Reasons for Cooperation

• Sometimes competition is not in the companies' best interests
  • 囚徒困境
• Sometimes companies need each other
  • 例：索尼與飛利浦，如果推行同一個標準則雙方都有很好收益。（兩個Nash Equilibrium）

In these situations, cooperation can help avoiding inefficient solutions

Achieving Cooperation(Mechanisms)

• Repeated games (for 囚徒困境)
• Commitment
  • Aggressive Commitment for many Nash Equilibrium in Simulataneous Games
  • Soft Commitment for

Repeated Games

Making the future matter.

• Interactions / games between competitors A and B take place not only once but repeatedly
• A can threaten B : if B does not behave cooperatively this time, A will retaliate next time - and vice versa

Finite Repetition

• It is clear from the beginning how often the game is repeated and when it ends

• Backward Induction (Also in the Note 1.2)

  • Can be used to analyse repeated games with finite repetitions
  • Process of reasoning backward in time :
  • First consider the last stage of a game and determine the best action at that time
  • With this information, determine what to do in the penultimate stage
  • Continue until the best strategy for every stage of the game is found

• 對於一個Finite Repetition Game，因為Endgame effect：

  • threat在最後一步不具意義，於是在倒數第一步沒有合作。
  • 在倒數第二步，不用顧忌倒數第一步的收益情況（總是沒有合作的格局），於是用於維持合作的threat不起作用，在倒數第二步沒有合作。
  • 以此類推，從一開始就不會有合作。

Endgame effect : In the last stage of the game, there's no further threat of retaliation.

Infinite Repetition

• There is no defined end of the game and the number of repetitions is not clear
• In infinitely repeated games, cooperation is possible

• Determinants

  • Likelihood of future payoffs
  • Relative value of payoffs

• Infinite Repetition Game中，不能夠使用Backward Induction，也就沒有Endgame effect

• 此時雙方只能用期望值E1來描述合作的將來收益，這涉及到對將來的估算
• 於是引入一個引數p用來表示將會有下一次Game的概率。
  • 例：設A在一輪中合作時的收益是v，以一個簡化的級數和公式來表示A的合作收益期望（包括本輪） E1 = v * （1 / (1 - p))，可以看到p越接近0，期望收益越小，越接近1則越大。
• 通過合作期望E1與背叛期望E2比較，得出是否值得合作。

Factors Infuencing Cooperation

• Large number of competitors (hindering cooperation)
  • 越多的Player意味著合作收益越小（對比背叛一次性大量收益）
• Low degree of punishment (hindering cooperation)
• High importance of future payoffs (enhancing cooperation)
  • 例：存款利率，因為存款利率提升意味著現在的錢變得更重要（存進銀行生錢），相對的，合作的吸引力變小
• 懲罰的力度

Aggressive Commitment

• In most situations, the players of a game lhave lots of options
• Agfresive commitment : Eliminate those moves which lead to unattractive equilibria
• Often, this means changing the game from a simultaneous to a sequential one

有多個納什均衡點時，採用Aggressive Commitment提前決策將Game引入自己希望的納什均衡點。

Cooperative Commitment

• Reputation Building
  • Make the company known as a reliable cooperator
  • Make it known that you treat others fairly

Reputation Building使行為更容易被對手預測 Reputation Building使背叛行為成本增大（建立信譽的成本作廢）

• Self-Binding Commitment

  • Make an investment that convinces potential partners that one is committed to act cooperatively
  • Eliminate those moves which would lead to competitive equilibria

• Most Favoured Customer Clause

  • Provision in sales contracts
  • Promises the customer that it will get refunded if another customer is charged a lower price in the future