What is the difference between the following formualas of the expected payoff $G$?
$$G_i(q|t_i)=\sum_{t_{-i}}p(t_{-i}|t_i)\sum_{a}q(a|t_{i},t_{-i})g_i((t_{i},t_{-i}),a)$$
and
$$G_i(q|t_i)=\sum_{t_{-i},a}p(t_{-i}|t_i)q(a|t_{i},t_{-i})g_i((t_{i},t_{-i}),a)$$
where $t_i$ is the type (or signal) of player $i$, $a=(a_i,a_{-i})$ the profile of actions and $g_i$ is the utility function