May 6th: We added one caution to the first page of PS1. If you form a group, please include all the members in CC (not BCC) when you submit your answer. Also, please set the name of the PDF file as "(Sender's ID)_PS1.pdf" (like "29-24XXXX_PS1.pdf").

May 4th: This is a clarification about 3.3.(c) which stands for 3.(c) in Question 3. The correspondence C in 3.3.(c) is the same as the one defined in 3.2. Namely, C in 3.3.(c) is defined on all nonempty subsets of X and a nonempty-valued correspondence. Additionally, C(B) is a subset of B. You can assume these properties in 3.3.(c). 

May 2nd: We have made additional clarifications to the confusing problem statements in Question 1 and 4. The revised version PS1_ver2 was posted.

June 12th: PS3_ver3 was posted. The definition of Irreversibility in the Question 3 was wrong. Sorry for the inconvenience.

June 12th: PS3_ver2 was posted. Regarding the Question 1 in the PS3, we have added an assumption that the utility function is continuous.