Rationalizable action profiles in nice symmetric games
Isn't the mixed extension of matching pennies a good example of this? The strategies $p,q$ are both elements of $[0,1]$, and
$$
\begin{align*}
U_1(p,q) &amp; = pq + (1-p)(1-q) \\
\\
U_2(p,q) &amp; = p(1-q) + (1-p)q.
\end{align*}
$$
There is a unique Nash-equilibrium at $p = q = 1/2$ but all $p$ and all $q$ are rationalizable, because in the equilibrium all strategies are best responses.



Even if you were to edit your definition of symmetry to include symmetric utility functions, a game with
$$
U(p,q) = -(1/2 - p)^2 \cdot (1/2 - q)^2
$$
yields the same result.



If you insist on some shrinkage one could easily edit the utility function to
$$
U(p,q) = - 1 \text{ if } p+q \leq 6/10. 
$$
Then some strategies - the ones under $1/10$ - would not be rationalizable.