strategic-play

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## Strategic play (game theory)

A facet of Play: the strategic layer beneath the prose. Each consequential beat is a **decision** the engine deconstructs and scores; the scores drive ELO and the player archetypes. Purely additive — written to `scene.gameAnalysis`, never mutating the force deltas.

**Decision** — A consequential beat, sealed and scored. Two kinds:

- **Duel** (2-player) — a strategic game against another agent. A full NxM matrix: each player picks from a menu, every pairing is a cell with both players' stake deltas.
- **Solo** (1-player) — a pivotal choice against the world, reality in the other seat. A *row*, not a matrix: one decider, a menu of options, one immediate stake delta per option (take the job, hold or fold, relocate, confess now or wait).

**Decision Matrix** — The per-scene sequence of decisions. Each carries an **action axis** and (for duels) a **game shape**, with integer **stake deltas** per cell. Also called **incentive structures** — the same artifact.

**Stake delta** — An integer in `[-4, +4]` scoring how much an outcome advances (+) or harms (−) a player's arc-level interests. *Magnitude is importance*: a pivotal beat uses the full ±4, a quiet beat stays ±1. Scored honestly per cell — never warped to justify what happened; a dominated cell landing as realized is signal.

**Action axis** — The dimension a decision trades on; both players' actions live on the SAME axis. Eleven: information, identity, trust, alliance, status, pressure, stakes, resources, obligation, commitment, timing.

**Game shape** — The strategic frame of a duel — one of sixteen: coordination, stag-hunt, dilemma, chicken, divergence, zero-sum, signaling, screening, principal-agent, stealth, stackelberg, bargaining, commitment-game, contest, collective-action, trivial. Solo decisions have no shape.

**Nash equilibrium** — A cell no player can improve on by switching alone. For a solo decision, the stake-maximising option (the rational pick against an indifferent world). **Realized cell** — what actually happened; landing off-Nash is signal (arc, identity, or principle over local stake), not error.

**Arc cost** — Stake a player left on the table: the best outcome available to them minus the realized one. For a solo decision, regret against the best option.

**Stake rank** — Where the realized cell sits in a player's preference order over the whole grid (1 = best).

**ELO** — Continuous skill rating per player, updated each decision. `ELO_INITIAL = 1500`, `ELO_K = 32`. The **margin score** folds margin-of-victory into the update — duel: `clamp(0.5 + (ΔA − ΔB)/16, 0, 1)`; solo: `clamp(0.5 + ΔA/8, 0, 1)` against **par** (reality, a fixed non-learning opponent at 1500, `ELO_PAR`). K is **stake-weighted** so high-stake beats move ratings far more than low-stake ones. The player archetypes fall out of the trajectory plus the outcome mix.

### Player archetypes

The behavioural tags a player earns from their decision record. Tag `id` matches its `label` (kebab-case) for consistency. Grouped:

- **Role** (one headline): *prime mover* (drives the game; the world bends toward them), *adversary* (dominates at others' expense), *tragic figure* (absorbs cost, declines anyway), *mentor* (gives more stake than they take), *comeback* (arc climbs from below), *slipping* (loses ground across the window), *trickster* (wins the information game, high variance), *counterforce* (exists to push against another's motion), *anchor* (stable, cooperative, near-baseline).
- **Relational outcome** (how realized cells split): *extractor* (gains at the other's expense), *sacrificial* (pays so others gain), *scorched-earth* (lands in both-lose cells), *uneven ally* (cooperates but takes the bigger slice), *ally* (genuine even cooperation).
- **Trajectory**: *dominant* (lands near the top of every grid), *rising* / *falling* (rating climbed / eroded), *high-variance* (wins big, loses big), *steady* (rating barely moves).
- **Solo decision style**: *soloist* (most calls are 1-player bets against the world), *sure-handed* (usually takes the stake-maximising option), *gambler* (passes up the safe-best, plays for the upside).
- **Strategic style**: *defies the odds* (keeps winning moments rational play says they shouldn't — the prime-mover signature), *strategist* (overwhelmingly plays the Nash move and it pays), *off-script* (rarely plays the rational move).
- **Agency** (from game-shape participation): *schemer* (wins information-asymmetric games), *power-broker* (sets the terms — first mover in commitment / bargaining), *combatant* (lives in zero-sum / chicken / divergence), *coordinator* (builds shared action in alignment games).
- **Arc shift**: *upward arc* / *downward arc* (late outcomes substantially better / worse than early).
- **Relationships**: *rival: X* (losing record concentrated against X), *leads: X* (winning record against X).
- **Role bias**: *initiator* (almost always the prime mover / Player A), *responder* (almost always reacting / Player B).
- **Affinity**: *axis: X* (characteristic action axis), *X-heavy* (characteristic game shape).

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