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第120行：
第120行： + − {| class="wikitable" style="text-align:center" − − |+ 正则 PD 支付矩阵 − − ! <font color = '#009'>蓝色</color>\<font color = '#900'>红色</color> − − ! scope="col" style="width:60px;" | <font color = '#009'>Cooperate</color> − − ! scope="col" style="width:60px;" | {{color|#900|Defect}} − − |- − − ! scope="row" style="width:60px;" | {{color|#009|Cooperate}} − − | {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}} − − | ||transparent}} − − | {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}} − − |- − − ! scope="row" | {{color|#009|Defect}} − − | {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}} − − | {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}} − − |} − − − ! {{diagonal split header|{{color|#009|蓝方}}|{{color|#900|红方}}}} − − ! |}} − − ! scope="col" style="width:60px;" | {{color|#900|合作}} − − ! scope="col" style="width:60px;" | {{color|#900|背叛}} − − |- − − ! scope="row" style="width:60px;" | {{color|#009|合作}} − − | {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}} − − | {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}} − − |- − − ! scope="row" | {{color|#009|背叛}} − − | {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}} − − | {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}} − − |} − − − − and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs: − − and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs: 第190行：
第129行： − − − The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents. − − The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents. 第200行：
第134行： − + − 特例：<font color="#ff8000">捐赠博弈 donation game </font> − The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus − − The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus + − {| class="wikitable" style="text-align:center" − − ! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}} − − ! scope="col" style="width:60px;" | {{color|#900|Cooperate}} − − ! scope="col" style="width:60px;" | {{color|#900|Defect}} − − |- − − ! scope="row" style="width:60px;" | {{color|#009|Cooperate}} − − | {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}} − − | {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}} − − |- − − ! scope="row" | {{color|#009|Defect}} − − | {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}} − − | {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}} − − |} − − − − {| class="wikitable" style="text-align:center" − − ! {{diagonal split header|{{navy (color)|蓝方}}|{{color|#900|红方}}}} − − ! scope="col" style="width:60px;" | {{color|#900|合作}} − − ! scope="col" style="width:60px;" | {{color|#900|背叛}} − − |- − − ! scope="row" style="width:60px;" | {{color|#009|合作}} − − | {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}} − − | {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}} − − |- − − ! scope="row" | {{color|#009|背叛}} − − | {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}} − − | {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}} − − |} − − − − Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section). − − Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section). − The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything. − The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.+ − 捐赠博弈可能适用于市场。假设种植者X 种橘子，种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b''，“b”比橙子的边际效用''c''高，因为X有橙子剩余而没有苹果。同样地，对于苹果种植者Y来说，橙子的边际效用是''b''，而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子，并且每个人都完成了交易，那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货，那么这个违约者将得到''b''的收益，而合作者将失去''c''的收益。 如果两者都违约，那么谁也不会得到或失去任何东西。+
→广泛形态
[[File:正则 PD 支付矩阵.png|400px|thumb|正则 PD 支付矩阵]]
要成为强意义下的囚徒困境博弈，收益必须满足以下条件:
要成为强意义下的囚徒困境博弈，收益必须满足以下条件:
:{{tmath|T > R > P > S}}
:{{tmath|T > R > P > S}}
回报关系{{tmath|R > P}}意味着相互合作优于相互背叛，然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。
回报关系{{tmath|R > P}}意味着相互合作优于相互背叛，然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。
===Special case: donation game===
===特例：捐赠博弈===
捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式，在这种博弈中，合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b''，而叛变意味着什么也不提供。收益矩阵如下：
捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式，在这种博弈中，合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b''，而叛变意味着什么也不提供。收益矩阵如下：
[[File:捐赠博弈.png|400px|thumb|捐赠博弈收益矩阵]]
请注意{{tmath|2R>T+S}}（即{{tmath|2(b-c)>b-c}}）这使得捐赠博弈成为一个重复博弈(见下一节)。
请注意{{tmath|2R>T+S}}（即{{tmath|2(b-c)>b-c}}）这使得捐赠博弈成为一个重复博弈(见下一节)。
捐赠博弈可能适用于市场。假设种植者X 种橘子，种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b''，“b”比橙子的边际效用''c''高，因为X有橙子剩余而没有苹果。同样地，对于苹果种植者Y来说，橙子的边际效用是''b''，而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子，并且每个人都完成了交易，那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货，那么这个违约者将得到''b''的收益，而合作者将失去''c''的收益。 如果两者都违约，那么谁也不会得到或失去任何东西。
<br>
==The iterated prisoner's dilemma==
==The iterated prisoner's dilemma==