$$ \newcommand \Soft {\mathit{soft}} \newcommand \Cert {\mathit{cert}} \newcommand \Bundle {\mathrm{Bundle}} $$

New Period

When a player observes that a new period \( (r, p) \) has begun, the player sets

• \( \bar{s} := s \),

• \( s := 0 \).

Also, the player sets \( \bar{v} := v \) if the player has observed \( \Bundle(r, p-1, s, v) \) given some values \( s > \Cert \) (or \( s = \Soft \)), \( v \neq \bot \); if none exist, the player sets \( \bar{v} := \sigma(S, r, p-i) \) if it exists, where \( p-i \) was the player’s period immediately before observing the new period; and if none exist, the player does not update \( \bar{v} \).

In other words, if \( \Bundle(r, p-1, s, v) \in V’ \) for some \( v \neq \bot, s > \Cert \) or \( s = \Soft \), then

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

and otherwise, if \( \Bundle(r, p-1, s, \bot) \in V’ \) for some \( s > \Cert \) with \( \sigma(S, r, p-i) \) defined, then

$$ N((r, p-i, s, \bar{s}, V, P, \bar{v}), L, \ldots) = ((r, p, 0, s, V’, P, \sigma(S, r, p-i)), L’, \ldots); $$

and otherwise

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

for some \( i > 0 \) (where \( S = (r, p-i, s, \bar{s}, V, P, \bar{v}) \)).

⚙️ IMPLEMENTATION

New period reference implementation.