第6章推导了竞争性企业的供给曲线：在 $P = MC$ 处生产。但这一结果假设企业是价格接受者——相对于市场而言太小，无法影响价格。许多现实市场违反了这一假设。单一卖方（垄断者）自行定价。少数大型企业（寡头垄断者）必须考虑竞争对手的反应。本章描绘市场结构的谱系，并引入博弈论作为战略互动的语言。
前置知识：第6章（成本曲线、利润最大化、拉格朗日乘数法）。
在第6章中，我们证明了竞争性企业在 $P = MC$ 处实现利润最大化。在长期中，自由进入和退出导致进一步的结果。
经济利润为零并不意味着企业遭受损失。这意味着它们获得了正常回报——恰好覆盖所有成本，包括资本的机会成本。会计利润仍然为正。
其中 $P(Q)$ 是反需求函数——它给出垄断者要销售 $Q$ 单位必须设定的价格。与竞争企业（以价格为给定）不同，垄断者认识到增加销量需要降低价格。
这说明了什么： The monopolist chooses how much to produce by balancing two forces: producing more means more revenue from additional sales, but it also means lowering the price on every unit. Profit is total revenue minus total cost, and the monopolist picks the quantity where the gap is largest.
为什么这很重要： Unlike a competitive firm that simply takes the market price and decides how much to make, the monopolist controls the price through its output decision. This single difference -- that the firm faces the entire demand curve rather than a flat price line -- is what generates all of monopoly theory: restricted output, higher prices, and deadweight loss.
什么发生变化： If costs rise, the monopolist produces less and charges more. If demand shifts outward (more consumers, higher willingness to pay), the monopolist produces more but also charges more -- pocketing much of the increase as profit rather than passing it through as lower prices.
In Full Mode, Eq. 6.2 states the formal optimization problem.边际收益由两部分构成：
对于向下倾斜的需求曲线，$dP/dQ < 0$，所以 $MR < P$。对于线性需求 $P = a - bQ$：$TR = aQ - bQ^2$，所以 $MR = a - 2bQ$。MR曲线与需求曲线有相同的截距但斜率是两倍。
垄断者永远不会在 $MR < 0$ 处生产（因为减少产量反而能增加收入），因此垄断者只在需求的弹性区间运营，即 $|\arepsilon_d| > 1$。
利润最大化条件：
这说明了什么： Marginal revenue is the extra revenue from selling one more unit. For a monopolist facing a downward-sloping demand curve, MR is always less than price because lowering the price to sell one more unit reduces revenue on all existing units.
为什么这很重要： The gap between price and MR is why monopolists restrict output — they stop producing before the competitive quantity because each additional unit erodes revenue on previous sales. The firm maximizes profit by producing until MR exactly equals MC.
什么发生变化： When demand becomes more elastic (consumers more price-sensitive), MR gets closer to price and the monopolist behaves more like a competitive firm. When demand is inelastic, MR is actually negative — the monopolist would never produce in the inelastic portion of demand.
In Full Mode, Eqs. 6.3–6.4 derive MR from the revenue function and show the profit-maximization condition.这说明了什么： A monopolist faces a dilemma that competitive firms do not: to sell one more unit, it must lower the price on every unit, not just the last one. So the extra revenue from selling one more unit (marginal revenue) is always less than the price. The monopolist produces where MR = MC and charges a markup. The Lerner Index measures that markup: it equals the inverse of demand elasticity. If customers have few alternatives (inelastic demand), the monopolist charges a bigger markup.
为什么这很重要： This is why monopolies restrict output and raise prices — not out of villainy, but because the math of facing a downward-sloping demand curve makes it profitable to sell less at a higher price. The deadweight loss comes from units that consumers value more than they cost to produce, but the monopolist withholds because selling them would require cutting the price on all other units.
什么发生变化： When demand becomes more elastic (consumers have more substitutes), the Lerner index falls and the monopolist's markup shrinks — the price moves closer to marginal cost. When demand is very inelastic (few alternatives), the monopolist can charge a much larger markup. This is why pharmaceutical companies with patented drugs charge far more above cost than, say, a local cable company facing satellite competition.
