Finitely+repeated+games,+the+end-of+period+problem,+infinitely+repeated++games

Ryan Bowen

1. An infinitely repeated game is one that is played over and over forever. During the game players receive payoffs during each playing of the game. Due to the fact that the game is played forever, there is an incentive between the two parties to collude. Collusion is where the two parties work together in order to alter the payoffs they both experience. Four factors are key in determining whether collusion will successfully occur: number of firms, firm size, history of the market & punishment mechanisms. Collusion will work between the two parties as long as neither “cheats” by acting in a manner different from the collusion agreement. Finitely repeated games are games which have an end period. During the game players receive payoffs during each playing of the game. There are two types of finitely repeated games: those in which the end period is not known and those in which the end period is known. When the end period in a finitely repeated game is not known the game functions just like that of an infinitely repeated game. When the end period of a finitely repeated game is known collusion cannot work and as a result the “end of period problem” arises. The end of period problem refers to the fact that since there is no “tomorrow”, there is no way to punish a player who cheats in the final period of the game. As a result, in the last period players will make their decision as if it was a one-shot game which results in making a self-serving decision.
 * What are infinitely repeated games, finitely repeated games and the end of period problem?**

2. There are many real world examples finitely repeated games, the end-of period problem and infinitely repeated games. Examples of infinitely repeated games can be seen between any two organizations that deal with each other on a continual and on-going basis. Boeing and Airbus are the world’s major producers of aircrafts. These two companies work with the airline companies on a continual basis because the aircraft producers need the airline companies to purchase their products and the airline companies need to have aircrafts in order to service their customers. The fact that these two entities deal with each other on a continual and on-going basis makes their interaction an example of an infinitely repeated game. A common example of a finitely repeated game is the prisoner’s dilemma. For example, two criminals are interrogated separately by the police and given the opportunity to confess or not confess to the crime. The below table shows the prisoner’s dilemma Bonnie & Clyde face regarding whether to confess or not.
 * What are some real world examples of these games?**


 * Prisoners' || Dilemma || Clyde || Clyde ||
 * ||  || Confess || Don't Confess ||
 * Bonnie || Confess || 5 years (Clyde) 5 years (Bonnie) || Set free (Clyde) 10 years (Bonnie) ||
 * Bonnie || Don't Confess || 10 years (Clyde) Set free (Bonnie) || 1 year (Clyde) 1 year (Bonnie) ||

Since this is a one-shot game which will not continue forever it is an example of a finitely repeated game. Since this is a one-shot finitely repeated game the two prisoners are not able to collude with one another to alter the game's outcome. An example of an end of period problem involves resigning from a job. If a worker plans to quit her job tomorrow, she has little incentive to work hard today because the fear of being fired is not a legitimate threat. On the other hand, the worker’s boss does not want to fire the worker immediately after learning of her intention to quit because it may set off a bad reaction among the other workers and more than likely the manager cannot take that action due to legal ramifications. Finally, some real world examples of collusion have been seen in the garbage collection industry, OPEC, NASDAQ and the airline industry.

Baye, Michael R. (2006). //Managerial Economics and Business Strategy//. New York: McGraw- Hill Irwin. Conley, John P. “One-shot prisoners’ dilemma games.” //Handout for Lecture 3 – MBA 405B//. Vanderbilt University. Retrieved March 22, 2007 from http://www.vanderbilt.edu/Econ/jpconley/documents/classes/MBA%20405B%20L3.pdf Duffy, J. “Repeated Games.” //Lecture Notes Week 9.// University of Pittsburgh. Retrieved on March 22, 2007 from http://www.pitt.edu/~jduffy/econ1200/LectNotesWk9.pdf Powell, Robert. “Repeated Games.” //Game Theory in the Social Sciences//. University of California-Berkeley. Retrieved on March 22, 2007 from http://www.polisci.berkeley.edu/courses/coursepages/Fall2005/ps135/syllabus.pdf
 * 3. References**

1. True or false, there are two types of finitely repeated games: those with a known end and those whose end is not known? A. True B. False
 * 4. Quiz Questions**

2. Which is not a factor affecting collusion in pricing games? A. Firm size B. Punishment mechanisms C. Price of the product being sold D. History of the market

3. True or false, collusion is possible in an infinitely repeated game? A. True B. False

4. The end of the period problem affects what type of game? A. Infinitely repeated games B. Repeated games without a known end period C. Multistage games D. Repeated games with a known end period

5. Which of the following is not a real world example of collusion? A. OPEC B. Computer industry C. Airline industry D. Garbage collection industry 6. True or false, in a finitely repeated game where the end period is not known, the situation acts just like that of an infinitely repeated game? A. True B. False

7. The end of the period problem arises because? A. The two parties don’t like each other B. There is no tomorrow C. The two parties have trouble colluding D. The fact the game continues forever

8. Collusion is most likely to occur in which type of game? A. Repeated games without a known end period B. Repeated games with a known end period C. Multistage games D. Infinitely repeated game

9. True or False, Infinite repetitions of the stage stage game potentially pose a problem: a player's repeated-game payoff may be infinite. A. True B. False

10. True or False, a Repeated Game can be described as an extensive game form which consists in some number of repetitions of some base game. A. True B. False

Answers: 1. A – This is true as these are the two types of finitely repeated games. 2. C – Price of the product being sold is not a factor affecting collusion in pricing games. 3. A – This is true because the game is played forever and consequently the two participants can work together to alter the game’s outcome. 4. D – End of the period problem affects repeated games with a known final period since there is no “tomorrow”. 5. B – The computer industry is not an example of collusion. 6. A – This is true because the unknown ending time period makes this finitely repeated game function like that of an infinitely repeated game. 7. B – The fact that there is no tomorrow and therefore no punishment can be effectively administered, the end of the period problem arises. 8. D – Collusion is most likely to occur in an infinitely repeated game because the game is played forever. 9. A - This is true because the players are uncertain about exactly when the period of the game ends. 10. A - The true definition of a repeated game focuses on the repetition of a base game whereas a single stage game or single shot game focuses on a non-repeating basis.