1、game theory is the science of strategy. It attempts to determine mathematically and logically the actions that “players” should take to secure the best outcomes for themselves in a wide array of “games.” The games it studies range from chess to child rearing and from tennis to takeovers. But the gam

2、es all share the common feature of interdependence. That is, the outcome for each participant depends on the choices (strategies) of all. In so-called zero-sum games the interests of the players conflict totally, so that one persons gain always is anothers loss. More typical are games with the poten

3、tial for either mutual gain (positive sum) or mutual harm (negative sum), as well as some conflict.都具有相互依賴的共同特征。也就是說，每個參與者的結(jié)果取決于所有人的選擇（策略）。在所謂的零和游戲中，玩家的利益是完全沖突的博弈論是戰(zhàn)略的科學(xué)。它試圖從數(shù)學(xué)和邏輯上確定“玩家”應(yīng)采取的行動，以確保他們在各種“游戲”中獲得最佳成果。所研究的游戲包括從國際象棋到兒童飼養(yǎng)，從網(wǎng)球到收購。但是這些游戲，所以一個人的收益總是另一個人的損失。更典型的是有相互收益（正數(shù)）或相互傷害（負(fù)數(shù)）的博弈，以及一些沖突。Ga

4、me theory was pioneered by Princeton mathematician john von Neumann. In the early years the emphasis was on games of pure conflict (zero-sum games). Other games were considered in a cooperative form. That is, the participants were supposed to choose and implement their actions jointly. Recent resear

5、ch has focused on games that are neither zero sum nor purely cooperative. In these games the players choose their actions separately, but their links to others involve elements of both competition and cooperation.博弈論由普林斯頓數(shù)學(xué)家約翰馮諾曼先生開創(chuàng)。早期的重點是純粹的沖突游戲（零和游戲）。其他比賽以合作形式考慮。也就是說，參與者應(yīng)該共同選擇和實施他們的行動。最近的研究集中在既不是

6、零和也不是純合作的游戲。在這些游戲中，玩家分別選擇他們的行為，但他們與其他人的聯(lián)系涉及競爭與合作的要素。Games are fundamentally different from decisions made in a neutral environment. To illustrate the point, think of the difference between the decisions of a lumberjack and those of a general. When the lumberjack decides how to chop wood, he does not

7、 expect the wood to fight back; his environment is neutral. But when the general tries to cut down the enemys army, he must anticipate and overcome resistance to his plans. Like the general, a game player must recognize his interaction with other intelligent and purposive people. His own choice must

8、 allow both for conflict and for possibilities for cooperation.游戲與中性環(huán)境下的決策有著根本的區(qū)別。為了說明這一點，想一想伐木工人的決定與一般人的決定之間的區(qū)別。當(dāng)伐木工人決定如何砍木頭時，他并不指望木頭能夠反擊;他的環(huán)境是中立的。但是當(dāng)將軍試圖削減敵人的軍隊時，他必須預(yù)見并克服對他的計劃的抵抗。和一般人一樣，玩家必須認(rèn)識到他與其他聰明和有目的的人的互動。他自己的選擇必須同時允許沖突和合作的可能性。The essence of a game is the interdependence of player strategies.

9、There are two distinct types of strategic interdependence: sequential and simultaneous. In the former the players move in sequence, each aware of the others previous actions. In the latter the players act at the same time, each ignorant of the others actions.游戲的本質(zhì)是玩家策略的相互依賴性。戰(zhàn)略相互依存有兩種截然不同的類型：順序式和同時式

10、。在前者中，球員依次移動，每個人都意識到其他人以前的行為。在后者中，參與者同時行動，每個人都無知其他人的行為。A general principle for a player in a sequential-move game is to look ahead and reason back. Each player should figure out how the other players will respond to his current move, how he will respond in turn, and so on. The player anticipates whe

11、re his initial decisions will ultimately lead and uses this information to calculate his current best choice. When thinking about how others will respond, he must put himself in their shoes and think as they would; he should not impose his own reasoning on them.玩家在順序移動游戲中的一般原則是向前看，回頭看。每個玩家都應(yīng)該弄清楚其他玩家

