Q4. Consider a society of n people. Everybody has access to a common meadow. Eac
ID: 1217264 • Letter: Q
Question
Q4. Consider a society of n people. Everybody has access to a common meadow. Each individual can choose either a high level of grazing on the meadow H or a low level of grazing L. If an individual chooses H, they receive a private benefit of b and impose a cost of c on each individual in society including themselves (i.e. a cost of c on individual 1, a cost of c on individual 2, etc.). If an individual chooses L, they receive a private benefit of a and impose no cost on anyone.
a. If b > a+c, what is the Nash equilibrium of this game? How about when b < a+c? Explain your reasoning. (4 marks)
b. Derive a condition under which a ban on high grazing would make everyone better off relative to the original Nash equilibrium of the game. (3 marks)
c. How does the condition in part (b) vary with the population size n? Explain the intuition behind this. (3 marks)
Explanation / Answer
Ans:
a)
If b > a+c a Nash equilibrium in an amusement happens when every player picks a methodology that gives it the most astounding result, given the systems picked by alternate players in the game.If an individual picks H, they get a private advantage of b and force an expense of c on every person in the public arena including themselves i.e. an expense of c on individual 1, an expense of c on individual 2, and so on. In the event that an individual picks L, they get a private advantage of an and force no expense on anybody.
In the event that players picked techniques that did not constitute a Nash harmony, then the players could pick another methodology that expanded their result given the systems picked by alternate players. Since players could build their settlements by picking different methodologies, systems that don't constitute a Nash balance are a far-fetched result in a diversion.
b) Condition under which a restriction on high touching would improve everybody off in respect to the first Nash harmony of the amusement whatever other system the player may take after regardless of what the other player does. A player has a commanded technique when it has different systems that give it a higher result regardless of what the other player does. A player would be unrealistic to pick a ruled technique in light of the fact that the player could simply enhance his result by picking another system paying little heed to the procedures picked by alternate players an amusement can have a Nash harmony despite the fact that neither one of the players has a predominant or ruled methodology. Truth be told, each diversion has a Nash harmony, potentially in blended techniques.
c)If players picked procedures that did not constitute a Nash concordance, then the players could pick another philosophy that extended their outcome given the frameworks picked by substitute players.Condition under which a restriction on high brushing would improve everybody off with respect to the first Nash harmony of the amusement some other technique the player may take after regardless of what the other player does. A player has an overwhelmed methodology when it has different procedures that give it a higher result regardless of what the other player does. Since players could assemble their settlements by picking distinctive techniques, frameworks that don't constitute a Nash equalization are an implausible result in a redirection.
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