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ECO290E: Game Theory

ECO290E: Game Theory. Lecture 11 Repeated Games. Bertrand Puzzle. Firms receive 0 profit under the (one-shot) Bertrand competition. But the actual firms engaging a price competition, e.g., gas stations locating next to each other, seem to earn positive profits.

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ECO290E: Game Theory

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  1. ECO290E: Game Theory Lecture 11 Repeated Games

  2. Bertrand Puzzle • Firms receive 0 profit under the (one-shot) Bertrand competition. • But the actual firms engaging a price competition, e.g., gas stations locating next to each other, seem to earn positive profits. • How come they can achieve positive profits?

  3. Long-term Relationship • Firms need some devises to prevent them from deviation, i.e., cutting its own price. • Contracts (explicit cartels): If deviation happens, a deviator must be punished by a court or a third party. • Illegal by antitrust law. • Long-term relationship (implicit cartels): Firms collude until someone deviates. After deviation, firms engage in a price war. • Long-term relationship helps achieve cooperation.

  4. Remarks Long-term relationship has an advantage over contracts when • Deviation is difficult to be detected by a court. • The definition of “cooperation” is vague. • There is no court, e.g., medieval history (economic history), developing countries (development economics), global warming (international relationship). • The best way to study the interaction between immediate gains and long-term incentives is to examine a repeated game.

  5. Repeated Games • A repeated game is played over time, t=1,2,…,T where T can be a finite number or can be infinity. • The same static game, called “a stage game,” is played in each period. • The players observe the history of play, i.e., the sequence of action profiles from the first period through the previous period. • The payoff of the entire game is defined as the sum of the stage-game payoffs possibly with discounting (especially in cases of infinitely repeated games).

  6. SPNE in Repeated Games • After all history of play, each player cannot become better off by changing her strategy only. which is equivalent to • After all history of play and for every player, immediate gains by deviation must be smaller than future losses triggered by deviation.

  7. Repeated Bertrand Games The following “trigger” strategies achieve collusion if δ≥1/2. • Each firm charges a monopoly price until someone undercuts the price, and after such deviation she will set a price equal to the marginal cost c, i.e., get into a price war.

  8. You can use the following formula. “Formula” Calculation

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