Example of reduction in communication complexity
Assume that each player gets a number in $[n]$, and they can compute $h_n(x,y)$. Each player knows $n$, so if $h_n$ is computable with less than $log(n)$ communication, they can compute $h_n(n-x,y)$ in under $log(n)$ bits of communication. Since you have $h_n(n-x,y)=1 \iff x=y$ then you managed to compute $\delta_{x,y}$ in sub logarithmic communication, contradiction.