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The author:(作者)归海一刀published in(发表于) 2014/5/5 7:17:22 Popular science： “stone， scissors strategy“ means，
Popular science: "stone, scissors strategy" strategy of significance-the stone scissors cloth, stone, paper, scissors, and scientific research-IT information Popular science: "stone, scissors strategy" means
Introduction: yesterday made a "stone, scissors strategy" popular articles , there are many user comments expressing support for scientific research and understanding, some netizens expressed surprise, what is behind this simple game. Xiaobian this residue is not clear, but there's always God to science, let us take a look at it, of course, if you do not understand like xiaobian, silently under the roof.
Yesterday, an article from Zhejiang University, Zhejiang gongshang University and the Chinese Academy of Sciences Institute of theoretical physics papers published in preprint website. According to media publicity, the researchers "found the stone scissors cloth winning strategies".
Naturally, a lot of netizens responded: "it's going to take you? ”
But just glance find, researchers unfortunately is heading the party pit. They are looking for is not a burden of scissors how to play win-hammer, but through baggage scissors hammer judge which theory is more able to predict human behavior--is the traditional game theory, Nash equilibrium, is evolutionary game theory.
Therefore, I intend to meddle from the angle I am familiar with evolutionary game theory, try reading this study, why not a waste of money.
In order to help you understand it, I'm going to tell four stories. These four stories from easy to difficult, if you are already familiar with this field, you can skip ahead a couple of stories.
The first story: prisoner's dilemma
A man was found dead in his home. Police arrested two suspects and seized the booty, but they argues they are just thieves, entered the room, the man had already died. Without more evidence, investigation stalled.
Police separated the two, respectively, and said to them:
If the two of you are not guilty, I sentence you to theft a year if he didn't recruit you with a, you count as meritorious, no jail time, and he got 15 years. If you didn't recruit him with a, and vice versa. But if he didn't recognize you, murder ten years per person.
Suspect x thought: If y does not move, so I don't recruit, will be sentenced to one year, I got an acquittal. In a pleasant atmosphere.
If y, then 15 years if I don't move, for only a decade. Still with a friendly atmosphere.
Apparently I should have.
Suspect y of course feel the same way. The result, both were sentenced to ten years. Any modified policy will only make your situation worse, and that is a Nash equilibrium.
However, if, on the whole, the best results are clearly two people don't, each sentenced to one year. Are rational and considered seeking their best interests of both parties, two people have turned out to be a bad scene; both overall best scenes (one year) or a personal best scene (immediate release) is not going to happen. This is why the prisoner's dilemma is a "dilemma". Everyone is smart and finally how to make such a mess?
▲ The prisoner's dilemma (see diagram or "income matrix")
In accordance with the terminology of the prisoner's dilemma, does not count as "cooperation" (cooperation and your cellmate, not police cooperation), and confessed as "betrayal". Best of both cooperation and both sides have betrayed each other. According to this story, cooperation appears impossible.
Reality scenes there are often similar to the prisoner's dilemma. However, the outcome seems to be more cooperation, not treason. Why?
Possible reason is that predicament more than once.
Second story: iterated prisoner's game
Suspected if x and y are strangers, so what happens when two people are for ten years. But they probably is a good dude, trust, or if there is blood or belong to the same organization--all in all, in game theory terms, they may wither, deals are likely to continue in the future. At this point, "cooperation" is not terribly imaginative things.
Therefore, a political scientist named luobote·akesiluode in the early 80, made a historic experiment. He set up a tournament in a computer, there are a lot of virtual players, killing caught on both sides – Oh no, for iterated prisoner's game is catching on. In accordance with the outcome of the game score, you betray him, you get 5 points he had 0 points, 3 points of cooperation on both sides, both sides betraying each received a 1 minute.
Then, he enrolled to the world strategy, each of the resulting strategy becomes a contestant. Submitted a total of 14 policy, from economics, sociology, political science and mathematics fields, coupled with a "completely random" control strategy, a total of 15 "man" in the race. It contains some extremely complex policy is extremely subtle, for example, has a policy with Markov process model the behavior for each other, and then use the best choice for Bayesian inference.
However, even with the highest final score is the most simple of all policies a-"a tit for" (TFT, tit for tat). This policy had only two rules: (1) a first step to cooperation, (2) starting from the second step, they round out what is, and what I'd pay. Submit to this strategy is the annatuo·labobote in Vienna, he wrote this policy with only 4 lines of BASIC code.
