# Thread: Game Theory Exercise! Help???

1. ## Game Theory Exercise! Help???

Consider the following guessing game. There are 100 participants, and each participant announces independently and simultaneously a number between 0 and 100 (only integer). There is a fee of 1! to participate to the guessing game, to be redistributed as a prize of 100 ! to the winner. The participant who guessed closest to a target won the prize.
a. Suppose the target is one half of the average guess, would you participate to this game? Explain why.
b. Suppose the target is one half of the average guess, what would be your best guess? Explain briefly
c. What is the Nash equilibrium of the game? Compare to your answer in part (b).

2. ## Re: Game Theory Exercise! Help???

Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

3. ## Re: Game Theory Exercise! Help???

Sorry!!! I didn't seen the forum rules!!!

Can be that my best guess will be 0 since there is the maximum probability to reach the average and, if I win, I'll get 99? So yes, I would participate?
If yes, what about the Nash equilibrium?

4. ## Re: Game Theory Exercise! Help???

It's been a long time since I've had a game theory course (for reference, I can't remember what Nash equilibrium is).

But if there were only 2 participants (me and 1 other person), then the person who guessed/shouted out a number the lowest would win. Because the target is one-half of the average. So both participants should guess 0, in which case they'd split the pot (of 2 !'s) and get all their money back. So no gain, no loss. I'm not sure if that means I should participate or not. As long as I shout 0, I won't lose any !.

Now if there were 3 participants...

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