膽小鬼博弈

膽小鬼博弈（英文：The game of chicken），又譯懦夫博弈，是博弈論中一個影響深遠的模型，邏輯就是「不要命的最大」。模型中，兩名車手相对驅車而行，誰最先轉彎的一方被恥笑為「膽小鬼」（chicken），讓另一方勝出，因此這博弈模型在英文中稱為The Game of Chicken（懦夫遊戲），但如果兩人拒絕轉彎，任由兩車相撞，最終誰都無法受益。這套模型在政治、經濟上經常使用，也被用來形容相互保證毀滅的核戰爭，其中1962年古巴導彈危機常列入膽小鬼博弈的典型例子。

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• Chicken (disambiguation)

  关于与「膽小鬼博弈」標題相近或相同的条目页，請見「Chicken (disambiguation)」。

The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. Template:其他用途雞遊戲，又稱鷹鳩遊戲或雪堆遊戲， The game has also been used to describe the mutual assured destruction of nuclear warfare, especially the sort of brinkmanship involved in the Cuban Missile Crisis. ==Popular versions== The game of chicken models two drivers, both headed for a single-lane bridge from opposite directions.

30。</ ref> ==熱門版本==雞遊戲的兩個司機，兩個從相反方向前往單車道橋。 The first to swerve away yields the bridge to the other.第一個轉向遠方的橋樑將橋樑交給另一個。 If neither player swerves, the result is a costly deadlock in the middle of the bridge, or a potentially fatal head-on collision.如果兩名球員都沒有轉彎，結果是在橋中間造成代價高昂的僵局，或者是一場可能致命的正面碰撞。 It is presumed that the best thing for each driver is to stay straight while the other swerves (since the other is the "chicken" while a crash is avoided).據推測，對於每個駕駛員來說最好的事情就是保持直線，而另一個則轉向（因為另一個是“雞”而避免碰撞）。 Additionally, a crash is presumed to be the worst outcome for both players.此外，對於兩名球員來說，撞車被認為是最糟糕的結果。 This yields a situation where each player, in attempting to secure their best outcome, risks the worst.這就產生了一種情況，即每個玩家在試圖獲得最佳結果時都會面臨最壞的風險。 The phrase game of chicken is also used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain, and only pride stops them from backing down. “雞肉遊戲”這個短語也被用來作為一種情形的隱喻，在這種情況下，兩方參與攤牌，他們沒有任何好處，只有驕傲才能阻止他們退縮。

Bertrand Russell famously compared the game of Chicken to nuclear brinkmanship:

Since the nuclear stalemate became apparent, the Governments of East and West have adopted the policy which [[John Foster Dulles|Mr. Bertrand Russell將雞的遊戲與[核戰爭] brinkmanship - [blockquote]比較著名，因為核僵局變得明顯，東西方政府採取了[[[]約翰福斯特杜勒斯|先生。 Dulles]] calls 'brinkmanship'.杜勒斯]稱之為“邊緣政策”。 This is a policy adapted from a sport which, I am told, is practiced by some youthful degenerates.這是一項改編自一項運動的政策，據我所知，這種運動是由一些年輕的墮落者實施的。 This sport is called 'Chicken!'.這項運動被稱為'雞！'。 It is played by choosing a long straight road with a white line down the middle and starting two very fast cars towards each other from opposite ends.通過選擇一條長直道，中間有一條白線，並從兩端開始兩輛非常快速的汽車來進行比賽。 Each car is expected to keep the wheels on one side of the white line.每輛車都應該將車輪保持在白線的一側。 As they approach each other, mutual destruction becomes more and more imminent.當他們彼此接近時，相互破壞變得越來越迫近。 If one of them swerves from the white line before the other, the other, as they pass, shouts 'Chicken!', and the one who has swerved becomes an object of contempt.如果他們中的一個在另一個之前從白線轉向，另一個，當他們經過時，喊“雞！”，而那個已經轉向的人成為蔑視的對象。 As played by irresponsible boys, this game is considered decadent and immoral, though only the lives of the players are risked.由不負責任的男孩扮演，這場比賽被認為是頹廢和不道德的，雖然只有球員的生命有風險。 But when the game is played by eminent statesmen, who risk not only their own lives but those of many hundreds of millions of human beings, it is thought on both sides that the statesmen on one side are displaying a high degree of wisdom and courage, and only the statesmen on the other side are reprehensible.但是，當遊戲由著名的政治家扮演時，他們不僅冒著生命危險而且冒著數億人的生命危險，雙方都認為政治家們一方面都表現出高度的智慧和勇氣，而且只有另一方的政治家才應該受到譴責。 This, of course, is absurd.當然，這是荒謬的。 Both are to blame for playing such an incredibly dangerous game.兩人都應該為這場極其危險的比賽負責。 The game may be played without misfortune a few times, but sooner or later it will come to be felt that loss of face is more dreadful than nuclear annihilation.遊戲可能會在沒有不幸的情況下進行幾次，但遲早會感到失去面部比核毀滅更可怕。 The moment will come when neither side can face the derisive cry of 'Chicken!'當雙方都無法面對“雞肉”的嘲諷吶喊時，那一刻將到來。 from the other side.從另一邊。 When that moment is come, the statesmen of both sides will plunge the world into destruction.

Brinkmanship involves the introduction of an element of uncontrollable risk: even if all players act rationally in the face of risk, uncontrollable events can still trigger the catastrophic outcome. In the "chickie run" scene from the film Rebel Without a Cause, this happens when Buzz cannot escape from the car and dies in the crash.當那一刻到來時，雙方的政治家都會讓世界陷入毀滅之中。 </ blockquote>邊緣政策涉及引入無法控制的風險因素：即使所有球員都面對的是合理的行為風險，無法控制的事件仍然可能引發災難性後果。 They can use threat displays (play Dove), or physically attack each other (play Hawk).

first2 = GA}} </ ref>他們可以使用威脅顯示（玩Dove），或者互相攻擊（玩Hawk）。 If both players choose the Hawk strategy, then they fight until one is injured and the other wins.如果兩個球員都選擇了Hawk策略，那麼他們會戰鬥直到一個人受傷而另一個人獲勝。 If only one player chooses Hawk, then this player defeats the Dove player.如果只有一名玩家選擇了Hawk，則該玩家將擊敗Dove玩家。 If both players play Dove, there is a tie, and each player receives a payoff lower than the profit of a hawk defeating a dove.如果兩個玩家都玩Dove，則會有一個平局，並且每個玩家獲得的收益低於鷹擊敗鴿子的利潤。

==Game theoretic applications== ===Chicken===

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正式版的雞遊戲一直是博弈論認真研究的主題。 The traditional payoff matrix for the Hawk–Dove game is given in Figure 3, where V is the value of the contested resource, and C is the cost of an escalated fight.用於Hawk-Dove遊戲的頁面=}} </ ref> 支付矩陣如圖3所示，其中V是有爭議資源的值，C是升級戰鬥的成本。

It is (almost always) assumed that the value of the resource is less than the cost of a fight, ie, C > V > 0. （幾乎總是）假設資源的價值小於戰鬥的成本，即C＆nbsp;＆gt;＆nbsp; V＆nbsp;＆gt;＆nbsp; 0。 If C ≤ V, the resulting game is not a game of Chicken but is instead a Prisoner's Dilemma.如果C＆nbsp;＆nbsp; V，結果遊戲不是雞遊戲，而是囚徒困境。 [[File:Hawk-Dove transforming into Prisoner's Dilemma.gif|thumb|Hawk–Dove transforming into Prisoner's Dilemma. [[檔案：Hawk-Dove轉變為囚徒的Dilemma.gif |拇指| Hawk-Dove轉變為囚徒困境。 As C becomes smaller than V, the mixed strategy equilibrium moves to the pure strategy equilibrium of both players playing hawk (see Replicator dynamics).]] The exact value of the Dove vs. Dove payoff varies between model formulations.當C變得小於V時，混合策略均衡轉向兩個玩鷹的戰略均衡（參見 Replicator dynamics）。]] Dove與Dove收益的確切值在模型配方。 Sometimes the players are assumed to split the payoff equally (V/2 each), other times the payoff is assumed to be zero (since this is the expected payoff to a war of attrition game, which is the presumed models for a contest decided by display duration).有時假設玩家平均分配收益（每個V / 2），其他時候假定收益為零（因為這是[[消耗戰（遊戲）|消耗戰]的預期收益]遊戲，這是由顯示持續時間決定的比賽的假定模型）。 While the Hawk–Dove game is typically taught and discussed with the payoffs in terms of V and C, the solutions hold true for any matrix with the payoffs in Figure 4, where W > T > L > X. ====Hawk–dove variants==== Biologists have explored modified versions of classic Hawk–Dove game to investigate a number of biologically relevant factors.雖然Hawk-Dove遊戲通常以V和C的方式進行教學和討論，但是對於任何具​​有圖4中的收益的矩陣，解決方案都適用，其中W＆nbsp;＆nbsp;＆nbsp; T＆nbsp;＆gt;＆nbsp; L＆nbsp; ＆gt;＆nbsp; X。 ==== Hawk-dove變體====生物學家已經探索了經典Hawk-Dove遊戲的修改版本，以研究許多生物學相關因素。 These include adding variation in resource holding potential, and differences in the value of winning to the different players, allowing the players to threaten each other before choosing moves in the game, and extending the interaction to two plays of the game. ====Pre-commitment==== One tactic in the game is for one party to signal their intentions convincingly before the game begins.這些包括增加資源保持潛力的變化，以及不同玩家獲勝價值的差異， This shows that, in some circumstances, reducing one's own options can be a good strategy.例如，如果一方在比賽開始之前誇張地禁用方向盤，那麼另一方將被迫轉向。 ==Symmetry breaking== In both "Chicken" and "Hawk–Dove", the only symmetric Nash equilibrium is the mixed strategy Nash equilibrium, where both individuals randomly chose between playing Hawk/Straight or Dove/Swerve. Hawk-Dove遊戲已被用作進化模擬的基礎，以探索這兩種混合模式中的哪一種應該在現實中占主導地位。 ===Correlated equilibrium and the game of chicken=== {{payoff matrix |這個觀察結果在兩個不同的背景下獨立完成，結果幾乎相同。 ==Related strategies and games== ===Brinkmanship=== "Chicken" and "Brinkmanship" are often used synonymously in the context of conflict, but in the strict game-theoretic sense, "brinkmanship" refers to a strategic move designed to avert the possibility of the opponent switching to aggressive behavior. Hawk-Dove和Chicken因此說明了一個有趣的案例，其中兩個不同版本的複制子動力學的定性結果差別很大。 The war of attrition is another very influential model of aggression in biology. ISBN 978-0-19-850231-9 </ ref> [[消耗戰（遊戲）|消耗戰]是另一個非常有影響力的生物攻擊模型。 The two models investigate slightly different questions.這兩個模型調查略有不同的問題。 The Hawk–Dove game is a model of escalation, and addresses the question of when ought an individual escalate to dangerously costly physical combat. Hawk-Dove遊戲是升級的典範，它解決了個人何時升級到危險的昂貴的物理戰鬥的問題。 The war of attrition seeks to answer the question of how contests may be resolved when there is no possibility of physical combat.消耗戰試圖回答在沒有實戰可能性時如何解決競賽的問題。 The war of attrition is an auction in which both players pay the lower bid (an all-pay second price auction).消耗戰是拍賣，其中兩個玩家支付較低的競價（全付第二價拍賣）。 The bids are assumed to be the duration which the player is willing to persist in making a costly threat display.假設出價是玩家願意持續進行昂貴威脅顯示的持續時間。 Both players accrue costs while displaying at each other, the contest ends when the individual making the lower bid quits.兩個玩家在彼此顯示時產生成本，當競爭較低的個人退出時，競賽結束。 Both players will then have paid the lower bid.然後兩位玩家都將支付較低的出價。 ===Chicken and prisoner's dilemma=== Chicken is a symmetrical 2x2 game with conflicting interests, the preferred outcome is to play Straight while the opponent plays Swerve. ===雞和囚犯的困境===雞是一個對稱的2x2遊戲，利益衝突，最好的結果是玩“直”，而對手玩轉向。 Similarly, the prisoner's dilemma is a symmetrical 2x2 game with conflicting interests, the preferred outcome is to Defect while the opponent plays Cooperate.同樣，囚徒困境是一個對稱的2x2遊戲，利益衝突，最好的結果是缺陷而對手玩合作。 Both games have a what seems a "sensible" cooperative outcome in which both players choose the less escalated strategy, Swerve-Swerve in the Chicken game, and Cooperate-Cooperate in the prisoner's dilemma, such that players receive the Coordination payoff C (see tables below).兩場比賽都有一個看似“明智”的合作結果，其中雙方球員選擇較少升級的戰略，在雞場比賽中選擇“Swerve-Swerve”，並在囚犯困境中選擇“合作 - 合作”，這樣球員獲得“協調”支付C（見下表）。 The obvious temptation away from this sensible outcome is towards the Temptation payoff, a Straight move in Chicken and a Defect move in the prisoner's dilemma.遠離這一明智結果的明顯誘惑是對誘惑的回報，對雞的“直接”行動以及囚徒困境中的“缺陷”行動。 The essential difference between these two games is that in the prisoner's dilemma, the Cooperate strategy is dominated, whereas in the Hawk–Dove game the equivalent move is not dominated since the outcome preferences when the opponent plays the more escalated move (Straight/Defect) are reversed.這兩場比賽之間的本質區別在於，在囚徒困境中，“合作”策略占主導地位，而在Hawk-Dove遊戲中，當對手進行更加升級的移動時，等效移動並不是主導的結果偏好（直/缺（）是相反的。