Axelrod made a tournament results, and invite you to submit a new round of policy lessons--this time, he won 62 policies, not only the areas mentioned above, and also included new disciplines such as evolutionary biology, physics, and computer science. Is provided only if a person had the audacity to submit the last defending champions, that's labobote I. You guessed right. Once again, he won.
TFT this "revenge" the secret of success is not complicated. Axelrod said, it has three key elements: it always work the first round, a goodwill gesture; it will punish traitors; if they mend it won't bite and hold.
However, Gandhi said: "an eye for an eye, universal blind. "The reality always forged enmity for various reasons, but we also don't have revenge ever since. Why's that?
Probably because, models of reality and Axelrod have some significant differences.
The third story: iterated prisoner's game of mutation and natural selection
(1) nature has found forgiveness
Axelrod tournament had two major defects.
For one thing, both sides is perfect, there is no misunderstanding, no mistake, even if it does not know what the other side wants to, at least, know what each other did. But misunderstanding of the real tragedy comes from both sides in the start! The important factors obviously shouldn't be ignored.
Second, each policy "environment" are arbitrary decisions. A strategy for success, and how policy has a lot to do around it. If the groups are always cheat, then revenge to take complete advantage of without any. Axelrod submitted by contestants in the tournament is artificial, and it can't be said to be a representative sample.
Therefore, Axelrod on an experimental basis, Martin · Nowak developed a new round of tournament: introduction to natural selection.
He no longer invites experts to design policies, but provides for a policy that fits the space, allowing policy in which "reproduction" and "mutation". Descendants of strategy much higher score each round, without descendants or even disappear even with low scores, but each offspring of policy and they have very small differences. In addition, every behavior has a certain "misunderstanding" probability – I should cooperate, but the actual shot is a betrayal.
At first, story development, and same as above. Starting up soon who mistrust, betrayal every inning, "Betrayer" sweep, but soon went on a bit of tit "revenge". Great chance for revenge on their own internal cooperation, which in turn pulled down defectors.
But now the story will not end here. Because of a misunderstanding.
Revenge is good at dealing with the bad guys. But if your partner is not a bad man, but a good man makes a mistake? Revenge-seekers too hold a grudge, won't let it, if your partner is also revenge, that would immediately betray each other for mutual cooperation, in a perpetual cycle of revenge.
At this time, mutation to a "forgiveness". Its policy called "generous tit" (GTFT). It is characterized, even betrayal, the next round has a certain probability of choosing who to work with, so that you can save in an endless betrayal. In the paper, Novak proudly announces: "natural selection found forgiveness."
It is clear that forgiveness on the assumption that there are enough good people around (revenge or forgiveness). If the bad guys all around (the traitor), your forgiveness will only be used by others.
Too many good people, and there will be another problem.
(2) the cycle of history
If you are surrounded by good people, all enjoyable, it's best to stop bad people, just to be a abuse man! No matter what, I will never cooperate. For misunderstanding than revenge and forgiveness, tolerance, and a chance for forgiveness does not excuse, which the good guys are always forgiven immediately back into cooperation "on track", so it scores higher. This is which the group as a whole will gradually become good guys –
However, the bad guys never go away. Groups will never be mutated and the emergence of new bad guy. A bunch of know is that cooperation in which good people, in the face of bad guys that's shining white fat. Successful bad guys will soon occupy large parts of the population.
And then all start all over again.
This evil-> revenge->-> forgiveness which the good-> back to the cycle of bad guys is extremely common, and generally more than exists in the cooperation game theory models-the good guys beat the bad guys, many years later good relaxed vigilance, bad back, the narrative model is widespread in various stories. Whether it could serve as an abstraction of a real peace cycle of war in human history, it's a matter of opinion.
(3) break the cycle?
So, we are doomed to face the endless cycle now? This is not the case. Novak first generation model, each policy can only be considered the last round of what's wrong with each other. If it has to consider not only each other, consider themselves? The policy if it is not of concern, but rather strategies bring results?
After the improvement model, accidentally came a new set of stability policies: "lose the change, win, there will be additional" (WSLS, win-stay, lose-shift).
This strategy is very simple. If I'm the last round taking advantage of (cooperation on both sides, or him, I betrayed), that this round of my strategy continue to join. If I'm the last round at a disadvantage (both betrayed, or if I were to cooperate, he betrayed), this round, I'll change my strategy. In other words, it is a "reflection".
When two reflections meet, they most of the time to work together. If encounter the noise, then the next round of betrayal on both sides; and the next round of parties to cooperate again. Correction delayed only 1 round. This is stronger than those who forgive, just a little bit weaker than abuse of good.
Reflections on fear which the good. Dealing and abuse of the good guys and start cooperation on both sides, but sooner or later there will be misunderstandings leading to rethink themselves betrayed, then ... ... Reflection discovers abuse good men do not know how to retaliate. So after every round is a reflection on betrayal, abuse of good cooperation, there is no resolution of the latter subjected to inhuman exploitation and quit the game. Such a reflection on society is not composed of as time goes by "ease" into which the good guys, and certainly won't suffer from the bad guy's subsequent invasion.
Wait a minute, "rethink" strategy--isn't that what the report says, rock scissors winning strategies?
That's right, stone scissors cloth is not a prisoner's dilemma. However, the story yet.
Fourth story: on human
Novak's Bank may count among evolutionary biologists. All they care about, is in the context of a natural selection, possibility of cooperation. View this framework, although the animals vary in intelligence, but natural selection strategies will be implanted in their brains. Good strategy can certainly spread, even animals do not understand why this policy is good, do not even know that they are implementing a policy. Only care about the results of natural selection.
Man and man's minds, is the product of natural selection. If their research could partly explain the Animal Kingdom game strategies probably can be partially applied to humans.
Evolutionary psychology is a very important assumption is the human way of thinking is not a "full-featured general-purpose computing" is not a program to handle all environments. The human brain is "application modules". When you need to make an immediate decision, or do less-critical decisions, you tend to call you "first response" of the application modules, rather than calm analysis, developing an optimal solution for specific situations--you don't have the time and energy, often not worth it. "Modern comic figure felt when facing will be worth well into, there are chuti compassion. "You need to figure out this boy and I am nothing, I am nosy be late for my own work, the child's parents will repay me? Don't need to. Feelings you call function already done with you, you want to do is cry or run over.
If a person is any thing first, we may say that he is "personally". But no one can entirely abandon feelings. Indeed, hindsight often made you is not the best--but the idea of a better decision making at a price! Clearly this is not economics that Apple would take ten minutes on drawing utility curves of "rational man", but you can't say it didn't seem to "rational".
And neither urgent nor important decisions, do you have a better example than scissors burden hammer?
So, from the perspective of evolutionary game theory, this study was not really looking for the how to play scissors burden the hammer approach, but the experiment proved that, when we face a repeated game, our brain's built-in applications really like Novak as they model, "reflection" tendencies; even this game just scissors albatross hammer rather than the prisoner's dilemma. We have not calculated like a rational economic man scissor burden hammer is the Nash equilibrium of equal probability randomly one of three gestures, but rather by our "basic instinct"--the impact of evolution for our application module, the module may was born in the context of iterated prisoner's dilemma.
Of course, now that we know the human brain there is this tendency, we designed a restraint strategy against it (reason people won't be afraid of any restraint of Nash equilibrium strategy). We can realize his "basic instinct" defects in certain situations, and a willingness to overcome it, which is more than most other animals sick, we place.
This is awesome please. Touch the essence of human thought is this stuff all right. Although it might be better to Axelrod and Novak so badass, but very good, too.
Of course, the real original papers are a little more complex, involving more studies for the prisoner's dilemma are far more than those discussed here. But I think this has been sufficient to demonstrate that the significance of the study. Don't be fooled by heading the party, if the title tell the whole story, you also need to do the body.
