Notation idea for game theory. - It's convenient to use notation u_i(a_i, a_{-i}) for the profile with i using a_i and others using a_{-i}. - It's convenient to order players and let a=(a_1,...,a_n). - These conventions can conflict: e.g. in a symmetric game, which payoff is u_2(x,y) talking about?
So I think we should start using u_i(a_i | a_{-i}) for the first one. Then, in my example: - Payoff u_2(x,y) will mean 1 uses x and 2 uses y. - Payoff u_2(x|y) will mean 1 uses y and 2 uses x.
If there a typo? U(y|x) instead?
I don’t think so. My preferred pronunciation of u_i(x|y) is “the utility of x given y”.