Microeconomics (2nd Edition) (Pearson Series in Economics)
2nd Edition
ISBN: 9780134492049
Author: Daron Acemoglu, David Laibson, John List
Publisher: PEARSON
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Chapter 13, Problem 12Q
To determine
Factors that can cause a socially efficient outcome to occur in a sequential version of the “Prisoner’s dilemma”.
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Describe an original social dilemma you observe in the real world -- i.e. a situation in which no one has an incentive to change what they're doing, but everyone would be better off if everyone changed what they were doing. Try to create two tables to present your dilemma as a 2×2 game. Your first table should be descriptive, Your second table should be a payoff matrix showing the payoffs for both players in each of the four situations Using your payoff matrix, describe the Nash equilibrium and the mutually preferred outcome.
For the operating system game, let us assume Windows is more superior than Mac intrinsically and that network effects are stronger for Macs. These modifications are reflected in different payoffs. Now, the payoffs from adopting Windows is 30 + 10 × w and from adopting Mac is 20 × m. n consumers are simultaneously deciding between Windows and Mac, where n > 10.
(a) Is there a Nash equilibrium in which everyone buys Windows? Explain your answer.
(b) Is there a Nash equilibrium in which everyone buys Mac? Explain your answer.
(c) Is there a Nash equilibrium in which some consumers buy Windows and some consumers buy Mac? Explain your answer.
Now answer the following questions:
Perform iterative elimination of dominated strategies on the game. Draw the new table for each iteration as shown in the lecture video. Write corresponding actions at left and up of the table. Explain why are you removing each row or column. You should reach a 2*2 game. Rewrite the table separately.
From the 2*2 game you get in question 1, find a mixed strategy σ1=(p,1−p) for Player 1 that will make Player 2 indifferent about two actions.
Find a mixed strategy σ2=(q,1−q) for Player 2 that will make Player 1 indifferent about two actions.
If the players are playing the mixed strategies σ1 and σ2, they both will indifferent about their strategies, hence the strategy profile (σ1,σ2) will be a Nash Equilibrium of this game. Find the expected utility for both Player 1 u1(σ1,σ2) and Player 2 u2(σ1,σ2) at this Nash Equilibrium.
Chapter 13 Solutions
Microeconomics (2nd Edition) (Pearson Series in Economics)
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