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

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

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be the payoff to country with ranking i when it chooses
IN and n others have chosen IN. Let

 

be the payoff to 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?

 

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