games where players form coalitions and share joint gains — the mathematical foundation for fair cooperation
solution concepts
Shapley value — the unique attribution satisfying efficiency, symmetry, null player, and additivity. each player earns their average marginal contribution across all orderings. in cyber, this distributes focus rewards proportionally to each neuron's causal impact on $\Delta\pi$
core — the set of allocations that no coalition can improve upon. a game has a non-empty core if and only if it is balanced (Bondareva-Shapley theorem). stability: no subgroup has incentive to break away
Nash bargaining — two-player cooperative solution maximizing the product of surplus gains. extends to $n$-player settings via axioms: symmetry, Pareto optimality, independence of irrelevant alternatives, invariance to affine transformations
in cyber
the cybergraph is a continuous cooperative game. neurons form implicit coalitions by contributing cyberlinks in the same epoch. the total value is the free energy reduction $\Delta\mathcal{F}$
probabilistic shapley attribution makes fair attribution tractable at scale — Monte Carlo sampling reduces $O(n!)$ to $O(k \cdot n)$, feasible for $10^6$+ transactions per epoch
implemented as an independent layer: cybernet (inspired by yuma consensus from bittensor). experimentally deployed in space pussy, with cybertensor providing CLI compatibility
see cooperation for evolutionary foundations. see learning incentives for the full reward mechanism