科普：“石头剪刀布策略”的意义 - 石头剪刀布策略,石头剪子布,科研 - IT资讯科普：“石头剪刀布策略”的意义
引言：昨天发过“石头剪刀布策略”引热评的文章，有很多网友留言表示对科研的支持和理解，也有些网友表示不解，这简单游戏的背后到底有何意义。小编这种学渣是无法讲清楚的，但总有大神来科普，让我们一起来看一下吧，当然，如果你和小编一样看不大懂，默默地顶下吧。
昨天，一篇来自浙江大学、浙江工商大学和中科院理论物理研究所的论文公布在了预印本网站上。根据媒体的宣传，研究者“找到了石头剪刀布的制胜策略”。
自然而然地，很多网友的反应是：“这还需要你研究？”
但是只需扫一眼就会发现，研究者不幸又被标题党坑了。他们寻找的不是怎样玩赢剪子包袱锤，而是通过人们在剪子包袱锤里的行为来判断哪一种理论更能预测人类——是传统博弈论的纳什均衡，还是演化博弈论。
因此，我打算从我熟悉的演化博弈论角度来越俎代庖，尝试解读这项研究为什么不是在浪费钱。
为了帮助理解它，我会讲四个故事。这四个故事从易到难，如果你已经对这个领域很熟悉了，可以跳过前面的几个故事。
第一个故事：囚徒困境
一个有钱人被发现死于家中。警方抓获了两个犯罪嫌疑人并查获了赃物，但两人辩称说他们只是小偷，进屋时那个人已经死了。没有更多证据，调查陷入僵局。
于是警方把两人分开，分别对他们说：
如果你俩都不认罪，我只能判你盗窃，一年了事；如果你招了他没招，你算作立功，不用坐牢，而他得十五年。如果如果他招了你没招，那反过来。但如果他和你都认了，谋杀罪每人十年。
嫌疑人X心想：如果Y不招，那么我也不招的话会判一年，我招了无罪释放。招了更划算。
而如果Y招了，那我不招的话十五年，招了只有十年。还是招了更划算。
显然我应该招啊。
而嫌疑人Y当然也是这么想的。结果，两人都判了十年。任何一人改策略都只会让自己处境更糟，这便是一个纳什均衡。
可是，如果从整体上看，最好的结果显然是两人都不招，各判一年。双方都是理性考虑谋求自己的最大利益，结果却是两人都遭遇了坏场景；无论是整体最好场景（各判一年）还是个人最好场景（直接释放）都不可能发生。这就是为何囚徒困境是个“困境”。每个人都很精明，最后怎么弄了这么个烂摊子？
▲囚徒困境示意图（或者，“收益矩阵”）
按照囚徒困境术语，不招的行为算作“合作”（和你的狱友合作，不是和警方合作），而招认的行为算作“背叛”。双方都合作最好，双方都背叛则两败俱伤。按照这个故事，合作根本不可能出现啊。
现实中类似囚徒困境的场景常常出现。但是，更多的结局似乎是合作，而不是背叛。为什么？
可能的原因是，困境不止这一次。
第二个故事：重复囚徒博弈
如果嫌疑人X和Y是陌生人，那么两人的下场都是十年。但是他们也许是两肋插刀的好哥们，或者有血亲，或者属于同一个组织——总而言之，用博弈论的术语，他们以前也许打过交道，将来还很可能继续打交道。这时，“合作”就不是什么难以想象的事情了吧。
因此，一位名叫罗伯特·阿克斯罗德的政治学家在上世纪80年代初做了一个名垂青史的实验。他在计算机里摆了一场锦标赛，有很多名虚拟的参赛选手，双方捉对厮杀——哦不，是捉对进行重复囚徒博弈。按照博弈的结果记分，你背叛他合作，则你得5分他得0分，双方都合作各得3分，双方都背叛各得1分。
然后，他向全世界征集策略，每一个得到的策略变成一个参赛选手。提交的策略共有14个，来自经济学、社会学、政治学和数学等等领域，再加上一个“完全随机”的对照策略，共15“人”进行比赛。这里面有些策略极其复杂极其精妙，比如有一个策略用马尔科夫过程为对方的行为建立模型，然后用贝叶斯推断最好的选择。
但是，最后得分最高的竟然是所有提交策略里最简单的一个——“一报还一报”（TFT, tit for tat）。这个策略一共只有两条规则：（1）第一步先合作，（2）从第二步开始，对方上一轮出的是什么，我就出什么。提交这个策略的是维也纳的安纳托·拉伯波特，他写这个策略只用了4行BASIC代码。
