$$ \newcommand \Vote {\mathrm{Vote}} $$

Garbage Collection

When a player observes that either a new round or a new period \( (r, p) \) has begun, then the player garbage-collects old state.

In other words,

$$ N((r-i, p-i, s, \bar{s}, V, P, \bar{v}), L, \ldots) = ((r, p, \bar{s}, 0, V’ \setminus V^\ast_{r, p}, P’ \setminus P^\ast_{r, p}, \bar{v}), L, \ldots) $$

where

$$ \begin{aligned} V^\ast_{r, p} &= \{\Vote(I, r’, p’, \bar{s}, v) | \Vote \in V, r’ < r\} \\\ &\cup \{\Vote(I, r’, p’, \bar{s}, v) | \Vote \in V, r’ = r, p’ + 1 < p\} \end{aligned} $$

and \( P^\ast_{r, p} \) is defined similarly.