维克瑞（第二价）拍卖有什么数学妙处？
What is mathematically neat about a Vickrey (second-price) auction?
你按真实估价出价是最优策略：你付的是第二高出价而非自己的出价，因此‘说真话’是占优策略，避免了抬价博弈的扭曲。
Bidding your true value is optimal: you pay the second-highest bid, not your own, so 'telling the truth' is a dominant strategy, avoiding the distortions of strategic bidding.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#拍卖 #机制设计
纳什均衡是什么意思？
What does a Nash equilibrium mean?
在一组策略中，没有任何一方能通过单独改变自己的策略而获益，这时各方策略构成纳什均衡。它不一定是整体最优，但却是‘没人想先动’的稳定点。
In a strategy profile, no player can benefit by unilaterally changing their own strategy; that profile is a Nash equilibrium. It need not be globally optimal, but it is a stable 'no one wants to move first' point.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#博弈 #均衡
稳定婚姻问题怎么保证‘稳定’配对？
How does the stable marriage problem guarantee a 'stable' matching?
用延迟接受算法：一方依次求婚，另一方保留当前最好并拒绝其余，最终收敛到无人愿意私奔的稳定配对。 Gale–Shapley 算法保证存在且可构造。
Use the deferred-acceptance algorithm: one side proposes in order, the other keeps the best so far and rejects the rest, converging to a stable match where no pair would elope. The Gale–Shapley algorithm guarantees existence and construction.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#匹配 #算法
‘胆小鬼博弈’（鸡博弈）想说明什么？
What does the 'chicken game' (game of brinkmanship) illustrate?
双方都不退让会两败俱伤，但一方退让另一方就全胜；存在两个不对称纳什均衡。它解释了军备竞赛与对峙中‘谁先眨眼’的张力。
If neither yields, both lose; if one yields, the other wins—with two asymmetric Nash equilibria. It explains brinkmanship in arms races and standoffs: who blinks first.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#博弈 #对抗
石头剪刀布有‘必胜策略’吗？
Is there a 'winning strategy' in rock-paper-scissors?
没有固定必胜招：若双方都随机出，每种手势胜率都是1/3，这是零和对称博弈的纳什均衡。想赢只能利用对手的非随机习惯。
No fixed winning move: if both play randomly each throw wins 1/3 of the time—a symmetric zero-sum Nash equilibrium. You can only win by exploiting an opponent's non-random habits.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#博弈 #零和