U (I) = -1000 + 20i U(NV) = -80i whether all countries investing is a NE. C is a NE. Show your work. here any NE for 1 ≤ i ≤ 199 (in words, find a ries choose I and some choose NI). Explain

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200 countries decide simultaneously whether to Invest in a Navy (I) or Not (NI).
Investing is expensive, but more valuable the more other countries invest. Not
investing is particularly dangerous when many other countries invest.
Let i be the number of countries investing. The payoffs for taking the investing
(I) and not investing (NI) are given below:
U (I) = -1000 + 20i
U(NV) = -80i
(a.)
Check whether all countries investing is a NE. Check whether no
country investing is a NE. Show your work.
(b.)
Are there any NE for 1 ≤ i ≤ 199 (in words, find all Nash equilibria
where some countries choose I and some choose NI). Explain your answer and
show your work.
Transcribed Image Text:200 countries decide simultaneously whether to Invest in a Navy (I) or Not (NI). Investing is expensive, but more valuable the more other countries invest. Not investing is particularly dangerous when many other countries invest. Let i be the number of countries investing. The payoffs for taking the investing (I) and not investing (NI) are given below: U (I) = -1000 + 20i U(NV) = -80i (a.) Check whether all countries investing is a NE. Check whether no country investing is a NE. Show your work. (b.) Are there any NE for 1 ≤ i ≤ 199 (in words, find all Nash equilibria where some countries choose I and some choose NI). Explain your answer and show your work.
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