12、將如何回應(yīng)他目前的行動，他將如何反應(yīng)，等等。玩家預(yù)期他最初的決定將最終導(dǎo)致并使用這些信息來計算他當(dāng)前的最佳選擇。當(dāng)想到別人會如何回應(yīng)時，他必須放下自己的想法，按照自己的想法去思考;他不應(yīng)該對他們施加他自己的推理。In principle, any sequential game that ends after a finite sequence of moves can be “solved” completely. We determine each players best strategy by looking ahead to every possible outcome. Simpl

13、e games, such as tic-tac-toe, can be solved in this way and are therefore not challenging. For many other games, such as chess, the calculations are too complex to perform in practiceeven with computers. Therefore, the players look a few moves ahead and try to evaluate the resulting positions on the

14、 basis of experience.原則上，在有限的一系列動作之后結(jié)束的任何連續(xù)游戲都可以完全“解決”。我們通過展望每一個可能的結(jié)果來確定每個玩家的最佳策略。簡單的游戲，如井字游戲，可以用這種方式解決，因此不具有挑戰(zhàn)性。對于許多其他游戲，如國際象棋，計算過于復(fù)雜，無法在實踐中執(zhí)行 - 即使使用計算機(jī)。因此，球員們會看到前進(jìn)的幾步，并嘗試根據(jù)經(jīng)驗評估所得到的位置。In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logica

15、l circle. Although the players act at the same time, in ignorance of the others current actions, each must be aware that there are other players who are similarly aware, and so on. The thinking goes: “I think that he thinks that I think . . .” Therefore, each must figuratively put himself in the sho

16、es of all and try to calculate the outcome. His own best action is an integral part of this overall calculation.與連續(xù)游戲的線性推理鏈不同，具有同時移動的游戲涉及邏輯循環(huán)。雖然玩家同時行動，但無視別人目前的行為，每個人都必須意識到還有其他玩家同樣意識到，等等。這個想法是：“我認(rèn)為他認(rèn)為我想。“因此，每個人都必須形象地把自己置于所有人的腳下，并試圖計算結(jié)果。他自己的最佳行為是整體計算的一個組成部分。This logical circle is squared (the circular

17、 reasoning is brought to a conclusion) using a concept of equilibrium developed by the Princeton mathematician john nash. We look for a set of choices, one for each player, such that each persons strategy is best for him when all others are playing their stipulated best strategies. In other words, e

18、ach picks his best response to what the others do.使用普林斯頓數(shù)學(xué)家約翰納什開發(fā)的均衡概念，將這個邏輯圓平方（圓形推理得出結(jié)論）。我們尋找一套選擇，每個選手都有一個選擇，這樣當(dāng)其他人都在玩他們規(guī)定的最佳策略時，每個人的策略對他來說都是最好的。換句話說，每個人都會對他人所做的最好的回應(yīng)。Sometimes one persons best choice is the same no matter what the others do. This is called a “dominant strategy” for that player. At

19、 other times, one player has a uniformly bad choicea “dominated strategy”in the sense that some other choice is better for him no matter what the others do. The search for an equilibrium should begin by looking for dominant strategies and eliminating dominated ones.無論別人做什么，有時一個人的最佳選擇是一樣的。這被稱為該球員的“主導(dǎo)

20、戰(zhàn)略”。在其他時候，一個球員有一個統(tǒng)一的不好的選擇 - 一個“主導(dǎo)策略” - 在某種意義上，無論別人怎么做，其他選擇對他都更好。尋求均衡應(yīng)首先尋找主導(dǎo)策略并消除主導(dǎo)策略。When we say that an outcome is an equilibrium, there is no presumption that each persons privately best choice will lead to a collectively optimal result. Indeed, there are notorious examples, such as the prisoners

21、dilemma (see below), where the players are drawn into a bad outcome by each following his best private interests.當(dāng)我們說結(jié)果是一種均衡時，并不假設(shè)每個人的私人最佳選擇將導(dǎo)致集體最優(yōu)結(jié)果。事實上，有一些臭名昭著的例子，比如囚徒困境（見下文），在這些情況下，玩家被各自追求最好的私人利益而陷入糟糕的結(jié)局。Nashs notion of equilibrium remains an incomplete solution to the problem of circular reasoni

22、ng in simultaneous-move games. Some games have many such equilibria while others have none. And the dynamic process that can lead to an equilibrium is left unspecified. But in spite of these flaws, the concept has proved extremely useful in analyzing many strategic interactions.納什的均衡概念仍然是解決同步移動游戲中循環(huán)

