戰昇的部落格

以下是Week 14的課程內容摘要與心得，今天的講義是「Game Theory and Cartel」。課程內容深入探討了有限次重複博弈、無限次重複博弈以及卡特爾（聯合壟斷）模式的可持續性，以下為重點整理

一、有限次重複博弈 (Finitely Repeated Game)

1. 定義與基本原則

- 有限次重複博弈是將同一個階段博弈 G  重複  T 次進行，並考慮折現因子 delta 。

2. 囚徒困境的例

- 使用逆推法分析，結果顯示玩家在每個階段都會選擇「坦白」（背叛），因此無法透過有限次重複博弈解決囚徒困境。

二、無限次重複博弈 (Infinitely Repeated Game)

1. 策略示例

- Tit-for-Tat：每一回合的行動模仿對手上一回合的行為。

- Grim Trigger：只要對手有一次背叛，所有後續回合皆選擇背叛。

- Modified Grim Trigger：初期合作，只要雙方保持合作，繼續選擇合作；若有任何背叛發生，則切換為永久背叛。

2. 穩定條件

- 當折現因子，合作策略對玩家具有吸引力，合作才可能持續。

三、卡特爾模式 (Cartel)

1. 卡特爾的收益分析

- 從需求曲線可以推算出兩家的最適產量

2. 偏離策略的影響

- 若廠商1背叛（偏離協議），收益更高，顯示出背叛的動機。

- 結論：由於偏離行為帶來更高利潤，卡特爾通常難以持續。

心得總結

這週的課程讓我對博弈理論在市場中的應用有了更深的理解，尤其是在有限次與無限次重複博弈中，合作的穩定性如何受到折現因子的影響。卡特爾部分則展示了企業之間的合作難題，即使協議能帶來整體利益，背叛的誘惑仍使其難以維持。

此外，課程也讓我思考了政策在限制卡特爾行為中的重要性，期待未來能更深入學習與反壟斷相關的實例分析與政策設計。

Below is the summary and reflection for Week 14. Today’s lecture covered Game Theory and Cartel. The content delved into the sustainability of finitely repeated games, infinitely repeated games, and cartel (joint monopoly) models. The key points are summarized as follows:

A. Finitely Repeated Game

1. Definition and Basic Principles

- A finitely repeated game involves repeating the same stage game \( G \) for \( T \) times, taking into account the discount factor \( \delta \).

2. Example: Prisoner’s Dilemma

- Using backward induction, the analysis shows that players will always choose to "defect" (betray) in every stage. Thus, finitely repeated games cannot resolve the prisoner’s dilemma.

B. Infinitely Repeated Game

1. Examples of Strategies

- Tit-for-Tat: Each round’s action mimics the opponent’s action in the previous round.

- Grim Trigger: Any single defection by the opponent triggers perpetual defection in all subsequent rounds.

- Modified Grim Trigger: Initial cooperation is maintained as long as both parties continue to cooperate; any defection switches to permanent defection.

2. Stability Conditions

- Cooperation becomes sustainable if the discount factor \( \delta \) reaches a certain threshold, making cooperative strategies attractive to players.

C. Cartel Model

1. Profit Analysis in a Cartel

- From the demand curve, the optimal output for two firms in a cartel can be calculated.

2. Impact of Deviation Strategies

- If Firm 1 defects (deviates from the agreement), its profits increase, revealing the incentive to betray the cartel.

- Conclusion: Since deviation results in higher profits, cartels are generally difficult to sustain.

Reflection Summary

This week’s lecture deepened my understanding of the application of game theory in markets, particularly how the stability of cooperation in finitely and infinitely repeated games is influenced by the discount factor. The section on cartels illustrated the challenges of cooperation among firms, where the temptation to defect often undermines agreements, even if they yield collective benefits.

Additionally, the lecture prompted me to reflect on the importance of policies in curbing cartel behavior. I look forward to learning more about case studies and policy designs related to antitrust regulation in the future.