牠們也對自身狀況非常執著 他認為,或許黑猩猩保留了 對牠們非常重要 用來協商條件和獲勝的腦部活動 並在成長過程中練習 這就像是在競爭中的策略思考 所以我們接著就去證實它 藉由讓黑猩猩玩個遊戲 藉由點擊兩個觸控螢幕
The chimps are interacting with each other through the computers. They'll press left or right. One chimp is called a matcher; they win if they press left-left, like a seeker finding someone in hide-and-seek, or right-right. The mismatcher wants to mismatch; they want to press the opposite screen of the chimp. And the rewards are apple cube rewards. So here's how game theorists look at these data. This is a graph of the percentage of times the matcher picked right on the x-axis and the percentage of times they picked right by the mismatcher on the y-axis. So a point here is the behavior by a pair of players, one trying to match, one trying to mismatch. The NE square in the middle -- actually, NE, CH and QRE -- those are three different theories of Nash equilibrium and others, tells you what the theory predicts, which is that they should match 50-50, because if you play left too much, for example, I can exploit that if I'm the mismatcher by then playing right. And as you can see, the chimps -- each chimp is one triangle -- are circled around, hovering around that prediction.
猩猩真的可以借由電腦互相交流 他們可以選擇按「左」或「右」 其中一隻猩猩作為「協調者」 在兩隻猩猩都選同一邊時獲勝 有點像是在玩捉迷藏 「不諧調者」希望不一樣的組合 牠們希望選擇和對手不同的選項 而得到蘋果塊的獎賞 賽局理論學家是這樣看待這些數據的 這圖的 X 軸表示 「協調者」選擇「右」的比率 而 Y 軸表示 是牠們預測「不諧調者」會選「右」的比例 所以上面的一點是由 兩位玩家共同決定的 一個試著選擇一樣, 另一個希望有不同組合 這個中間標示 NE 的正方形, 事實上包含 NE 、 CH 、 QRE 代表三種包含 納許均衡理論在內的三個理論 對於牠們選擇的預測 牠們的選擇應該是 50 比 50 因為如果你選了太多左邊 而我是「不諧調者」, 我就會傾向選右邊進行破壞 如你們所見, 每隻黑猩猩都以三角形表示 三角形都坐落在預測位置的附近
Now we move the payoffs. We're going to make the left-left payoff for the matcher a little higher. Now they get three apple cubes. Game theoretically, that should make the mismatcher's behavior shift: the mismatcher will think, "Oh, this guy's going to go for the big reward, so I'll go to the right, make sure he doesn't get it." And as you can see, their behavior moves up in the direction of this change in the Nash equilibrium. Finally, we changed the payoffs one more time. Now it's four apple cubes, and their behavior again moves towards the Nash equilibrium. It's sprinkled around, but if you average the chimps out, they're really close, within .01. They're actually closer than any species we've observed.
然後我們改變獎勵條件 我們要讓選擇「左」的 「協調者」獲得比較高的獎勵 現在牠們會得到三個蘋果塊 依據賽局理論 這會讓「不諧調者」行為改變 因為「不諧調者」會想 牠的對手會選則獲利大的地方 所以我要選「右」,讓牠拿不到 而你們可以看到牠們的行為 逐漸趨向納許均衡的預測 最後,我們再次改變獎勵條件 現在是四個蘋果塊 他們的行為會更接近納許平衡 如果將所有黑猩猩的選擇平均 會出現一個高峰 它們會非常接近,間距在 0.1 之內 結果會比我們觀察的 任何一種物種都接近
What about humans? You think you're smarter than a chimpanzee? Here's two human groups in green and blue. They're closer to 50-50; they're not responding to payoffs as closely. And also if you study their learning in the game, they aren't as sensitive to previous rewards. The chimps play better than the humans, in terms of adhering to game theory. And these are two different groups of humans, from Japan and Africa; they replicate quite nicely. None of them are close to where the chimps are.
那人類又會如何呢? 你們認為人類比黑猩猩聰明? 這裡用藍、綠色表示兩組人類 他們選擇接近 50 比 50, 但對獎勵的反應和納許平衡相距較遠 而且你如果研究 他們在遊戲中學習的能力 他們對之前獲得的獎勵較不敏感 黑猩猩玩得比人類好 是以接近賽局理論而言的好 而這兩組分別來自日本和非洲的人 他們的結果相互吻合 但都不及黑猩猩
So, some things we learned: people seem to do a limited amount of strategic thinking using theory of mind. We have preliminary evidence from bargaining that early warning signs in the brain might be used to predict whether there'll be a bad disagreement that costs money, and chimps are "better" competitors than humans, as judged by game theory.
所以今天我們學到了一些事情 從大腦理論的角度 人類的策略思考似乎是有極限的 我們有些從議價得到的初步證據 有些大腦活動可以作為 可能造成協商破裂虧損的警訊 從賽局理論看來 黑猩猩是比人類更好的競爭者
Thank you.
謝謝大家
(Applause)
(掌聲)