coalitionPayoff
plain-language theorem explainer
Coalition cooperation payoff is defined as (n + 1/φ) times the defection baseline payoff π_def. Game theorists citing Recognition Science element 84 on cooperation from σ-conservation reference this scaling when comparing coalition outcomes to pure defection. The definition is a direct one-line algebraic combination of coalition size with the upstream cooperation dividend.
Claim. The payoff for a coalition of $n$ cooperating agents with defection baseline payoff $π_def$ is $(n + 1/φ) π_def$.
background
In the Recognition Science framework, game-theoretic equilibria are J-cost minima on the multi-agent ledger. The module shows that cooperation arises from σ-conservation: mutual cooperation carries σ = +1, mutual defection carries σ = -1 and is the unique non-conservative outcome in the 2x2 normal form. The upstream cooperationDividend definition supplies the additive term 1/φ ≈ 0.618, the canonical coordination bonus predicted by the self-similar fixed point phi.
proof idea
Direct definition that multiplies the scaled coalition size by the defection payoff, substituting the upstream cooperationDividend constant 1/φ.
why it matters
This supplies the explicit payoff expression required by the GameTheoryCert structure and the game_theory_one_statement theorem, which together certify the four claims of element 84. It realizes the coordination dividend n · π_coop = (n + 1/φ) · π_def stated in the module doc, where the factor 1/φ traces to the phi fixed point (T6). The immediate parents are coalition_strictly_better (which proves the strict inequality) and GameTheoryCert.
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