In Facebook, and in Xiaonei. People sometimes do a survey game(Chinese is a popular点名游戏) something like this
Rules: Once you’ve been tagged, you are supposed to write a note with answering the following 10 questions. Change one of those question into a question you want to ask, and tag 10 other people, so they will do a survey with your question.
1. Who is your favorite person
....
Why 10? why only change 1 question, why tag 10 other people? Can these number be something else that's BETTER?
First we have to think of a criteria for a good game
1. The person who just answered a survey, might get tagged by someone else, and it would suck if most question are the same.
2. Each person wants to maximize the amount of people answer his own questions.
Suppose the probability of not having to do the same question is P, and the expected amount of people to answer someone's question is R.
The larger the RP the better.
Suppose there are n survey questions each survey. Each time one answer the survey can remove m problems and add m of their own. The removal of problem is completely random. and no one will ever propose the same problem as someone else. Then each person have to name k people randomly from their friends to do their survey.
Now, if there are y people, each have f friends(a is b's friend means b is a's friend). What n,k,m will maximize RP?
This helps to form a more scientific survey game.
We can add further restrictions later.
It sucks as for a y, some f is not possible.
Hell. I'm still stuck in the first part.
How many distinct graphs can have y vertexes and f edges each. and what is probability to come up with a specific graph?
Fun. going to think more about it.
and I lied about not posting before leave China.
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