Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.correlated-equilibrium

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/correlated_equilibrium.clj1 definitions, 4 theorems

AHoF D78 Correlated Equilibrium: a distribution over joint action profiles from which no player has an incentive to deviate from the mediator's recommendation; the per-player adherence test compares a deviation payoff against the recommended one: follows-recommendation? recommended deviation = decide (deviation <= recommended). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.correlated-equilibrium` prints this classification.

correlated/follows-recommendation? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

correlated/adheres-to-recommendation :
  → bo/is-safe 3/4 1/2 = data/true

correlated/boundary-adheres :
  → bo/is-safe 1/2 1/2 = data/true

correlated/adherence-certificate :
  → 1/2 ≤ 3/4

correlated/profitable-deviation-breaks :
  → bo/is-safe 1/2 3/4 = data/false