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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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18. 信息集和子博弈完美
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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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<h1 id="lecture-22">Lecture 22</h1>
<p>这一节是上一节的延续，还是关于合作。</p>
<p>本节最关键的公式：</p>
<p>gain if cheat today <script type="math/tex; ">\le</script> [value of relation after cooperation] - [value of relation after cheating]</p>
<p>右边的式子第一项表示的是promise，第二项表示的是threat。</p>
<h2 id="扳机策略（grim-trigger）">扳机策略（grim trigger）</h2>
<p>有下面的囚徒困境博弈：</p>
<table>
<thead>
<tr>
<th></th>
<th>C</th>
<th>D</th>
</tr>
</thead>
<tbody>
<tr>
<td>C</td>
<td>2, 2</td>
<td>-1, 3</td>
</tr>
<tr>
<td>D</td>
<td>3, -1</td>
<td>0, 0</td>
</tr>
</tbody>
</table>
<p>扣扳机策略：</p>
<p>如果前面一直合作，那么一直合作；一旦对方叛变，以后都不合作。</p>
<p>为了让双方有合作共赢的动机，假设每轮有<script type="math/tex; ">\delta</script>的概率进行下一轮的博弈（实际上还有不同的方式来激励下一轮的博弈）：</p>
<p><script type="math/tex; ">3-2 \le ((2+2*\delta+2*\delta^2+\dots)-0)\delta</script></p>
<p>假设博弈无数轮：</p>
<p><script type="math/tex; ">3-2 \le ((\frac{2}{1-\delta})-0)\delta</script></p>
<p>最后得到<script type="math/tex; ">\delta范围为\delta \ge \frac{1}{3}</script></p>
<p>lesson:</p>
<ol>
<li>如果使用扳机策略（背叛的代价），并且继续合作的概率大于<script type="math/tex; ">\frac{1}{3}</script>（合作的动机），我们能够在囚徒困境中达到合作的关系。</li>
<li>为了未来提供合作，必须提供充足的动机。</li>
</ol>
<h2 id="一回合惩罚机制">一回合惩罚机制</h2>
<p>如果之前一直合作，那么就一直合作；一旦产生叛变，下一回就叛变，经过一个回合后继续合作，相当于增加一个回合的惩罚。</p>
<p>那么上面的公式为</p>
<p><script type="math/tex; ">3-2 \le ((\frac{2}{1-\delta})-\delta*\frac{2}{1-\delta})\delta</script></p>
<p>求解出来<script type="math/tex; ">\delta \ge \frac{1}{2}</script></p>
<p>lesson:</p>
<p>如果惩罚的力度越小，那么未来合作的概率应该越大。反过来说，如果未来的合作机会不明朗，那么就增加惩罚力度。</p>
<h2 id="市场聘用">市场聘用</h2>
<p>一个跨国公司决定在某地进行投资和雇佣，如果进行投资，那么应该给工人多少的薪水？</p>
<p><img src="L22-1.png" alt=""></p>
<p>投资的分额假设是1</p>
<p>如果不进行投资，那么跨国公司不赚钱，工人当地的薪水为1；</p>
<p>若进行投资，如果工人携款潜逃了，那么收益矩阵为(-1, 2);</p>
<p>如果双方进行合作，那么收益是(3-w, w)。</p>
<p>考虑到下一次合作的概率为<script type="math/tex; ">\delta</script>。</p>
<p>那么得到公式：<script type="math/tex; ">2-w \le (\frac{w}{1-\delta}-\frac{1}{1-\delta})\delta</script></p>
<p>解的<script type="math/tex; ">w \ge 2-\delta</script></p>
<p>如果<script type="math/tex; ">\delta = 0</script>，那么只有一次合作，那么工人一定携款潜逃。</p>
<p>如果<script type="math/tex; ">\delta = 1</script>，那么这个跨国公司就相当于是本地开的，w = 1。</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>如果想要有好的表现，那么必须有奖励机制。（这里应该cue研究生导师，别想用国家补助骗我好好干活）</li>
<li>奖励的大小是与未来前景正相关的。</li>
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