I'm a little confused with the work I am currently doing in Game Theory.
Here is the questions I'm working on:
1) Suppose we modify the $p$-Beauty contest by requiring every guess to be an integer. What are all of the Nash equilibria? Why?
2) The $1$-Beauty contest is the $p$-Beauty contest with $p = 1$, i.e., a winner is anyone who chooses a number that’s closest to the average of all the choices. What are all of the Nash equilibria? Why?
I don't understand how these change anything. The Nash equilibrium of the $p$-Beauty contest is $0$. Requiring every guess to be an integer shouldn't change anything correct? The nash equlibria would just be $\{ 0 \}$?
How does changing the $P$ to equal $1$ change this? $1\times 0$ is still $0$. So would the nash equilibria stay as $0$? I feel like it should change, but I don't understand how. I feel like it could be any number
In the $p$-beauty contest game (Moulin $1986$), all participants are asked to simultaneously pick a number between $0$ and $100$. The winner of the contest is the person(s) whose number is closest to $p$ times the average of all numbers submitted, where $p$ is some fraction, typically $\frac23$ or $\frac12$.