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Chapter 15

# ECON 1050 Chapter 15: Econ 1050 Chapter 15 Premium

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Economics
Course
ECON 1050
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Fall

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Chapter 15 (344-350) “Oligopoly price fixing game” Oligopoly Games  Economist think about oligopoly as a game between a few players, and to study oligopoly markets they use game theory.  Game Theory- is a set of tools for studying strategic behavior- behavior that takes into account the expected behavior of others and the recognition of mutual interdependence. The Prisoners Dilemma  Art and Bob are caught red-handed stealing a car. Facing airtight cases, they will receive a sentence of two years each for their crime.  During interviews with the two prisoners, the Crown attorney believes and suspects that they were involved in a multi million dollar bank robbery, but this is suspicion.  So he will make the prisoners play a game. 4 parts of a game  Rules o Each prisoner will be placed in separate room and cannot communicate with the other prisoner. Each are told that they are suspected of robbing the car.  If they both confess to the larger crime, they will receive a sentence of 3 years.  If he alone confesses and his accomplice does not, he will receive only a 1-year sentence while the accomplice receives 10.  Strategies o Strategies are all possible actions of each player. o 2 strategies  Confess to the bank robbery  Deny having committed the bank robbery. o Since there are 2 players there is 4 possible outcomes.  Both confess  Both Deny  Art confesses, and bob denies  Bob confesses, Art Denies  Payoffs o Each prisoner can work his payoff in each of these possible situations, and we can tabulate the four possible payoffs for each of the prisoners in what is called a payoff matrix for the game. o Payoff Matrix- is a table that shows the payoffs for every possible action by each player for every possible action by each other player. o Table 15.1 shows the Payoff Matrix between Art and Bob  Outcome o The choices of both players determine the outcome of the game. To predict the outcome we use an equilibrium idea proposed by John Nash of Princeton University. o Nash Equilibrium- Player A takes the best possible action Given the action of player B and Player B takes the best possible action given the action of player A. o In this case Nash equilibrium occurs when Art makes the best choice given Bobs choice, and when Bob makes the best choice given Art’s choice.  Finding Nash Equilibrium o Ex- Look at situation from arts view, if Bob confesses, arts best action is to confess also because its 3 years rather than 10. o If bob denies, art should confess because its one year rather than 2. o Now Bobs situation- If art confesses, bob should also confess. o If art denies, bob should confess since he will only serve one year. o Dominant-Strategy equilibrium- is an equilibrium in which the best strategy of each player is to cheat (confess) regardless of the strategy of the other player.  The dilemma- arises as each prisoner contemplates the consequences of his decision and puts himself in the place of his accomplice, but each also know that if he denies it is in the best interest of the other to confess.  Each consider to deny and rely on his accomplice to deny or to confess hoping that his accomplice denies but expecting him to confess. The dilemma leads to the equilibrium of the game.  A bad outcome- For prisoners, the equilibrium of the game, with each confessing is not the best outcome. If neither of them confesses, each only get 2 years for the lesser of crime. There is no better situation since the players cannot communicate with each other.  Each know if they deny they will serve only 2 years, but that’s not the best outcome and they must trust each other to deny. This causes a dilemma. An Oligopoly Price-Fixing Game o We can use this game theory and a game like the prisoners dilemma to understand price fixing, price wars and other aspects of firms in the oligopoly. o We study the specifi
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