Consider the following normal form game between duopolists who are trying to collude. Each firm can...

 

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Consider the following normal form game between duopolists who are trying to collude. Each firm can choose to cooperate and produce a low output (QL) or cheat and produce a high output (QH). The profits are as follows (the first and second numbers in each cell represent the profits of firms 1 and 2, respectively): Firm 2 QH QL Firm 1 QH 1,1 10,0 QL 0,10 8,8 a. Find the pure strategy Nash equilibrium(s) of the one-shot game. [10%] b. Now suppose this one-shot game is repeated for an infinite number of time periods, t = 1, 2, .... Both firms use the same discount factor 8, 0<8 <1. Assume both firms use a grim-trigger strategy. Derive the condition(s) for which there is a subgame perfect Nash equilibrium of this game in which both firms cooperate in each repetition of the game. [50%] c. Explain the conditions for the successful formation of a cartel. [20%] d. Explain how, in practice, a cartel arrangement can be enforced. [20%] Consider the following normal form game between duopolists who are trying to collude. Each firm can choose to cooperate and produce a low output (QL) or cheat and produce a high output (QH). The profits are as follows (the first and second numbers in each cell represent the profits of firms 1 and 2, respectively): Firm 2 QH QL Firm 1 QH 1,1 10,0 QL 0,10 8,8 a. Find the pure strategy Nash equilibrium(s) of the one-shot game. [10%] b. Now suppose this one-shot game is repeated for an infinite number of time periods, t = 1, 2, .... Both firms use the same discount factor 8, 0<8 <1. Assume both firms use a grim-trigger strategy. Derive the condition(s) for which there is a subgame perfect Nash equilibrium of this game in which both firms cooperate in each repetition of the game. [50%] c. Explain the conditions for the successful formation of a cartel. [20%] d. Explain how, in practice, a cartel arrangement can be enforced. [20%]

Answer rating: 100% (QA)

aThere is one pure strategy Nash equilibrium in which both firms produce the high output QH In this equilibrium each firm earns a profit of 10 There are two possible pure strategy Nash equilibria in t... View the full answer