阿克斯罗德发表了锦标赛的分析结果，并邀请大家吸取经验教训提交新一轮策略——这次他获得了62个策略，不但有上面提到的领域，还包括了演化生物学、物理学和计算科学等新学科。只有一个人厚颜无耻地原样提交了上次的卫冕冠军，那就是拉伯波特本人。你猜对了。他又一次获得了胜利。
TFT这个“报仇者”成功的秘诀并不复杂。阿克斯罗德说，它有三个要素：它第一轮总是合作，先表示善意；它会惩罚背叛者；如果对方改过自新，它也不会咬住不放。
但是甘地说过：“以眼还眼，举世皆盲。”现实中总会因为各种原因结下仇怨，但我们也没有从此冤冤相报何时了。这又是为什么？
可能是因为，现实本来也和阿克斯罗德的模型有些重大差别。
第三个故事：有突变和自然选择的重复囚徒博弈
（1）自然发现了宽恕
阿克斯罗德锦标赛有两个重大缺陷。
其一，双方的行为都是完美的，没有误会，没有失误，哪怕不知道对方想什么，至少知道对方做了什么。但现实里多少悲剧源于双方一开始的误会啊！这个重要因素显然不该忽略。
其二，每一个策略的“环境”都是武断决定的。一个策略能否成功，和它身边别的策略如何有很大的关系。假如群体里全都是永远背叛者，那么报仇者完全占不到任何便宜。而阿克斯罗德锦标赛里的参赛选手都是人为提交的，这可不能说是有代表性的样本。
因此，在阿克斯罗德实验的基础上，马丁·诺瓦克制定了一轮新的锦标赛：引入了自然选择。
他不再邀请人类专家设计策略，而是规定了一个大小合适的策略空间，允许策略在里面进行“繁殖”和“突变”。每一轮得分高的策略后代多，得分低的没有后代甚至自己都消失掉，但每个后代的策略也都和自己有十分微小的差异。此外，每次行为都有一定的“误会”概率——本来我应该合作，但实际出手的却是背叛。
一开始，故事的发展和上面一样。起始的一团糟很快被谁都不信任、每一局都背叛的“背叛者”横扫，但其中很快又出现了一小团一报还一报的“报仇者”。然后报仇者有很大的概率靠自己内部合作，反过来推倒背叛者。
但是现在故事不会到此结束了。因为有误会。
报仇者很擅长对付坏人。但是如果对方不是坏人，而是犯了错误的好人呢？报仇者太记仇，不会放过这一点，如果对方也是报仇者，那相互合作立刻会变成相互背叛，就要陷入冤冤相报何时了的永远循环之中了。
这时，突变出现了“宽恕者”。它的策略学名叫“慷慨的一报还一报”（GTFT）。它的特点是，即使对方出了背叛，下一轮也有一定的概率选择合作，这样就可以挽救陷入无穷背叛的可能。在论文里，诺瓦克骄傲地宣布：“自然选择发现了宽恕”。
显然，宽恕存在的前提是周围有足够多的好人（报仇者或者其他宽恕者）。如果周围都是坏蛋（背叛者），你的宽恕只会被别人利用。
可好人太多了，又会有另一个问题。
（2）历史的循环
如果周围都是好人，大家其乐融融，那么最好别坏了人家心情，干脆做个滥好人得了！不管怎么样我都永远合作。这比报仇者和宽恕者对误会的忍受能力更强，宽恕者还有一定概率不原谅，滥好人则是永远原谅，立刻拉回合作的“正轨”，所以它的得分更高。这整个群体会逐渐变成都是滥好人——
但是，坏人从未远去。群体里永远会因为突变而出现新的坏人。而一群只知道合作的滥好人，面对坏蛋那就是白花花的肥肉啊。很快无比成功的坏人会占据群体的大部分。
于是，一切重新开始。
这个坏人->报仇者->宽恕者->滥好人->回到坏人的循环是极其普遍的，而且它的普遍不止存在于博弈论模型里——好人合作打败了坏人，多年以后好人放松了警惕、坏人于是东山再起，这个叙事模型在各种故事传说里都十分普遍。至于这能否作为现实人类历史上战争和平循环的抽象表述，那就见仁见智了。
（3）打破轮回？
那么，我们注定只能面对这个无尽循环了吗？并非如此。诺瓦克的初代模型里，每个策略只能考虑上一轮对方出了什么。如果它不但考虑了对方，还考虑了自己呢？如果它关注的不是对方的策略，而是策略带来的结果呢？
