Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land.                                                   Farmer 2   Farmer1                                                1 cow                  2+ cows                       1 cow                             8,8                    2,10                        2+cows                           10,2                     4,4   What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off)

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land.

 

                                                Farmer 2  
Farmer1                                                1 cow                  2+ cows
                      1 cow                             8,8                    2,10
                       2+cows                           10,2                     4,4

 

  1. What kind of game is this?
  2. What is/are the Nash equilibrium/equilibria?
  3. What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off)

 

The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:

                                                                    Farmer 2
                                                 1 cow                  2+ cows
Farmer 1                     1 cow                           15,15                    2,10
                       2+cows                           10,2                     4,4

 

  1. What kind of game is this?
  2. What is/are the Nash equilibrium/equilibria?
  3. What is/are the Pareto efficient outcome(s) in this game?

Finally,

  1. What is the relationship you observe between Pareto efficiency and Nash equilibria? How do these differ across the two games?
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