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PD是關於合作的不可能性，而雞是關於衝突的必然性。 Iterated play can solve PD but not Chicken.迭代遊戲可以解決PD而不是雞。 ===Penis game=== An activity where individuals compete to shout "penis!" ===陰莖遊戲===個人競爭喊“陰莖的活動！” in an increasingly loud voice while trying not to get in trouble with some authority figure.在試圖不與某些權威人物陷入困境時，聲音越來越響亮。 This game is often played in public places such as schools and shopping malls. === Kiss game === An activity where two people sit across from each other and move closer to each other, eventually going face to face, and the first person who moves/flinches away from the "kiss" gets to be called a "wussy".這個遊戲經常在學校和商場等公共場所播放。 is used in project management and software development circles. ==安排雞和項目管理==術語“schedule chicken” often results in contagious schedule slips due to the inter-team dependencies and is difficult to identify and resolve, as it is in the best interest of each team not to be the first bearer of bad news.

“計劃雞”的做法 ==See also== *Brinkmanship *Coordination game *Fireship, a naval tactic of intentional suicidal ramming into an enemy ship *Matching pennies *Volunteer's dilemma *War of attrition *Prisoner's dilemma ==Notes==

==References== * {{cite journal|author = Bergstrom, CT and Godfrey-Smith, P.|year = 1998|title = On the evolution of behavioral heterogeneity in individuals and populations|journal = Biology and Philosophy|在許多方面強調“時間表雞”行為的心理驅動因素模仿了鷹派或[衝突的困境#Iterated snowdrift | snowdrift model]衝突。<ref> Martin T. Macronomics：2012年2月. Macronomy.blogspot.in. [2012-08-13].  </ ref> ==參見= = Brinkmanship * 協調遊戲 * Fireship，一種故意自殺性撞擊敵艦的海軍戰術* 匹配便士 * 志願者的困境 * [[戰爭]消耗（遊戲）|消耗戰]] * 囚徒困境 ==註釋==