In Full Mode, Eq. 6.5 derives the Lerner index from the MR = MC condition.边际成本之上的加价等于需求价格弹性（绝对值）的倒数。需求弹性越大意味着市场力量越小。
需求：$P = 100 - 2Q$。成本：$TC = 20Q$（常数 $MC = 20$）。
$TR = 100Q - 2Q^2$，$MR = 100 - 4Q$。
$MR = MC$：\$100 - 4Q = 20 \implies Q_M = 20$，$P_M = 60$。
$\Pi = (60 - 20)(20) = 800$。
竞争结果：$P = MC = 20$，$Q_C = 40$。
$DWL = \frac{1}{2}(60 - 20)(40 - 20) = 400$。
勒纳指数：$(60 - 20)/60 = 2/3$。验证：$\varepsilon_d = (dQ/dP)(P/Q) = (-1/2)(60/20) = -1.5$，所以 $1/|\varepsilon_d| = 2/3$。✓
调整边际成本，观察垄断者的最优价格、产量、利润和无谓损失如何变化。切换竞争结果叠加层进行比较。
图 6.2.垄断者将产量限制在MR = MC处，定价高于边际成本。蓝色矩形是垄断利润；黄色三角形是无谓损失。切换竞争叠加层可以看到有效结果。
Lina Khan was a 28-year-old law student when she published "Amazon's Antitrust Paradox" — an argument so influential it got her appointed chair of the FTC. Her claim: the consumer welfare standard that has governed antitrust since the 1980s is blind to Amazon's power because it only looks at prices. Amazon keeps prices low, so the standard says there's no problem. Khan says the standard is broken. By the Lerner index you just learned, she's making a radical claim — that market power can exist even when $(P - MC)/P$ is near zero.
中级企业对每个消费者收取其最高支付意愿。这提取了全部消费者剩余。产量是有效的（$Q = Q_C$）——没有无谓损失——但所有剩余归企业所有。
企业提供不同的定价方案（数量折扣、捆绑销售、版本定价）让消费者自行选择。例如：机票（商务舱与经济舱）、软件（基础版与专业版）、批量定价。
企业识别具有不同弹性的群体，对每个群体收取不同的价格：
Since $MR = P(1 - 1/|\varepsilon|)$ (from the MR-elasticity relation), equal MR across markets implies the group with less elastic demand (fewer alternatives, higher switching costs) must be charged a higher price. The optimal price ratio satisfies $P_1/P_2 = (1 - 1/|\varepsilon_2|)/(1 - 1/|\varepsilon_1|)$.
这说明了什么： A price-discriminating firm sets marginal revenue equal across all markets and equal to marginal cost. This means the firm charges higher prices to customers who are less price-sensitive (more inelastic demand) and lower prices to those who are more price-sensitive.
为什么这很重要： This is the logic behind student discounts, senior pricing, regional pricing, and surge pricing. The firm is not being charitable to students -- it is extracting more total revenue by charging different prices to groups with different willingness to pay. Airlines do this with extraordinary precision: business travelers pay more because they have less flexibility.
什么发生变化： If the elasticity gap between markets narrows (both groups become equally price-sensitive), the optimal prices converge and discrimination becomes unprofitable. If arbitrage becomes possible (students resell to adults), the price discrimination collapses to a single price.
In Full Mode, the MR-elasticity relation shows exactly how the price ratio depends on the elasticity ratio.需求弹性更低的群体支付更高的价格。
一家剧院面对两个市场。成人需求：$P_A = 20 - Q_A$。学生需求：$P_S = 12 - Q_S$。$MC = 2$。
成人：$MR_A = 20 - 2Q_A = 2 \implies Q_A = 9$，$P_A = 11$。
学生：$MR_S = 12 - 2Q_S = 2 \implies Q_S = 5$，$P_S = 7$。
总利润：$(11-2)(9) + (7-2)(5) = 81 + 25 = 106$。
两个需求弹性不同的市场。调整MC，观察每个市场的最优价格和产量如何变化。
市场A（成人）： $P_A = 20 - Q_A$
市场B（学生）： $P_S = 12 - Q_S$
短期：企业可能获得正利润或负利润。长期：进入和退出驱动经济利润归零。每家企业在其需求曲线与平均成本曲线相切处生产——而非平均成本的最低点。
In long-run equilibrium, each firm produces where its demand curve is tangent to its AC curve. The tangency condition imposes two simultaneous requirements:
Because the firm faces a downward-sloping demand curve, the tangency point occurs to the left of the AC minimum — firms produce below the efficient scale.
