EBK MICROECONOMICS
EBK MICROECONOMICS
2nd Edition
ISBN: 8220103679701
Author: List
Publisher: YUZU
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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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Common pool resource game) Consider a common pool resource game with two appropriators. (If you don’t know what is a common pool resource, read the Wikipedia article about the ”Tragedy of the Commons”.) Each appropriator has an endowment e > 0 that can be invested in an outside activity with marginal payoff c > 0 or into the common pool resource. Let x ∈ X ⊆ [0, e] denote the player’s investment into the common pool resource (likewise, y denotes the opponent’s investment). The return from investment into the common pool resource is x x+y · ((x + y) − (x + y) 2 ). So the symmetric payoff function is given by π(x, y) = c · (e − x) + x x+y · ((x + y) − (x + y) 2 ) if x > 0 and c · e otherwise. Assume 1 − e < c < 1. Find Nash equilibrium of the game. Proceed by deriving the best response correspondences first. How does Nash equilibrium depend on parameters c and e (varying one at a time and keeping the others fixed)?
There is a city, which looks like chopped isosceles triangle, as shown below. Citizens live uniformly distributed all over the city.  Two ice-cream vendors, A and B, must independently set up stores in the city. Each citizen buys from the vendor closest to their location and when equidistant from both vendors they choose by coin toss. Each vendor’s aim is to maximize the expected number of customers. A choice of location by the two vendors is a Nash equilibrium if no vendor can do better by deviating unilaterally. Does this game have a Nash equilibrium? If so, describe it. If not, explain why not
In this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant.  The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.
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