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1. 五个入门结论
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2. 学会换位思考
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3. 迭代剔除和中心选民定理
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4. 足球比赛和商业合作的最佳对策
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7. 纳什均衡：伯川模型与选民投票
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8. 纳什均衡：立场选择、种族隔离
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9. 混合策略：网球比赛
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10. 混合策略：棒球、约合与付税
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11. 进化稳定：合作、冲突与平衡
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12. 进化稳定：社会公约、侵略和周期
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13. 顺序游戏：道德风险、奖励和饥饿狮子
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14. 落后的感应：间谍与先手优势
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15. 落后的感应：道德风险、战略和可信威胁
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16. 落后的感应：声誉和决斗
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19. 招商引资和战略投资
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20. 战争的消耗
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21. 合作
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22. 作弊、惩罚与外包
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23. 沉默、信令和教育
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24. 拍卖和获奖者的诅咒
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<a href="." >16. 落后的感应：声誉和决斗</a>
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<h1 id="lecture-16">Lecture 16</h1>
<h2 id="chain-of-paradox">chain of paradox</h2>
<p>在上一节课中，讲到了一个关于垄断者和新进者的博弈例子。</p>
<p>当只有两者的sequential game时，我们通过之前通过收益举着分析有两种纳什均衡点：</p>
<ul>
<li>进军者进入，垄断者允许进入。（backward induction推测是这种结果）</li>
<li>进军者不进入，是因为垄断者声张自己要严重打击。（实际上这种结果两者都不好）</li>
</ul>
<p>我们下面重点分析第二种情形：通过收益矩阵进行分析，发现这种情况是一种纳什均衡点。</p>
<p><strong>但是</strong></p>
<p>如果我们假设有10个准备进军的玩家。</p>
<p>通过back induction，现在分析第10个玩家，那么垄断者一定不能通过对其制裁造成杀鸡儆猴的作用，因此第十个玩家毫不惧怕。最终垄断者和第十个玩家之间达成和平相处的局面。</p>
<p>第九个玩家也分析到这个层面了，于是就是到后面的达成和解了，因此也毫不惧怕，最后玩家9和垄断者达成和平共处。</p>
<p>...</p>
<p>最终就是全部和平共处。</p>
<p><strong>这似乎和我们之前垄断者一开始要起到杀鸡儆猴的作用不太一样，与直觉是不一样的！</strong></p>
<p>假设1%的几率垄断者是一个激进的人。</p>
<p>那么这个时候进军者就会想是否要进入。</p>
<p>因此这个问题的决策取决于是否是有疯子。现实生活着不可能这么的理想，因此会有杀鸡儆猴的现象存在。理想世界中，应该是和谐共处的。</p>
<p>（这波啊又是千层饼套路）/(ㄒoㄒ)/~~</p>
<p><div class="alert alert-success" style="display: table"><i class="fa fa-check" style="float: left; padding: 5px"></i><div style="margin-left: 32px"><ol>
<li>小概率的不理性的事情会改变很多的结果。</li>
<li><p>声望是很重要的，哪怕有些不理性的因素在里面。</p>
</li>
<li><p>人质绑架千万不要和绑匪谈条件，道理是相同的。警察要建立威信</p>
</li>
<li>医生，教授，会计</li>
</ol>
</div></div></p>
<h2 id="扔海绵游戏">扔海绵游戏</h2>
<p>扔海绵，每个玩家有两个选择：</p>
<ul>
<li>扔出自己仅有的一块海绵</li>
<li>往前移动一步</li>
</ul>
<p>一旦仍中游戏结束，未中并且对方没有仍则游戏继续。</p>
<p>概率分布：</p>
<p><img src="L16-1.png" alt=""></p>
<p>并且两个人的概率是不同的。</p>
<p>一个重要的假设：每一个选手射击的概率是已知并且确定的。</p>
<p>对于弱的一方进行决策：</p>
<p>决策指导：</p>
<ul>
<li>若知道下一步对手一定不会出手，那么这一步自己一定是往前走一步</li>
<li>若对手下次一定出手：</li>
</ul>
<p><strong>决策的关键：目前自己投中的概率大于下一轮对手失手的概率。</strong></p>
<p><strong>因为只能投掷一次，这一次赢的概率就是投中的概率，下一次投赢的概率就是对手失误的概率（因为一旦对手投出，那么我接下来只要足够的接近，一定会赢）。</strong></p>
<p>上面是整个游戏最关键的地方！
<script type="math/tex; ">
p_i(d)>1-p_j(d-1)\\
p_i(d)+p_j(d-1)>1
</script>
<img src="L16-2.png" alt=""></p>
<p>一开始正向的推理，然后得到不会射击的区间。<strong>使用dominance strategy进行推测</strong></p>
<p>然后<strong>通过backward induction</strong>推测出整个<script type="math/tex; ">d^*</script>的左区间都是射击区间。</p>
<p>实验证明：大部分的人投的太早了，他们高估了自己的实力。</p>
<p><div class="alert alert-success" style="display: table"><i class="fa fa-check" style="float: left; padding: 5px"></i><div style="margin-left: 32px"><ol>
<li>这道难题通过dominance strategy 和BI来进行解决。</li>
<li>如果对手有点傻，因为不要提前射击</li>
<li>有时候耐心等待也是一个很好的策略！（通过之前的实验结果）</li>
</ol>
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