在改进之后的模型里，意外出现了一个新的稳定策略：“输则改之，赢则加勉”（WSLS, win-stay, lose-shift）。
这策略很简单。如果我上一轮占了便宜（双方都合作，或者他合作了我背叛），那这一轮我继续上轮策略。如果我上一轮吃了亏（双方都背叛，或者我合作了他背叛），那这一轮我就换一种策略。换言之，这是一种“反思”型。
当两个反思者相遇，它们大部分时间都合作。万一遭遇了噪音，那么下一轮双方都背叛；再下一轮双方又合作了。纠错延迟只有1回合。这一点比宽恕者更强，只比滥好人弱一点点。
但反思者不怕滥好人。和滥好人打交道，开始双方都合作，但是早晚要出现误会导致反思者背叛，接下来……反思者发现滥好人不懂得报复。于是以后每一轮都是反思者背叛、滥好人合作，没有分辨力的后者遭到惨无人道的剥削而退出游戏。这样一个反思者组成的社会不会随着时间推移而“放松警惕”变成滥好人，当然也就不会遭受坏蛋的后续必然入侵。
等一下，这“反思”策略——不就是报道里说的，石头剪刀布的制胜策略？
没错，石头剪刀布不是囚徒困境。但是，故事还没完。
第四个故事：关于人类
诺瓦克的本行可以算作是演化生物学家。他们关心的，是在一个自然选择的框架下，合作何以可能。这个框架认为，虽然动物的智力各不相同，但自然选择会将策略植入它们的大脑中。好的策略自然能流传，哪怕动物本身不理解这个策略为何好、甚至不知道自己正在执行一个策略。自然选择只在乎结果。
而人和人的心智，也是自然选择的产物。如果他们的研究能部分解释动物界的博弈策略，恐怕也可以部分应用到人身上。
演化心理学有个很重要的假设，就是人的思维方式不是“全功能通用计算”，不是一个程序处理所有环境。人脑子是有“应用模块”的。当你需要做紧急决策、或者做不太重要的决策时，你往往会调用你“第一反应”的那个应用模块，而不是冷静分析局势、为具体情境开发一个最佳方案——你没这时间精力，很多时候也不值得。“今人乍见孺子将入于井，皆有怵惕恻隐之心。”你需要计算一下这孩子和我是什么关系、我多管闲事会不会耽误我自己的工作、孩子的父母会不会报答我吗？不需要。你调用的感情函数已经帮你处理完了，要做的只是喊出声或者跑过去。
如果一个人遇到任何事情都是靠第一反应，我们可能会说他是“感情用事”。但是没有人能完全抛弃感情。的确，事后看来你这样做出的常常不是最好决策——但是构想一个最好决策也是有代价的啊！这显然不是经济学上那种买个苹果也要花十分钟画效用曲线的“理性人”，但你似乎也不能说这就不“理性”。
而既紧急又不重要的决策，还有比剪子包袱锤更好的例子吗？
所以，从演化博弈论角度来看的话，这个研究并不是真的为了寻找怎么玩剪子包袱锤的办法，而是实验证明了，在我们面对重复博弈时，我们的脑子的内置应用果然像诺瓦克他们模型做出来的那样，有“反思”的倾向；哪怕这博弈只是剪子包袱锤而不涉及囚徒困境。我们没有像一个理性经济人那样计算出剪子包袱锤的纳什均衡是等概率随机出三种手势之一，而是受到我们“本能”的影响——演化留给我们的那个应用模块，这模块也许就是在重复囚徒困境的环境下诞生的。
当然，现在我们既然知道了人的大脑有此倾向，我们就可以针对它设计一套克制策略（而理性人的纳什均衡就不怕任何克制策略）。我们能意识到自己的“本能”在特定场合下的缺陷，并主动地克服它，这是我们比大部分别的动物厉害的地方。
这很牛逼好吗。这是触及人类思维本质的东西好吗。虽然也许不如阿克斯罗德和诺瓦克那么牛逼但也非常厉害了好吗。
当然，真正的原论文还要更复杂，涉及的层面也更多，而对于囚徒困境的研究也远不止这里讨论的那些。但是我想，这已经足以证明这项研究的意义。不要被标题党欺骗了，如果标题能说明一切，还需要正文干什么呢。
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