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Lecture 17

Economics 2151B - Lecture 17.docx

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Economics 2150A/B
Kristin Denniston

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Economics 2151B Monday March 12 Lecture 17 Chapter 14 Homework 4 • Chapter 14 and 15 • To be posted tonight (around midnight) • Will be due Friday March 21 (Starting with the bottom of page 7 of the notes) Repeated Gains • You will end up with a different result in the prisoner’s dilemma problem 1. You can have a gain that repeats a finite number of times OR o This will lead to different outcomes (a different Nash equilibrium) 2. The gain can repeat indefinitely into the future How does repetition affect equilibrium in the Prisoner’s Dilemma problem? • 1) Originally: o Both players played once o The players could not communicate (they could not collude) o They knew each other’s payoffs (they knew what the other player would do o  Result: a non-cooperative Nash equilibrium  Both players were worse off than if they had colluded • 2) Finite # of Repetitions: o Same result as we originally had o We can interact in the first period, and you decide if you want to cheat.  If you cheat in the first period, the other player could potentially punish you o Example: Player 1 Cheat Cooperat e Cheat 5,5 14,1 Cooperate 1,14 10,10 Player 2  If we played once, both players would cheat  If we played twice, the question is whether we should cheat or not.  Both players have a dominant strategy to cheat  After some repetition, they may see that if they both cheat, they’re worse off (so they should try to cooperate)  If both players cooperate in the first period and Player 1 wants to punish Player 2, Player 1 can cheat (both would have a dominant strategy to cheat), but they both do better if they can cooperate  If you assume the other player is still cooperating, you will try to cheat in the last period. • Each player knows the other has an incentive to cheat, so to optimize their profit they will cooperate up until the last period and then cheat in the end. o When the repetitions are finite, there will be a cheating equilibrium in all periods.  Collusion (cooperation) is not possible.  You can punish the other player by also cheating so that you both only reach the lower equilibrium • 3) Infinite # of Repetitions: o Now we can attain the cooperative equilibrium where we both make higher profits (shared monopoly/cartel equilibrium) o We don’t know when the last interaction is going to be o Two possible punishment strategies players can use to keep the other player in line: 1) Grim Trigger • Both players are cooperating as a cartel and getting the higher shared monopoly profit. One player cheats, and the other player also cheats indefinitely into the future. • Each player knows that punishment is possible into the future. If you give the player a threat that you could cheat all the way into the future, it deters the other player from cheating. • Not as good as the tit-for-tat strategy • The problem with this strategy is that you hurt yourself as well by having lower profits. 2) Tit-for-Tat • The best solution • You do what the other player did in the previous period • Allows you to cooperate again • If all of a sudden the other player decides to cheat, you would then cheat in the next period (you both end up at
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