18.16: 无限次重复博弈

无限次重复博弈指的是博弈者重复参与相同的博弈，而没有预先确定结局的场景。这一概念对于理解社会科学中各个领域（包括经济学和国际关系）的长期互动来说是至关重要的。

示例：

1.  企业定价：企业不断地调整价格。
2.  贸易谈判：各国持续地谈判贸易条款。

针锋相对策略

合作开局：博弈者通过合作行动开始，例如设定高价。

互惠：博弈者对对手之前的行动进行匹配，如果对手也会这样做，则会维持高价。

报复和宽恕：如果一个博弈者在一轮中降低了价格，那么 另一个博弈者会在下一轮中进行效仿，但在对手做出同样的事情以后，这一轮的价格就会恢复到高价。

博弈者意识到，相互维持高价（或其他的这类合作行动）会比非合作行动的短期收益产生更好的长期利益。

在无限次重复博弈的背景下，博弈者会采用能够将长期利益最大化的策略，从而认识到相互合作是有利的。

除了定价之外，这一策略还适用于各国同意减少排放的环境协议，从而通过保持合作来避免长期的不利影响。

无限重复的游戏是指玩家反复参与同一游戏而没有预定结局的游戏。

例如，公司多年来反复设定价格或国家/地区进行贸易条款谈判。

在这些游戏中，公司通常采用针锋相对的策略。

例如，考虑两家竞争公司 Alpha 和 Beta 为其软饮料设定价格。

他们在每个月月初决定价格。如果两家公司都保持高价，它们就会享受高利润。

针锋相对的策略涉及从合作行动开始，例如设定高价。

只要 Alpha 这样做，Beta 就会继续设定高价。

如果 Alpha 降低价格，Beta 也会在下一轮降低其价格。这给 Alpha 带来了利润优势，而给了 Beta 那一轮的利润劣势。当 Alpha 返回到高价时，Beta 会匹配它。

无限重复博弈的结果是持续的合作。公司认识到，降价的短期收益小于低价的长期损失。

保持高价格成为两家公司的合理策略，随着时间的推移实现互惠互利。

• Infinitely Repeated Games – A strategic engagement undertaken without a definitive end.
• Tit-For-Tat Strategy – A reciprocative strategy utilized in repeated games.
• Cooperative Start – Initial collaboration during the commencement of a game.
• Reciprocity – Matching opponent's previous actions during gameplay.
• Retaliation and Forgiveness – Reacting to non-cooperation and reverting to cooperation afterward.

• Define Infinitely Repeated Games – Understand its role in economic theory (e.g., long-term business strategies).
• Contrast One-Time vs Repeated Games – Discern key differences (e.g., benefits of long-term cooperation).
• Explore Examples – Understand its practical applications (e.g., pricing strategies).
• Explain Tit-For-Tat Strategy – Understand how it encourages optimal behavior in repeated games.
• Apply in Context – Understand how various strategies play out in real-life situations.

• What does the 'infinitely repeated games' term imply in game theory and how does it impact economic behavior?
• What is the 'tit-for-tat' strategy and how can it promote optimal behavior in repeated games?
• How do 'reciprocity' and 'retaliation and forgiveness' contribute to long-term benefits in a repeated game?

• Students – Gain understanding of game theory and repeated games, which are crucial concepts in economics.
• Educators – Provides a basis for teaching game theory, equipping students with an insight into strategic behavior.
• Researchers – Explore the depth of strategic behavior in economic and social contexts, informing research in game theory.
• Economics Enthusiasts – Offer insights into infinitely repeated games, enriching their understanding and interest in game theory.