Cartels as a Prisoner's Dilemma | Microeconomics by Game Theory 101

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In previous lectures, we have seen that a monopolist can extract more profits than a pair of firms under duopoly when those two firms act competitively. This raises the possibility that both would benefit by forming a cartel to cut production. However, this comes with its own problem: each firm is better off increasing its production beyond the cartel's recommended quantity if the other firm plays by the cartel's rules.
This lecture explores how the firms can resolve the problem using the shadow of the future. Under grim trigger strategies, the firms begin by cutting production. They then maintain that reduced level of production as long as each has played by the rules. But failure to comply leads the firms to switch to producing the competitive quantity. Some analysis reveals that the cartel is sustainable under these conditions as long as the firms are sufficiently patient.
For more on what a discount factor is conceptually, watch this lecture: • Game Theory 101 (#55):...
For more on how to calculate an infinite stream of payoffs using a discount factor, watch this lecture: • Game Theory 101 (#56):...
For some more nuance on how grim trigger works, watch this lecture: • Game Theory 101 (#58):...
0:00 Comparing Cournot Competition to Monopoly
1:16 The Benefits of Forming a Cartel
2:47 The Cartel Credibility Problem
4:17 Model Setup
6:33 Grim Trigger Strategies
8:28 Today's Payoff for Cheating
11:32 Punishment Payoff for Cheating
12:04 When Is the Cartel Sustainable?

[@harshbhardwaj5022]

How is this channel not blowing up!! Concepts and videos are amazingly simple and effective..

[@PunmasterSTP]

Cartel? More like “This is swell!” Thanks for another amazing video.

[@reshobrouth8123]

Thank you so much!!! It helped me a lot.

[@rationalagent6927]

Since the game is symetric are we assuming Delta is the same for each or is 9/17 simply a threshold and they each have different Delta's I ask because it would seem to me if it's the same Delta for both then it would seem to me both forms would choose to cheat at the same time reducing the payoffs to strictly worse ones I'm enjoying the series

[@Gametheory101]

Here, we have assumed that the firms have identical discount factors. Relaxing this is simple. The 9/17 cutpoint is calculated the same way for each firm, and you need each firm to be willing to follow the cartel's rules for the cartel to work. Thus, the cartel can only work if delta_1 > 9/17 AND delta_2 > 9/17.

[@klairehoang667]

Hi, at 0:47 you said in Cournot Competition firms' profit is equal to 0 but I think this is not quite correct. I think what you mean is Bertrand?

[@Gametheory101]

I said that profit is relatively low, not zero. That's an importance distinction!
(Profits are indeed zero under a symmetric Bertrand game, though..)

[@klairehoang667]

@@Gametheory101 Thank you for your answer. Happy New Year!