这说明了什么： In the long run, monopolistic competition produces a distinctive outcome: firms earn zero economic profit (free entry competed away the profits), but they still charge above marginal cost (product differentiation gives each firm a small monopoly on its particular variety). The firm operates below the scale that minimizes average cost.
为什么这很重要： This is the "price of variety." Having 50 different restaurants instead of 50 identical cafeterias means each restaurant serves fewer customers and operates below its most efficient scale. Whether this is truly inefficient depends on how much consumers value the differentiation itself.
什么发生变化： If products become less differentiated (more substitutable), each firm's demand curve becomes more elastic, the markup shrinks, and the outcome approaches perfect competition. If entry barriers increase, firms can sustain positive profit in the long run — moving the outcome toward monopoly.
In Full Mode, Eq. 6.8 shows the tangency condition that pins down the long-run equilibrium.这意味着垄断竞争相对于完全竞争有两种"低效"：
这些是否真的低效是有争议的。Dixit-Stiglitz框架表明消费者重视多样性——拥有50家不同的餐厅比50家相同的餐厅更有价值，即使相同的餐厅更便宜。边际成本之上的加价是"多样性的价格"。
In Chapter 2, comparative advantage made a clean case for free trade under perfect competition. You now have monopolistic competition and strategic interaction. Here's how imperfect competition complicates that story.
Under monopolistic competition (Krugman 1980), trade allows more product variety and exploits economies of scale — gains from trade that go beyond comparative advantage. Countries trade not because they're different, but because consumers value variety and firms benefit from larger markets. But under Cournot oligopoly (Brander-Spencer 1985), a government subsidy to a domestic firm can shift the Nash equilibrium in its favor, capturing rents from the foreign rival. The infant industry argument also gets a formal foundation: if production involves learning-by-doing (costs fall with cumulative output), temporary protection can move a firm down the cost curve and make it competitive in the long run. Strategic trade theory says that with imperfect competition, trade policy can shift profits between countries — free trade is no longer automatically optimal.
Against strategic trade: It requires the government to pick winners — to identify which industries have the right market structure and learning curves for intervention to work. Government failure (lobbying, corruption, information problems) makes this dangerous in practice. The theoretical conditions for beneficial strategic trade are knife-edge: the government must know demand elasticities, cost structures, and the rival government's response. Against infant industries: The historical record is mixed — many "infant" industries never grow up. Protection creates rents for politically connected firms rather than genuine learning. And once protection is granted, the political economy of removing it is brutal — the beneficiaries lobby to keep it forever.
The mainstream view shifted after the China shock literature. Pre-2010, the consensus was strongly pro-free-trade with redistribution as a side policy. Post-2010, the profession acknowledged that adjustment costs from trade are larger, longer-lasting, and more geographically concentrated than previously assumed (Autor, Dorn & Hanson 2013, 2016). The trade adjustment assistance programs that were supposed to compensate the losers have been small and ineffective. Krugman himself — who won the Nobel partly for showing gains from trade under imperfect competition — acknowledged that the distributional effects were understated for decades.
Free trade remains net positive for most countries most of the time — the comparative advantage logic from Chapter 2 is robust, and Krugman's monopolistic competition model adds further gains from variety and scale. But the unconditional case has weakened. The distributional effects are larger than the profession acknowledged for decades, and compensation mechanisms have failed. Strategic trade and infant industry arguments have theoretical merit but are dangerous in practice — government failure is the binding constraint. The honest answer: free trade is the right default, strategic intervention can work but usually doesn't, and the losers from trade need real compensation, not promises.
The models here are static — they compare one equilibrium to another. How should we think about trade in a world with supply chain dependencies (semiconductors, rare earths, energy)? Economic security arguments for protection are different from efficiency arguments. And the macroeconomic dimension is missing entirely: trade deficits, capital flows, and exchange rates all affect the story. Come back in Chapter 17 (§17.1–17.7), where the open-economy macro framework adds balance-of-payments accounting, the impossible trinity, and global imbalances to the picture.
