Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.fictitious-play

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/fictitious_play.clj2 definitions, 3 theorems

AHoF D79 Fictitious Play: in a repeated game each player best-responds to the empirical frequency of the opponent's past actions. With two candidate actions the best response keeps the higher expected payoff and prefers action 0 when its payoff is at least action 1's: prefers-action-zero? p0 p1 = decide (p1 <= p0) best-response-value p0 p1 = if (p1 <= p0) then p0 else p1 (the larger payoff) over exact rationals. Proved native and axiom-free: the preference decision, the best-response (max) value, and the switch when action 1 pays more. Requires audit/decide-nnrat-at-most, logic/if-data (both 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.fictitious-play` prints this classification.

fictitious/prefers-action-zero? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

fictitious/best-response-value :
  (x₁ x₂ : ℚ≥0)
  → ℚ≥0

fictitious/prefers-higher-payoff :
  → bo/is-safe 3/4 1/2 = data/true

fictitious/best-response-is-larger :
  → ac-mcts/node-value 3/4 1/2 = 3/4

fictitious/switches-when-lower :
  → bo/is-safe 1/2 3/4 = data/false