A group of 12 countries is considering whether to form a monetary union. They differ in...

 

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A group of 12 countries is considering whether to form a monetary union. They differ in their assessments of the costs and benefits of this move, but each stands to gain more from joining, and lose more from staying out, when more of the other countries choose to join. The countries are ranked in order of their liking for joining, 1 having the highest preference for joining and 12 the least. Each country has two actions, IN and OUT. Let B(i,n) = 2.2 + n-i be the payoff to a country with ranking i when it chooses IN and n others have chosen IN. Let S(in) = i-n be the payoff to a country with ranking i when it chooses OUT and n others have chosen IN. (a) Show that for country 1, IN is the dominant strategy. (b) Having eliminated OUT for country 1, show that IN becomes the dominant strategy for country 2. (c) Continuing in this way, show that all countries will choose IN. (d) Contrast the payoffs in this outcome with those where all choose OUT. How many countries are made worse off by the formation of the union? A group of 12 countries is considering whether to form a monetary union. They differ in their assessments of the costs and benefits of this move, but each stands to gain more from joining, and lose more from staying out, when more of the other countries choose to join. The countries are ranked in order of their liking for joining, 1 having the highest preference for joining and 12 the least. Each country has two actions, IN and OUT. Let B(i,n) = 2.2 + n-i be the payoff to a country with ranking i when it chooses IN and n others have chosen IN. Let S(in) = i-n be the payoff to a country with ranking i when it chooses OUT and n others have chosen IN. (a) Show that for country 1, IN is the dominant strategy. (b) Having eliminated OUT for country 1, show that IN becomes the dominant strategy for country 2. (c) Continuing in this way, show that all countries will choose IN. (d) Contrast the payoffs in this outcome with those where all choose OUT. How many countries are made worse off by the formation of the union?

Answer rating: 100% (QA)

ANSWER a For country 1 rank 1 so i1 Now the payoff for choosing IN B1 22n1 12n where n could be 0 to 11 so worst case scenerio is n0 so minimum payoff ... View the full answer