“关税人”说关税让美国更富。经济学家说这是对美国消费者征税。2018年贸易战提供了现代数据中的首个重大检验案例。
中级企业同时选择产量。每家企业的最优产量取决于其他企业的产量。
设定。两家企业，需求 $P = a - b(q_1 + q_2)$，两家的边际成本均为常数 $c$。
企业1的最优反应函数：
Firm 1 maximizes $\Pi_1 = [a - b(q_1 + q_2) - c] \cdot q_1$. Taking the first-order condition:
Solving for $q_1$ gives the best response function:
古诺-纳什均衡（联立求解）：
这说明了什么： Each firm picks its quantity by asking: "Given what my rival produces, what quantity maximizes my profit?" The best response function captures this strategic interdependence -- if my rival produces more, I should produce less (since total output drives the price down). The equilibrium is where both firms are simultaneously best-responding: neither wants to change. Each duopolist produces one-third of the competitive output; together they produce two-thirds.
为什么这很重要： Cournot shows that oligopoly outcomes fall between monopoly and perfect competition. More firms push the market closer to the competitive outcome. This is the formal basis for antitrust intuitions about market concentration: fewer firms means higher prices and more deadweight loss.
什么发生变化： When a rival expands production, the best response is to contract -- the reaction functions slope downward. Adding more firms to the market shrinks each firm's share and pushes the price toward marginal cost. With 2 firms, the industry produces 2/3 of competitive output; with 5 firms, 5/6; with 20 firms, the market is essentially competitive. Higher marginal costs shift the equilibrium toward lower output and higher prices for all firms.
In Full Mode, Eqs. 6.7-6.10 derive the best response functions and solve for the Cournot-Nash equilibrium.对称的 $n$ 家企业，$q_i = (a-c)/((n+1)b)$ 且当 $n \to \infty$ 时 $P \to c$。
这说明了什么： As the number of firms grows, each firm's share of the market shrinks, and the total output rises. With enough firms, the oligopoly outcome becomes indistinguishable from perfect competition: price equals marginal cost, economic profit vanishes, and deadweight loss disappears.
为什么这很重要： This is the Cournot convergence result -- it provides the bridge between monopoly (one firm, maximum market power) and perfect competition (many firms, zero market power). It gives precise meaning to the idea that "more competition is better": each additional firm moves the price closer to cost.
什么发生变化： With 2 firms, the markup is substantial. With 5 firms, it is much smaller. With 20 firms, the market is essentially competitive. The speed of convergence depends on cost structure: when marginal costs are high relative to demand, fewer firms suffice to drive the market toward competition.
In Full Mode, the n-firm Cournot formula shows the exact relationship between the number of firms and the market outcome.需求：$P = 100 - Q$，$c = 10$。最优反应：$q_i^* = 45 - q_j/2$。
均衡：$q_1^C = q_2^C = 30$。$Q^C = 60$，$P^C = 40$。$\Pi_i = 900$。
| 结构 | 产量 | 价格 | 行业利润 | 无谓损失 |
|---|---|---|---|---|
| 竞争 | 90 | 10 | 0 | 0 |
| 古诺双寡头 | 60 | 40 | 1,800 | 450 |
| 垄断 | 45 | 55 | 2,025 | 1,012.5 |
将企业数量从1（垄断）滑动到20。观察总产量上升、价格下降、无谓损失趋近于零——市场趋向完全竞争。
图 6.3a。随着N增加，古诺结果趋向完全竞争。N=1时为垄断。柱状图展示关键指标如何随市场结构变化。
调整每家企业的边际成本，观察反应函数如何移动以及均衡点如何变化。不对称成本导致不对称产出。
图 6.3b。每家企业的反应函数向下倾斜：对手产量增加会降低最优反应产量。交叉点是古诺-纳什均衡。拖动成本滑块可以看到不对称成本如何移动反应函数和均衡点。
In Chapter 2, the competitive model gave a clean answer: a minimum wage above equilibrium creates unemployment. You now have monopoly, oligopoly, and the tools to model market power. Here's what happens when the labor market isn't competitive.
