While reading Pearce(1984), I can't understand what "agent" $j$ and agent $ij$ mean on page 1041:
Consequently I associate a conjecture $$ c^{ij} = (c^{ij}(1), ... , > c^{ij}(N)) $$ with each information set $I^{ij}$ in $\Gamma$; $c^{ij}(k)$ represents what an "agent" $j$ for player $i$ believes, once $I^{ij}$ is reached, about what player $k$'s mixed strategy is. A conjecture $c^{ij}(k)$ over a set $A^k \subseteq M^k$ can be regarded as an element of $\bar{A}^k$ (see Appendix A).
I have noted that an agent $ij$, upon being reached, should not entertain a conjecture that does not reach $I^{ij}$. A further restriction, not invoked in other solution concepts, is appropriate: if the information set can be reached without violating the rationality of any player, then the agent's conjecture must not attribute an irrational strategy to any player.
Some notations:
$I_{ij}$ is player $i$'s $j$th information set, $M_k$ is player $k$'s mixed strategy set and $\bar{A}^k$ is the convex cone of $A^k$.
So an agent is definitely different from a player, but what else can it be to form a belief?