The Game of Peers: Toward a Credential Algebra for Human-AI Actor Networks

This paper develops a formal credential algebra for human-AI actor networks, in which human and AI actors participate as structural peers with independent credential sets combined via four set-algebraic operators (intersection, union, left join, right join) on the edges of a directed actor graph. A game-theoretic layer governs strategic disclosure and coalition formation via Shapley value attribution, and a VCG mechanism elicits truthful credential disclosure. Four worked examples in the finance domain demonstrate the framework, including a six-actor cross-border stress test using all four operators. A signature result: an actor with an intersection edge can have negative Shapley marginal contribution to a coalition — a "destructive intermediary" phenomenon invisible to classical delegation models, which assume monotonic restriction. The framework provides the algebraic theory that protocols such as Authenticated Workflows and zero-trust identity frameworks currently lack, and applies generally to any domain where discrete, combinable attributes propagate over actor networks with strategic disclosure.