What does "agent" mean in Pearce's formulation of extensive form rationalizability? While reading Pearce(1984), I can't understand what "agent" $j$ and agent $ij$ mean on page 1041:


  Consequently I associate a conjecture $$ c^{ij} = (c^{ij}(1), ... ,
&gt; c^{ij}(N)) $$ 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?
I have not read this paper in full, I am merely guessing based on some parts.

It seems to me that agent $ij$ is short for "agent $j$ for player $i$".

A player's strategy assigns a move/choice of action to each information set $I^{ij}$. Depending on the story of the game you can think about this move as being executed by the player herself or maybe just agents of the player. Kind of like with subgame perfection you can assume that the strategy must fullfil some conditions in each information set $I^{ij}$. When explaining these conditions it is easier to assume that the player does not have independent but somehow 'logically restricted beliefs' in every information set, but that all her agents have 'logically restricted beliefs'. So an agent $ij$ is basically just a player's strategy in $I^{ij}$.

By 'logically restricted beliefs' I mean the restrictions posed on conjectures.