==參考文獻== * [{Carl Bergstrom. 關於個體和人群中行為異質性的演變 (2). doi:10.1023/A:1006588918909.  體積= (帮助); <span class= (帮助) * (2). doi:10.1023 / A：1006588918909 .  pages= (帮助); * 兩階段Hawk-Dove遊戲的進化穩定性. Rocky Mountain Journal of Mathematics. 1995, 25: 145–155.  作者= (帮助); <span class= (帮助) * Deutsch, M. The Resolution of Conflict: Constructive and Destructive Processes. Yale University Press, New Haven. 1974.  doi= (帮助) * Deutsch，M。. 衝突的解決方案：建設性和破壞性過程.  <span class= (帮助) * Dixit, AK and Nalebuff, BJ. Thinking Strategically. WW Norton. 1991.  isbn= (帮助) * {{cite book | author = Dixit，AK和 Nalebuff，BJ | title = [[思考戰略] ] | publisher = WW Norton | year = 1991 | isbn=0-393-31035-3}} * Fink, EC; Gates, S.; Humes, BD. Game Theory Topics: Incomplete Information, Repeated Games, and N-Player Games.  isbn= (帮助) * Fink，EC; Gates，S。; Humes，BD. 遊戲理論主題：不完整信息，重複遊戲和N - 遊戲遊戲.  年= (帮助); <span class= (帮助); publisher= (帮助) * Hammerstein, P. The Role of Asymmetries in Animal Contests. Animal Behaviour.  isbn= (帮助) * Hammerstein，P。. 不對稱在動物競賽中的作用. 1981. doi:10.1016/S0003-3472(81)80166-2.  <span class= (帮助); 體積= (帮助) * . 1981. doi:10.1016 / S0003-3472（81）80166-2 .  pages= (帮助); * . 1965. ISBN 978-0-313-25163-4.  作者= (帮助); <span class= (帮助); title= (帮助); * Kim, YG. Status signaling games in animal contests. Journal of Theoretical Biology. 1995. ISBN 978-0-313-25163-4.  紐約公司” (帮助) * Kim，YG。. 動物競賽中的狀態信號遊戲 (2): 221–231. 1995. PMID 7475112. doi:10.1006/jtbi.1995.0193.  <span class= (帮助) * Osborne, MJ and Rubenstein, A. . 1994: 221–231. PMID 7475112. doi:10.1006 / jtbi.1995.0193 .  volume= (帮助); * Osborne，MJ and Rubenstein，A。. MIT press. 1994.  <span class= (帮助); title= (帮助); * Maynard Smith, J. Evolution and the Theory of Games. Cambridge University Press. 1982. ISBN 978-0-521-28884-2.  *   * Maynard Smith，J。. Evolution and the Theory of Games. 1982. ISBN 978-0-521-28884-2.  * Animal Behavior. 1976, 24.  title= (帮助); author= (帮助); <span class= (帮助); 頁數= (帮助); *   * 動物衝突的邏輯 journal = Nature. 1973. doi:10.1038 / 246015a0 .  journal= (帮助); <span class= (帮助); pages= (帮助); 問題= (帮助); author= (帮助); 體積= (帮助) * Moore, CW.  bibcode= (帮助); * Moore，CW. Jossey-Bass，舊金山. ISBN 978-0-87589-673-1.  <span class= (帮助); title= (帮助); * . ISBN 978-0-87589-673-1.  年= (帮助); * The Game of Chicken. 1966.  作者= (帮助); <span class= (帮助); DOI= (帮助); 體積= (帮助); journal= (帮助); * Russell, BW. 1959.  pages= (帮助); * Russell，BW. George Allen and Unwin, London. 1959. ISBN 0-04-172003-2.  <span class= (帮助); * . George Allen and Unwin，London. ISBN 0-04-172003-2.  title= (帮助); * Evolution of the Social Contract. New York: Cambridge University Press. 1996. ISBN 0-521-55583-3.  <span class= (帮助) * Weibull, Jörgen W. Evolutionary Game Theory. Cambridge, MA: MIT Press. 1995. ISBN 0-262-23181-6.  ==External links== * The game of Chicken as a metaphor for human conflict * Game-theoretic analysis of Chicken * Game of Chicken – Rebel Without a Cause by Elmer G. Wiens. author = Skyrms，Brian | title =社會契約的演變| year = 1996 | publisher = Cambridge University Press | location = New York | isbn = 0-521-55583-3}} * Weibull, JörgenW。. 進化博弈論. Cambridge，MA. ISBN 0-262-23181-6.  ==外部鏈接= = * [1] * .gametheory.net / Dictionary / Games / GameofChicken.html雞的遊戲理論分析* * [http://www.egwald.ca/operationsresearch/chickengame.php雞的遊戲 - 無因的反叛作者：Elmer G. Wiens 。 * Online model: Expected Dynamics of an Imitation Model in the Hawk-Dove Game * Online model: Expected Dynamics of an Intra-Population Imitation Model in the Two-Population Hawk-Dove Game Template:Game theory * [2] * [3] Template:Game theory Template:DEFAULTSORT：Chicken（Game） Category：Non-cooperative games [[Category：進化博弈論] ] 類別：耐力遊戲

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