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前言
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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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5. 纳什均衡：坏风气与银行挤兑
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6. 纳什均衡：约会与古诺模型
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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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17. 最后通牒和讨价还价
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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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术语表
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<a href="." >19. 招商引资和战略投资</a>
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<h1 id="lecture-19">Lecture 19</h1>
<p>上一节定义了非常多的定义，这一节将会讲三个例子进行验证。</p>
<p>上一节引出的定义subgame perfection，就是为了将同时博弈和线性博弈进行融合，填补他们之间的隔阂。</p>
<h2 id="第一个游戏">第一个游戏</h2>
<p><img src="L19-1.png" alt=""></p>
<p>这个游戏能够找到3个NE（Nash Equilibrium），但是只有一个SPE（subgame perfect NE）。并且仅有的的这一个是符合BI(back induction)推导的。</p>
<h2 id="matchmaker-game">matchmaker game</h2>
<p>三个玩家的游戏，玩家1尝试着撮合玩家2和玩家3当成某项共识。</p>
<p><img src="L19-2.png" alt=""></p>
<p>混合策略下的概率，之前已经推导过了第一个玩家选择(G, S)的概率为(2/3, 1/3)；同理玩家2选择(G, S)的概率为(1/3, 2/3)。</p>
<p>这个游戏通过推导可以看出pure strategy有两个SPE，混合策略情况下也有SPE。</p>
<h2 id="strategic-investment">strategic investment</h2>
<p>在Lecture 6中，我们已经讨论了两个玩家，进行古诺博弈。</p>
<p>先进行一些简单的复习：</p>
<p>商品的价格是根据<script type="math/tex; ">p = a-b(q_1+q_2)</script>来决定的。</p>
<p>假设现在的边际成本是 $1M/t</p>
<p>根据lecture 6中的计算结果，如果最后达到纳什均衡，那么最后的产量<script type="math/tex; ">q^* = \frac{a-c}{3b} = \frac{2-1}{3/3} = 1</script></p>
<p>因此最后的<script type="math/tex; ">p^* = \frac{4}{3}</script></p>
<p>每一个公司的利润为<script type="math/tex; ">(\frac{4}{3}-1)*1 = \frac{1}{3}</script></p>
<p>现在有一台新的机器：</p>
<ul>
<li>仅能被A使用</li>
<li>费用 $0.7 M/年</li>
<li>能够降低A的生产成本$0.5 M/吨</li>
</ul>
<p>问题：要不要租赁该机器？</p>
<h3 id="会计的答案">会计的答案</h3>
<p>每一年生产量为1，因此节约的成本0.5<0.7，因此不租赁。</p>
<h3 id="经济学答案">经济学答案</h3>
<p>会计的计算的产量是错误的，因为一旦价格变化了，那么产量就会变化，也需要将产量的变价计算其中。</p>
<p>如果计算变化的产量，通过价格-需求曲线进行计算：</p>
<p><img src="L19-3.png" alt=""></p>
<h3 id="博弈论的答案">博弈论的答案</h3>
<p>通过最佳对策曲线进行决策：</p>
<p><img src="L19-4.png" alt=""></p>
<p>在这个博弈中，不仅有商品价格下降带来的产量的增加，还有对手减产自己产量的增加，一共有两部分的增加。</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>通过计算子游戏的收益，然后进行回代。</li>
<li>不要忘记对手变化对自己的影响。</li>
</ol>
</div></div></p>
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