Apply the monopoly framework from §6.2 to a labor market, but flip the direction: instead of a single seller with market power, consider a single buyer of labor — a monopsonist. The firm faces an upward-sloping labor supply curve $w(L)$ with $w' > 0$. The marginal cost of labor exceeds the wage: $MC_L = w + w' \cdot L$. The firm hires where $MC_L = MRP_L$, at a wage below the competitive level and employment below the competitive level. Now impose a minimum wage between the monopsony wage and the competitive wage. The firm's marginal cost of labor becomes flat at the minimum wage (up to a point), which means it hires more workers, not fewer. A minimum wage can increase both employment and earnings simultaneously. Above the competitive wage, the standard unemployment prediction returns.
Even if individual firms have some labor market power, workers can move between employers, industries, and cities. Labor mobility limits monopsony power in the long run. The empirically relevant question is how much monopsony power exists in practice — and this varies enormously by sector, geography, and worker type. Fast food in a small rural town may approximate monopsony; tech hiring in San Francisco is close to competitive. The "new monopsony" literature (Manning 2003) argues that search frictions and moving costs create monopsony power even with many employers — but the degree of that power, and therefore the employment effect of minimum wages, remains an empirical question that theory alone cannot settle.
The mainstream absorbed monopsony as a theoretical possibility early on — Joan Robinson formalized it in 1933. But before Card and Krueger's landmark 1994 study, the profession treated monopsony as empirically rare and the competitive model's unemployment prediction as the dominant result. The "new monopsony" literature broadened the concept from "one employer in a company town" to "employers have some wage-setting power due to search frictions, moving costs, and information asymmetries" — which is much more common than the textbook monopsony suggests.
The theory is now clear: the effect of minimum wages depends on the degree of monopsony power. Both "always causes unemployment" and "never causes unemployment" are wrong as general claims. The correct theoretical answer is "it depends on market structure" — and market structure varies across labor markets. The Cournot model from §6.5 offers an analogy: just as the welfare effects of oligopoly depend on the number of firms and the degree of market power, the employment effects of minimum wages depend on the structure of the labor market. The competitive model and the monopsony model are two ends of a spectrum.
Theory gives a conditional prediction: the employment effect depends on market structure. But which market structure is empirically relevant? We need data to adjudicate. Come back in Chapter 10 (§10.4), where Card and Krueger's natural experiment is analyzed using difference-in-differences — the econometric method that launched a 30-year empirical war between the competitive and monopsony predictions.
The monopsony model says moderate increases can raise employment. But \$15 in San Francisco is very different from \$15 in rural Mississippi. The answer depends on the local wage bite — and the local degree of employer market power.
中级在伯特兰模型中，企业同时选择价格（而非产量）。在产品相同且边际成本相等时：
仅有两家企业，价格竞争就复现了完全竞争结果。这就是伯特兰悖论：古诺模型说需要很多企业才能实现竞争；伯特兰模型说两家就够了。
这说明了什么： When two firms sell identical products and compete on price, a relentless undercutting logic drives the price all the way down to marginal cost. If Firm A charges \$20 and Firm B charges \$19.99, every customer goes to Firm B. So Firm A cuts to \$19.98, then Firm B cuts to \$19.97 -- and this continues until neither can go lower without losing money. The result: the competitive outcome with just two firms.
为什么这很重要： This is the Bertrand paradox -- it says the number of firms is not what determines market power. What matters is how firms compete. Quantity competition (Cournot) preserves market power with few firms; price competition (Bertrand) destroys it immediately. The real-world question is which model better fits a given industry.
什么发生变化： The paradox dissolves when products are differentiated (a small price cut does not steal the entire market), when firms have capacity constraints (they cannot serve everyone), when firms interact repeatedly (enabling tacit collusion), or when consumers face search costs (they do not instantly switch). Most real markets have some combination of these frictions, which is why we rarely see pure Bertrand outcomes.
