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Recently, I have been feeling deeply depressed—because of both my relationships and my research. I feel terrible about myself. Why can’t I handle things better? Why do I suffer every day? Why can’t I make progress in my research? Why can’t I solve the problems in microeconomics when I consider myself a theorist?
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In the winter of 2025, I took my first Game Theory course. However, some of the topics were quite obscure, and due to time constraints, I didn’t fully grasp them. In particular, Perfect Bayesian Nash Equilibrium involves a belief system. For future reference, I will write rigorous notes on this topic during my first year.
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Now consider the following problem: If each box of a given product contains a coupon, and there are $n$ different types of coupons, what is the expected number of boxes that you have to buy in order to collect all types of coupons?
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Yesterday I found a very interesting problem. It states: