I am interested in estimating Nash Equilibria to symmetric, continuous two-player games of the following form. Let :
$x_1$ - Player A's action
$x_2$ - Player B's action
where $x_1$, $x_2$ $\in [0,1]$ (the unit interval)
We denote the payoffs of the 2 players to be $f(x_1,x_2)$ and $-f(x_1,x_2)$ respectively.
where:
f is a known symmetric, non-convex function, ie. $f(x_1,x_2)$ = $-f(x_2,x_1)$ and is continuous almost everywhere.
Thus, the NE for both players is an unknown probability distribution over the interval, which is a 'function' of $f$.
No-regret algorithms should converge to the NE if the action space is finite, but in the above case it is continuous. Are there any general algorithms which 'converge' to the NE for games with continuous action spaces?