In Full Mode, the undercutting argument is stated precisely: any P > MC is not a Nash equilibrium because a rival can profitably deviate.悖论消解的条件：
两家企业销售差异化产品。企业 $i$ 的需求：$q_i = 100 - 2p_i + p_j$（产品是替代品但非完全相同）。边际成本：$c = 10$。
企业1最大化：$\Pi_1 = (p_1 - 10)(100 - 2p_1 + p_2)$。
一阶条件：\$100 - 4p_1 + p_2 + 20 = 0 \implies p_1^*(p_2) = \frac{120 + p_2}{4} = 30 + p_2/4$。
由对称性：$p^* = 30 + p^*/4 \implies p^* = 40$。
每家企业：$q^* = 100 - 80 + 40 = 60$。$\Pi^* = 30 \times 60 = 1{,}800$。
在差异化产品下，均衡价格（\$40$）超过边际成本（\$10$）。伯特兰悖论消解了，因为小幅降价不再能夺取整个市场。
在施塔克尔伯格模型中，一家企业（领导者）先行动，选择其产量。跟随者观察领导者的选择后进行优化。领导者将跟随者的反应函数内部化。
Step 1 (Follower's problem): The follower observes $q_1$ and maximizes $\Pi_2 = [a - b(q_1 + q_2) - c] \cdot q_2$. This yields the same best-response function as Cournot: $q_2^*(q_1) = \frac{a - c}{2b} - \frac{q_1}{2}$.
Step 2 (Leader's problem): The leader substitutes the follower's best response into its own profit function: $\Pi_1 = [a - b(q_1 + q_2^*(q_1)) - c] \cdot q_1$. Maximizing gives:
这说明了什么： When one firm moves first, it can commit to a large quantity, forcing the follower to accommodate by producing less. The leader produces half the competitive output (the monopoly quantity); the follower produces only half of what the leader does. Total output exceeds Cournot, so the price is lower.
为什么这很重要： Commitment has strategic value. By going first and locking in a large quantity, the leader effectively says "I am flooding the market -- adjust accordingly." This is the formal logic behind first-mover advantages in industries where capacity decisions are hard to reverse (factories, infrastructure, spectrum licenses).
什么发生变化： If the leader's cost advantage grows, it produces even more and squeezes the follower further. If commitment becomes less credible (the leader can easily reverse its decision), the game reverts toward the Cournot outcome because the follower no longer needs to accommodate. The asymmetry depends entirely on the irreversibility of the leader's move.
In Full Mode, Eqs. 6.12-6.13 derive the Stackelberg quantities via backward induction.领导者生产垄断产量，跟随者生产其一半。总产量超过古诺；价格更低。先行者优势来自于在跟随者选择之前承诺大产量。
$P = 100 - Q$，$c = 10$：
$q_1^S = 45$，$q_2^S = 22.5$。$Q^S = 67.5$，$P^S = 32.5$。
$\Pi_1 = 1{,}012.5$（领导者），$\Pi_2 = 506.25$（跟随者）。
领导者利润超过古诺（\$1{,}012.5 > 900$）。跟随者境况更差（\$506.25 < 900$）。
在同时博弈（古诺）和序贯博弈（施塔克尔伯格）之间切换，使用 $P = 100 - Q$、$c = 10$ 比较产量和利润。
图 6.4.比较古诺（对称）和施塔克尔伯格（领导者优势）。在反应函数图上，施塔克尔伯格均衡位于古诺的右下方：领导者产量更多，跟随者产量更少。
这说明了什么： A Nash equilibrium is a situation where every player is doing the best they can, given what everyone else is doing. Nobody can improve their outcome by changing their own strategy alone. Think of it as a "no regrets" outcome -- once you see what everyone else chose, you would not change your choice.
为什么这很重要： Nash equilibrium is the central solution concept in game theory and applies far beyond economics -- to politics, biology, and any situation with strategic interaction. It does not mean the outcome is good for society (the Prisoner's Dilemma shows it can be terrible), just that it is self-enforcing: no individual has an incentive to deviate.
什么发生变化： When payoffs change, equilibria shift. If the penalty for defection increases (stronger enforcement, higher fines), cooperation becomes easier to sustain. If a new strategy becomes available, old equilibria may dissolve. Some games have multiple Nash equilibria (coordination games), some have exactly one (Prisoner's Dilemma), and some have none in pure strategies -- requiring randomization (mixed strategies).
