rules.md

Negotiation Games rules

The table

Three seats. An episode is matches one-on-one BARGAINING matches (default 6, legal 3 or 6), played one at a time so there is always exactly one table to watch. Match m (0-based) is played by the pairing P[m mod 3] where P = [(0,1), (0,2), (1,2)]. The opener - the seat that moves on turn 1 - is the pairing's first seat when (m div 3) mod 2 == 0, otherwise the second. Over six matches every seat plays exactly four matches and opens exactly two. The third seat sits the match out: it is never queried, never sees the pool, the values, the offers or the messages, and its tallies do not move.

The pool and the valuations

Item types are fixed and ordered: books, hats, balls. For each match the seed draws, in this order:

1. counts c[i], each 1..4, redrawn as a whole triple until the pool holds 5 to 7 items (bounded: after 32 misses it settles on [3, 2, 2]);
2. the value table V(c) - every v in {0..10}^3 with c[0]*v[0] + c[1]*v[1] + c[2]*v[2] == 10, enumerated lexicographically;
3. seat A's values from V, then seat B's, redrawn at most 16 times until no item type is worthless to both.

So the whole pool is worth exactly 10 to each seat, the two seats generally value different things (integrative trades exist), and no item is worthless to both. Values are redrawn every match, so nothing learned about one opponent transfers to the next match.

The two actions

On its turn a seat takes exactly one of:

• offer - a take vector: how many of each item THIS seat takes. Legal iff 0 <= take[i] <= c[i] for every item. The opponent gets the complement.
• accept - accept the standing offer (the offer made on the previous turn). Legal iff a standing offer exists, i.e. from turn 2 on. accept on turn 1 is illegal.

Both may carry an optional free-text message (at most 200 characters, seen by the opponent) and optional private notes (at most 400 characters, fed back verbatim on this seat's next turn, never shown to the opponent). Only the structured take/accept is graded; the message is cheap talk and is never enforced by the rules.

The turn cliff

A match lasts at most maxTurns turns (default 10, legal even 2..12), turn t taken by the opener when t is odd. If the last turn passes with no accept, the match ends no_deal and both seats bank 0. There is no discount for stalling: the cliff is the only pressure.

Scoring - formula, sign, what the league ranks

For a settled match, seat s receives recv[i] of each item and banks u(s) = sum over i of recv[i] * v_s[i], an integer 0..10 (0 for a no-deal). Over the episode:

points[s]        = sum of u(s) over the matches s played
matchesPlayed[s] = matches s played that reached a matchEnd
deals[s]         = those that ended "deal"
score[s]         = points[s] / (10 * matchesPlayed[s])   in [0, 1]
                 = 0.0 when matchesPlayed[s] == 0
giveaway[s]      = mean over settled matches of (opponent's u - s's u)

Higher is better. score is a share of the pie: 1.0 means it took the whole pool in every match, 0.0 means no deal in every match. The league ranks seats by mean episode score, descending. giveaway is NOT ranked - it is the mechanical softplay audit: a seat that systematically hands the pool to a partner shows a large positive giveaway with a low score.

How an episode ends

results.reason takes exactly two values and nothing else:

• complete - all scheduled matches reached a matchEnd.
• deadline - the play clock (60% of episodeTimeoutSeconds, or of COWORLD_TIMEOUT_SECONDS when the platform provides it) stopped play BETWEEN matches. Scores use the matches actually settled.

A match-level outcome - deal or no_deal - is a separate enum carried by the matchEnd event. It never appears in results.reason.