Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.nash-equilibrium

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/nash_equilibrium.clj1 definitions, 3 theorems

AHoF D77 Nash Equilibrium (support enumeration): a strategy profile is a Nash equilibrium when no player can gain by unilaterally deviating. The per-player stability test compares the payoff of a candidate deviation against the current payoff: no-profitable-deviation? current deviation = decide (deviation <= current). When every player's every deviation is no better than the current payoff, the profile is an equilibrium. Proved native and axiom-free: the no-deviation decision, a stable profile, the native at-most stability certificate, and a profitable deviation that breaks stability. 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 3 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.nash-equilibrium` prints this classification.

nash/no-profitable-deviation? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

nash/stable-profile :
  → bo/is-safe 3/4 1/2 = data/true

nash/stability-certificate :
  → 1/2 ≤ 3/4

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