In Full Mode, Eq. 6.14 states the formal condition: no player can improve their payoff by unilateral deviation.每个参与者都在对其他人做最优反应。在其他人的行为给定的情况下，没有人有理由偏离。
| 参与者2：合作 | 参与者2：背叛 | |
|---|---|---|
| 参与者1：合作 | (3, 3) | (0, 5) |
| 参与者1：背叛 | (5, 0) | (1, 1) |
占优策略：无论对方如何选择，背叛都是最优的。纳什均衡：(背叛, 背叛)，收益为(1, 1)。双方都比相互合作(3, 3)更差，但都无法单方面改善。
这说明了什么： The Prisoner's Dilemma captures a fundamental tension: what is rational for each individual leads to a bad outcome for everyone. Each player reasons: "No matter what the other does, I am better off defecting." But when both think this way, they end up with (Defect, Defect) -- worse for both than if they had cooperated.
为什么这很重要： This structure appears everywhere in economics and beyond. Firms in a cartel each have an incentive to secretly increase output. Countries each want to free-ride on others' carbon reductions. Arms race participants each prefer to build weapons while the other disarms. The core insight: markets, institutions, and enforcement mechanisms exist precisely to solve Prisoner's Dilemmas -- converting individual incentives toward socially better outcomes.
什么发生变化： If the temptation payoff (defecting while the other cooperates) shrinks -- through penalties, reputation effects, or social norms -- cooperation becomes easier. If the game is repeated, future punishment can sustain cooperation (see repeated games below). If communication is allowed, players can coordinate -- but only if commitments are enforceable.
囚徒困境为何重要：
输入2×2博弈的任意收益。工具自动识别占优策略、纳什均衡和帕累托最优结果。绿色单元格为纳什均衡；蓝色边框标记帕累托最优结果。
| 参与者2：L | 参与者2：R | |
|---|---|---|
| 参与者1：U | (,\n ) | (,\n ) |
| 参与者1：D | (,\n ) | (,\n ) |
蓝色 = 参与者1的收益 | 红色 = 参与者2的收益
协调博弈：
| B：左 | B：右 | |
|---|---|---|
| A：左 | (2, 2) | (0, 0) |
| A：右 | (0, 0) | (1, 1) |
两个纳什均衡：(左, 左)和(右, 右)。挑战在于协调，而非冲突。
性别之战：
| B：歌剧 | B：足球 | |
|---|---|---|
| A：歌剧 | (3, 1) | (0, 0) |
| A：足球 | (0, 0) | (1, 3) |
两个纯策略纳什均衡，每个参与者有不同的偏好结果。
两家企业选择是否投放广告(A)或不投放(N)：
| 企业2：A | 企业2：N | |
|---|---|---|
| 企业1：A | (4, 4) | (7, 2) |
| 企业1：N | (2, 7) | (5, 5) |
第一步——检查占优策略。
企业1：如果企业2选择A，企业1获得4(A)对2(N) → A更好。如果企业2选择N，企业1获得7(A)对5(N) → A更好。因此A是企业1的占优策略。由对称性，A也是企业2的占优策略。
第二步——找出纳什均衡。
唯一的纳什均衡是(A, A)，收益为(4, 4)。两家企业都投放广告，尽管(N, N) = (5, 5)帕累托占优。这是一个囚徒困境：投放广告的个体激励导致了集体更差的结果。
当囚徒困境被重复进行（且参与者有耐心）时，合作可以维持。未来惩罚（回归背叛）的威胁使当前合作具有自我执行力。这就是无名氏定理。
Under the grim trigger strategy (cooperate until the other defects, then defect forever), cooperation is sustainable if:
where $\pi_C$ is the per-period cooperation payoff, $\pi_D$ is the one-shot deviation payoff, and $\pi_N$ is the Nash (punishment) payoff. With standard prisoner's dilemma payoffs (CC=3, DC=5, DD=1): $\delta \geq (5-3)/(5-1) = 1/2$.
这说明了什么： Cooperation in a repeated game is a cost-benefit calculation: the short-run temptation to cheat (the one-time gain from defecting while the other cooperates) versus the long-run punishment (being stuck in mutual defection forever). If players are patient enough (high discount factor), the future punishment outweighs the immediate gain, and cooperation is self-enforcing.
为什么这很重要： This explains why cartels, arms agreements, and trade deals can work even without external enforcement. The threat of retaliation (price wars, tariff escalation, arms races) sustains cooperation -- as long as the relationship is expected to continue. It also explains why cooperation breaks down when firms are impatient, when the game has a known end date, or when cheating is hard to detect.
