`market_eq_health`

proved

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module: IndisputableMonolith.CrossDomain.JEquilibriumUniversality
domain: CrossDomain
line: 42 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.JEquilibriumUniversality on GitHub at line 42.

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formal source

  39
  40/-- Universality: all three propositions are definitionally the same. -/
  41theorem nash_eq_market : NashEquilibrium = MarketEquilibrium := rfl
  42theorem market_eq_health : MarketEquilibrium = HealthEquilibrium := rfl
  43theorem all_three_equal :
  44    NashEquilibrium = MarketEquilibrium ∧
  45    MarketEquilibrium = HealthEquilibrium := ⟨rfl, rfl⟩
  46
  47/-- A perturbation of J is the same in all three domains:
  48    for any r, the cost is given by the single J-cost function. -/
  49theorem shared_sensitivity (r : ℝ) (hr : 0 < r) (hne : r ≠ 1) :
  50    Jcost r > 0 := Jcost_pos_of_ne_one r hr hne
  51
  52structure JEquilibriumUniversalityCert where
  53  nash : NashEquilibrium
  54  market : MarketEquilibrium
  55  health : HealthEquilibrium
  56  three_are_one : NashEquilibrium = MarketEquilibrium ∧
  57                  MarketEquilibrium = HealthEquilibrium
  58  shared_pert : ∀ r : ℝ, 0 < r → r ≠ 1 → Jcost r > 0
  59
  60def jEquilibriumUniversalityCert : JEquilibriumUniversalityCert where
  61  nash := nash_eq
  62  market := market_eq
  63  health := health_eq
  64  three_are_one := all_three_equal
  65  shared_pert := shared_sensitivity
  66
  67end IndisputableMonolith.CrossDomain.JEquilibriumUniversality

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