[原创]竞合游戏+结果分析
<div class="tit"> </div><table style="TABLE-LAYOUT: fixed;"><tbody><tr><td><div class="cnt"><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"> 经典外国电影《美丽心灵》中的均衡理论，是打开我对<span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">“</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">博弈论</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">”</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">好奇的大门。因为曾经在学生时代，我对竞争战略有一定的兴趣，也在竞争与合作方面，作了一定的思考，试图得出一种结论，但由于当时思考仍未透彻，于是还有很多盲点和疑问未解决，但在</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">“</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">博弈论</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">”</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">里，我发现我的很多疑问都找到了答案！</span><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"> 理论少说，还是实例为证。</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">来看这样一个“狩猎”游戏：设想在原始社会，人们靠狩猎为生。某一天有两个猎人围住了一头鹿，他们各卡住鹿可能逃跑的两个路口中的一个。只要他们齐心协力，鹿就会成为他们的猎物，不过仅凭一个人的力量是无法猎捕到鹿的。如果此时周围跑过一群兔子，两位猎人中的任何一个只要去抓兔子一定会获得成功，他会抓住</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">4</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">只兔子。从能够填饱肚子的角度来看，</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">4</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">只兔子可以供一个人吃</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">4</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">天，</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">1</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">只鹿如果被抓住将被两个猎人平分，可供每人吃</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">10</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">天。这里不妨假设两个猎人叫</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">A</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">和</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">B</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">。</span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"> 朋友，你会做何选择？</span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><span style="FONT-SIZE: 12pt;"><span></span></span></span></p></span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"> 理论少说，还是实例为证。</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">来看这样一个“狩猎”游戏：设想在原始社会，人们靠狩猎为生。某一天有两个猎人围住了一头鹿，他们各卡住鹿可能逃跑的两个路口中的一个。只要他们齐心协力，鹿就会成为他们的猎物，不过仅凭一个人的力量是无法猎捕到鹿的。如果此时周围跑过一群兔子，两位猎人中的任何一个只要去抓兔子一定会获得成功，他会抓住</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">4</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">只兔子。从能够填饱肚子的角度来看，</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">4</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">只兔子可以供一个人吃</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">4</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">天，</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">1</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">只鹿如果被抓住将被两个猎人平分，可供每人吃</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">10</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">天。这里不妨假设两个猎人叫</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">A</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">和</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">B</span><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">。</span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"> 朋友，你会做何选择？</span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><span style="FONT-SIZE: 12pt;"><span></span></span></span></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"> </span><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><span style="FONT-SIZE: 12pt;"><span></span></span></span></p></div></td></tr></tbody></table>[此贴子已经被作者于2008-2-29 23:47:54编辑过] <p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><em><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;">游戏结果分析:</span></em></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><em><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><table class="MsoNormalTable" cellspacing="0" cellpadding="0" align="left" border="0" style="MARGIN: auto 6.75pt; BORDER-COLLAPSE: collapse; mso-table-layout-alt: fixed; mso-table-lspace: 9.0pt; mso-table-rspace: 9.0pt; mso-table-anchor-vertical: paragraph; mso-table-anchor-horizontal: page; mso-table-left: 210.6pt; mso-table-top: 12.7pt; mso-padding-alt: 0cm 0cm 0cm 0cm;"><tbody><tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes;"><td valign="top" width="151" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 4cm; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent;"><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #ff0000;"> 4 </font></span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #ff0000;">4 </font></span></p></td><td valign="top" width="147" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 110.25pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent;"><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #ffff00;"> 0</font></span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #ffff00;">4 </font></span></p></td></tr><tr style="HEIGHT: 38.25pt; mso-yfti-irow: 1; mso-yfti-lastrow: yes;"><td valign="top" width="151" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 4cm; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 38.25pt; BACKGROUND-COLOR: transparent;"><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #3366ff;"> 4 </font></span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #3366ff;">0 </font></span></p></td><td valign="top" width="147" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 110.25pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 38.25pt; BACKGROUND-COLOR: transparent;"><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 36pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #ff6600;"><span style="mso-spacerun: yes;"> </span> 10</font></span></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 9pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly; mso-element: frame; mso-element-frame-hspace: 9.0pt; mso-element-wrap: around; mso-element-anchor-vertical: paragraph; mso-element-anchor-horizontal: page; mso-element-left: 210.65pt; mso-element-top: 12.7pt; mso-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><font style="BACKGROUND-COLOR: #ff6600;">10 </font></span></p></td></tr></tbody></table></span></em></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-line-height-rule: exactly;"><span style="FONT-SIZE: 12pt; mso-font-kerning: 0pt;"><span style="FONT-SIZE: 12pt;"> </span><span style="FONT-SIZE: 12pt;"><font face="宋体, MS Song">在这个矩阵图的四个格子中，每一个格子都代表一种博弈的结果。每个格子都代表猎人<span>A</span>和<span>B的收获，格子的右上角代表猎人<span>A</span>，左下角代表猎人<span>B</span></span>。具体说来，红色的格子表示，猎人<span>A</span>和<span>B</span>都抓兔子，结果是猎人<span>A</span>和<span>B</span>都能吃饱<span>4</span>天；蓝色的格子表示，猎人<span>A</span>抓兔子，猎人<span>B</span>打鹿，结果是猎人<span>A</span>可以吃饱<span>4</span>天，<span>B</span>则一无所获；黄色的格子表示，猎人<span>A</span>打鹿，猎人<span>B</span>抓兔子，结果是猎人<span>A</span>一无所获，猎人<span>B</span>可以吃饱<span>4</span>天；橙色的格子表示，猎人<span>A</span>和<span>B</span>合作抓捕鹿，结果是两人平分猎物，都可以吃饱<span>10</span>天。</font><span><br/><br/></span><font face="宋体, MS Song"> 在这个博弈中，根据纳什均衡的定义，可以得到该博弈有两个纳什均衡点，那就是：要么分别打兔子，每人吃饱<span>4</span>天；要么合作，每人吃饱<span>10</span>天。</font><span><br/><br/></span><font face="宋体, MS Song"> 两个纳什均衡，就是两个可能的结局。两种结局到底哪一个最终发生，这无法用纳什均衡本身来确定。比较<span></span>和<span></span>两个纳什均衡，明显的事实是，两人一起去猎鹿比各自去抓兔子可以让每个人多吃<span>12</span>天。按照经济学的说法，合作猎鹿的纳什均衡，分头抓打兔子的纳什均衡，具有帕累托优势。与<span></span>相比，<span></span>不仅有整体福利改进，而且每个人都得到福利改进。换一种更加严密的说法就是，<span></span>与<span></span>相比，其中一方收益增大，而其它各方的境况都不受损害。这就是双赢策略！</font></span></span></p>
[此贴子已经被作者于2008-2-29 23:49:18编辑过]
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