23、推理問題的不完全解決方案。一些游戲有很多這樣的均衡，而其他游戲則沒有。并且可以導(dǎo)致均衡的動態(tài)過程未指定。但是，盡管存在這些缺陷，但這一概念在分析許多戰(zhàn)略互動中證明是非常有用的。It is often thought that the application of game theory requires all players to be hyperrational. The theory makes no such claims. Players may be spiteful or envious as well as charitable and empathetic. Recall G

24、eorge Bernard Shaws amendment to the Golden Rule: “Do not do unto others as you would have them do unto you. Their tastes may be different.” In addition to different motivations, other players may have different information. When calculating an equilibrium or anticipating the response to your move,

25、you always have to take the other players as they are, not as you are.人們經(jīng)常認(rèn)為，博弈論的應(yīng)用要求所有參與者都是超理性的。這個理論沒有提出這樣的說法。玩家可能是惡毒或嫉妒，以及慈善和同情。回想蕭伯納對黃金法則的修正案：“不要像別人那樣對待他人。他們的口味可能不同。“除了不同的動機(jī)外，其他玩家可能會有不同的信息。當(dāng)計算均衡或預(yù)測對你的舉動的反應(yīng)時，你總是必須讓其他玩家保持原樣，而不是像現(xiàn)在這樣。The following examples of strategic interaction illustrate some of

26、 the fundamentals of game theory.下面的戰(zhàn)略交互例子說明了博弈論的一些基本原理。The prisoners dilemma. Two suspects are questioned separately, and each can confess or keep silent. If suspect A keeps silent, then suspect B can get a better deal by confessing. If A confesses, B had better confess to avoid especially harsh tr

27、eatment. Confession is Bs dominant strategy. The same is true for A. Therefore, in equilibrium both confess. Both would fare better if they both stayed silent. Such cooperative behavior can be achieved in repeated plays of the game because the temporary gain from cheating (confession) can be outweig

28、hed by the long-run loss due to the breakdown of cooperation. Strategies such as tit-for-tat are suggested in this context.囚犯的困境。兩名嫌疑人分別受到質(zhì)疑，每個人都可以坦白或保持沉默。如果嫌疑人A保持沉默，那么懷疑B可以通過承認(rèn)獲得更好的交易。如果A承認(rèn)，B最好承認(rèn)避免特別苛刻的治療。認(rèn)罪是B的主導(dǎo)策略。A也是如此，因此在平衡中都承認(rèn)。如果兩人都保持沉默，兩人的表現(xiàn)都會更好。這種合作行為可以在游戲的重復(fù)中實現(xiàn)，因為由于合作中斷而造成的長期損失可以超過作弊（懺悔）的暫時收

29、益。在這種情況下，建議采取針鋒相對的策略。Mixing moves. In some situations of conflict, any systematic action will be discovered and exploited by the rival. Therefore, it is important to keep the rival guessing by mixing your moves. Typical examples arise in sportswhether to run or to pass in a particular situation in f

30、ootball, or whether to hit a passing shot crosscourt or down the line in tennis. Game theory quantifies this insight and details the right proportions of such mixtures.混合動作。在一些沖突的情況下，任何系統(tǒng)性行動都會被對手發(fā)現(xiàn)并利用。因此，通過混合你的動作來保持對手猜測是很重要的。典型的例子出現(xiàn)在體育運動中 -無論是在足球的特定情況下跑步還是傳球，還是在網(wǎng)球場上擊中傳球射門或下線。博弈論量化了這種見解，并詳細(xì)說明了這種混合物的正

31、確比例。Strategic moves. A player can use threats and promises to alter other players expectations of his future actions, and thereby induce them to take actions favorable to him or deter them from making moves that harm him. To succeed, the threats and promises must be credible. This is problematic bec

32、ause when the time comes, it is generally costly to carry out a threat or make good on a promise. Game theory studies several ways to enhance credibility. The general principle is that it can be in a players interest to reduce his own freedom of future action. By so doing, he removes his own temptat

