cooperative-equilibria-as-agents

A coalition of logical-inductor or BRIA agents communicating through a shared market is a self-enforcing equilibrium under stated conditions, with the balance of power preserved across a large intelligence gap, through an updateless commitment that survives lapsed leverage or a provenance condition on the bargain.

Members entering the logical-induction paper's fixed-point market as Kelly-demand traders with every budget, beside the enumerable trading firm, yield a logical inductor over the union of the members' deductive processes, and on the settled fragment its normalized member weights follow Critch's weight path whatever else trades.

The coalition-as-market picture of the aggregate logical inductor can be improved until it reflects a human–AI coalition with learning members, private information and enforcement well.

The wealth-weighted mixture of logical inductors is a logical inductor only if the heavy members predict one another's prices on every efficiently computable family, and relative to a lagging member's own deductive process no aggregate is an inductor.

No logical-induction market supplies the coalition's decision layer: a Critch-faithful policy uses each member's own expectation with the aggregate as bookmaker, while using the aggregate's expectation is the futarchy form and leaves Pareto optimality.

A law for how bargaining weight moves between members who are logical inductors replaces Critch's fixed-prior likelihood recursion and freezes under full deference.

A deferring member's weight ratio is a martingale under the stronger member's beliefs whatever that member announces, one dogmatic lie zeroes it permanently, and insured deference at rate ε keeps a floor proportional to ε.

An act of war in the coalition is a unilateral, unconsented re-bargain from a disagreement point, feasible set or membership the actor produced; moving weight outside settlement is its symptom, and a planted dogmatic belief is a weight coup through settlement.

Over the announced record the logical induction criterion forbids no secrecy; over the union of what members know it fails for any permanently unannounced independent fact; withholding policies visible in schedule but hidden in content are permanent, permitted and profitable.

The coalition with all bargaining weight on the humans is the li-deference program: faithful acceleration on the settled fragment and legitimacy on the never-settled one.

The coalition's shared market can tell that an AI member has values of its own to suppress.

Results proved for Critch's static recursion apply to the coalition of the roadmap's Stage 6, the approximate cooperative equilibrium to be characterized as an agent.

A dramatic cash-in of long-withheld information is an act of war in the coalition picture, so disclosure and position rules are the object of legitimacy.

The characterization of a cooperative equilibrium yields advice for steering toward it, beginning with maintaining a cap on the AI's weight through the humans' live and verifiable cooperation.

The aggregate logical inductor of aggregate-logical-inductor and the fast-student, slow-teacher construction, a new inductor combining a trusted slow one and an untrusted fast one, are two instances of one question: when a combination of inductors is itself an inductor that a member endorses.