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How should we define "rarity"?

Abbreviated Question: 
How should we define "rarity"?
Answer: 

In the strictest (or standard) sense of the word, you would be correct that game A is “rarer,” given that there are fewer of these in existence than game B. However, the other person is not totally wrong because, in the words of economists, the “quantity supplied” of game B is less than that of game A.