33、ion to renege on a promise or to forgive others transgressions.戰(zhàn)略舉措。玩家可以使用威脅和承諾來改變其他玩家對未來行為的期望，從而誘使他們采取有利于他的行動，或阻止他們采取行動傷害他。要成功，威脅和承諾必須可信。這是有問題的，因為到時候，執(zhí)行威脅或承諾承諾通常是昂貴的。博弈論研究幾種提高可信度的方法。總的原則是，為了降低自己未來行動的自由，符合玩家的利益。通過這樣做，他消除了自己的背叛，或者原諒別人的過失的誘惑。For example, Corts scuttled all but one of his own ships on

34、his arrival in Mexico, purposefully eliminating retreat as an option. Without ships to sail home, Corts would either succeed in his conquest or perish. Although his soldiers were vastly outnumbered, this threat to fight to the death demoralized the opposition, who chose to retreat rather than fight

35、such a determined opponent. Polaroid Corporation used a similar strategy when it purposefully refused to diversify out of the instant photography market. It was committed to a life-or-death battle against any intruder in the market. When Kodak entered the instant photography market, Polaroid put all

36、 its resources into the fight; fourteen years later, Polaroid won a nearly billion-dollar lawsuit against Kodak and regained its monopoly market. (Polaroids focus on instant film products later proved costly when the company failed to diversify into digital photography.)例如，科爾特斯在抵達(dá)墨西哥時鑿沉了他自己的所有船只中的一艘

37、，并有目的地消除了撤退。如果沒有船舶回家，科爾特斯要么成功征服，要么滅亡。盡管他的士兵數(shù)量眾多，但這種與死亡作斗爭的威脅使反對派士氣低落，他們選擇撤退而不是與這樣堅定的對手作戰(zhàn)。寶麗來公司在有意拒絕從即時攝影市場多元化時采用了類似的策略。它致力于對抗市場上的任何入侵者的生死戰(zhàn)。當(dāng)柯達(dá)進(jìn)入即時拍攝市場時，寶麗來將所有資源投入到戰(zhàn)斗中; 14年后，寶麗來贏得了對柯達(dá)的近億美元的訴訟并重新獲得了壟斷權(quán)市場。（寶麗來專注于即時膠片產(chǎn)品的后來證明，當(dāng)該公司未能實現(xiàn)數(shù)字?jǐn)z影多樣化時，昂貴的成本。）Another way to make threats credible is to employ the a

38、dventuresome strategy of brinkmanshipdeliberately creating a risk that if other players fail to act as you would like them to, the outcome will be bad for everyone. Introduced by Thomas Schelling in The Strategy of Conflict, brinkmanship “is the tactic of deliberately letting the situation get somew

39、hat out of hand, just because its being out of hand may be intolerable to the other party and force his accommodation.” When mass demonstrators confronted totalitarian governments in Eastern Europe and China, both sides were engaging in just such a strategy. Sometimes one side backs down and concede

40、s defeat; sometimes tragedy results when they fall over the brink together.另一種使威脅可信的方法是采用冒險的冒險策略 - 故意制造一種風(fēng)險，即如果其他玩家沒有按照自己的愿望行事，結(jié)果將會對每個人都不利。托馬斯謝林在“沖突戰(zhàn)略”中介紹說，“邊緣戰(zhàn)術(shù)”是故意讓局勢略微失控的策略，僅僅是因為它的失控可能讓對方無法忍受，并迫使他們的住所。“當(dāng)群眾示威者面對時東歐和中國的極權(quán)政府雙方都在制定這樣的戰(zhàn)略。有時一方支持并承認(rèn)失敗; 有時候會一起陷入瀕臨崩潰的悲劇結(jié)局。Bargaining. Two players decide ho

41、w to split a pie. Each wants a larger share, and both prefer to achieve agreement sooner rather than later. When the two take turns making offers, the principle of looking ahead and reasoning back determines the equilibrium shares. Agreement is reached at once, but the cost of delay governs the shares. The player more impatient to reach agreement gets a smaller share.討價還價。兩名球員決定如何分割一個餡餅。每個人都希望有更大的份額，并且都希望盡早達(dá)成協(xié)議，而不是晚些時候。當(dāng)兩人輪流提出要約時，展望未來和推理的原則決定了均衡份額。協(xié)議立即達(dá)成，但延遲的成本支配股份。玩家更不耐煩達(dá)成協(xié)議的份額較小。Concealing and revealing informat