什么发生变化： Higher discount factor (more patience) makes cooperation easier. Larger temptation payoff makes it harder. If the punishment is mild (Nash payoff close to cooperation payoff), cooperation requires more patience. This is why OPEC struggles to maintain output quotas: the temptation to overproduce is large, detection is slow, and punishment is weak.
In Full Mode, Eq. 6.15 derives the critical discount factor from the grim trigger strategy.直觉是：今天的合作维持了关系。欺骗带来短期收益但永远触发惩罚。如果折现因子 $\delta$ 足够高，惩罚的长期成本超过短期收益。
在标准囚徒困境（收益：CC=3, CD=0, DC=5, DD=1）中，通过冷酷触发策略实现合作需要折现因子 $\delta$ 超过某个门槛值。滑动 $\delta$ 查看合作是否可持续。
图 6.5.水平线表示维持合作所需的最低折现因子 $\delta^*$。当 $\delta > \delta^*$ 时，合作的长期价值超过一次性背叛的诱惑。图表比较了永久合作的现值与背叛一次然后永远受罚的现值。
| 市场结构 | 企业数量 | 价格 | 产量 | 利润 | 无谓损失 | 战略性？ |
|---|---|---|---|---|---|---|
| 完全竞争 | 多 | $P = MC$ | 最高 | 零（长期） | 无 | No |
| 垄断竞争 | 多 | $P > MC$ | 低于竞争 | 零（长期） | 小 | No |
| 古诺寡头垄断 | Few | $MC < P < P_M$ | 介于之间 | 正 | 中等 | 是（Q） |
| 施塔克尔伯格 | Few | 低于古诺 | 更高 | 领导者 > 古诺 | 更少 | 是（序贯） |
| 伯特兰（同质） | Two | $P = MC$ | 竞争水平 | 零 | 无 | 是（P） |
| 垄断 | One | 最高 | 最低 | 最高 | 最大 | No |
竞争对手内特在街对面开了一个柠檬水摊。两人有相同的成本结构。社区需求为 $P = 5 - (Q_M + Q_N)/20$，$MC = 1.50$。
古诺均衡： $Q_M^* = Q_N^* = 23.3$ 杯。$P = 2.67$。玛雅的利润：\$17.2$/天（仅材料成本）。
施塔克尔伯格（玛雅为领导者）： $Q_M^S = 35$，$Q_N^S = 17.5$。$P = 2.375$。玛雅的利润：\$10.6$/天——由于先行者优势略高。
内特进入市场后，玛雅的产量从45杯降至23.3杯，价格从\$1.75降至\$1.67。
| 标签 | 公式 | 描述 |
|---|---|---|
| 式 6.1 | $P = MC = AC_{min}$, $\Pi = 0$ | 长期竞争均衡 |
| 式 6.2 | $\max \Pi = P(Q)Q - TC(Q)$ | 垄断者的问题 |
| 式 6.3 | $MR = P + Q(dP/dQ)$ | 边际收益 |
| 式 6.4 | $MR = MC$ | 垄断利润最大化条件 |
| 式 6.5 | $(P-MC)/P = 1/|\varepsilon_d|$ | 勒纳指数 |
| 式 6.6 | $MR_1 = MR_2 = MC$ | 三级价格歧视 |
| 式 6.7–6.8 | 最优反应函数 | 古诺反应函数 |
| 式 6.9 | $q_i^C = (a-c)/(3b)$ | 古诺对称均衡 |
| 式 6.10 | $P^C = (a+2c)/3$ | 古诺价格 |
| 式 6.11 | $P^B = c$ | 伯特兰均衡（同质产品） |
| 式 6.12–6.13 | $q_1^S = (a-c)/(2b)$, $q_2^S = (a-c)/(4b)$ | 施塔克尔伯格产量 |
| 式 6.14 | $u_i(s_i^*, s_{-i}^*) \geq u_i(s_i, s_{-i}^*)$ 对所有 $s_i$ 成立 | 纳什均衡 |
| Eq. 6.15 | $\delta \geq (\pi_D - \pi_C)/(\pi_D - \pi_N)$ | Cooperation threshold (grim trigger) |
| B: X | B: Y | |
|---|---|---|
| A: X | (3, 3) | (1, 4) |
| A: Y | (4, 1) | (2, 2) |
Coming in Part III: macroeconomics changes the scale from firms to countries.
