From b1fcf9859c0a4ff3232c17356ea3e2284347b33b Mon Sep 17 00:00:00 2001 From: jsboige Date: Sun, 4 Oct 2026 08:00:22 +0200 Subject: [PATCH 1/2] fix(notebook-python,#18874): GameTheory-15c -- argumentation figee sortie des print() P1 de #18874 (1 notebook sur les 364 recenses). Trois cellules code portaient de l'argumentation statique dans des print() au lieu du markdown, et la preuve du Core vide y etait recopiee en dur alors que le markdown suivant la porte deja. - cell[8] : retire les 3 prints d'interpretation figee (le tableau markdown adjacent dit la meme chose) ; garde les valeurs calculees et le total. - cell[17] : la preuve statique devient une VERIFICATION CALCULEE sur la fonction caracteristique (v(N), somme des v(S) sur les paires, contradiction 2 < 3). Le recit de la preuve reste en markdown (cell[18]). - cell[19] : retire les 2 prints de note figee ; garde la verification chiffree du blocage que la prose suivante cite explicitement. - cell[20] : prose realignee -- elle citait la ligne de print retiree. Re-verification de l'audit (protocole audit-reassessment) : le compte ne reproduit pas -- 2 cellules degen mesurees pour 4 annoncees ; la cellule source du ticket porte 3 prints et non 9 ; le chemin cite par l'issue (sans le 'c' de 15c) n'existe pas dans l'arbre. La substance designee est reelle et corrigee ; le faux positif de comptage est rapporte sur l'issue, pas propage. Re-execution complete (C.2) : papermill, kernel coursia-ml-training, 21 cellules code, 0 execution_count nul, 0 sortie vide, 0 erreur. Controles : source-parses 0 finding, check_c2_compliance 1/1 conforme, interp-positioning 0 finding, C.1 0 occurrence. metadata.papermill normalise au basename (2 chemins machine). See #18874 Co-Authored-By: Claude Sonnet 5.5 --- ...meTheory-15c-CooperativeGames-Python.ipynb | 669 ++++++++++-------- 1 file changed, 359 insertions(+), 310 deletions(-) diff --git a/MyIA.AI.Notebooks/GameTheory/GameTheory-15c-CooperativeGames-Python.ipynb b/MyIA.AI.Notebooks/GameTheory/GameTheory-15c-CooperativeGames-Python.ipynb index cf595ad94d..392926099f 100644 --- a/MyIA.AI.Notebooks/GameTheory/GameTheory-15c-CooperativeGames-Python.ipynb +++ b/MyIA.AI.Notebooks/GameTheory/GameTheory-15c-CooperativeGames-Python.ipynb @@ -5,10 +5,10 @@ "id": "8d2d1c46", "metadata": { "papermill": { - "duration": 0.010736, - "end_time": "2026-08-23T16:04:25.298838+00:00", + "duration": 0.00458, + "end_time": "2026-10-04T05:59:17.984820+00:00", "exception": false, - "start_time": "2026-08-23T16:04:25.288102+00:00", + "start_time": "2026-10-04T05:59:17.980240+00:00", "status": "completed" }, "tags": [] @@ -57,16 +57,16 @@ "id": "65dc3847", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:25.318738Z", - "iopub.status.busy": "2026-08-23T16:04:25.318738Z", - "iopub.status.idle": "2026-08-23T16:04:29.233677Z", - "shell.execute_reply": "2026-08-23T16:04:29.232670Z" + "iopub.execute_input": "2026-10-04T05:59:17.994541Z", + "iopub.status.busy": "2026-10-04T05:59:17.994541Z", + "iopub.status.idle": "2026-10-04T05:59:20.846125Z", + "shell.execute_reply": "2026-10-04T05:59:20.845448Z" }, "papermill": { - "duration": 3.926787, - "end_time": "2026-08-23T16:04:29.235389+00:00", + "duration": 2.857608, + "end_time": "2026-10-04T05:59:20.847705+00:00", "exception": false, - "start_time": "2026-08-23T16:04:25.308602+00:00", + "start_time": "2026-10-04T05:59:17.990097+00:00", "status": "completed" }, "tags": [] @@ -96,10 +96,10 @@ "id": "11c24553", "metadata": { "papermill": { - "duration": 0.008414, - "end_time": "2026-08-23T16:04:29.253675+00:00", + "duration": 0.003475, + "end_time": "2026-10-04T05:59:20.855407+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.245261+00:00", + "start_time": "2026-10-04T05:59:20.851932+00:00", "status": "completed" }, "tags": [] @@ -120,16 +120,16 @@ "id": "46862ef1", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.268997Z", - "iopub.status.busy": "2026-08-23T16:04:29.267999Z", - "iopub.status.idle": "2026-08-23T16:04:29.276345Z", - "shell.execute_reply": "2026-08-23T16:04:29.275339Z" + "iopub.execute_input": "2026-10-04T05:59:20.863413Z", + "iopub.status.busy": "2026-10-04T05:59:20.863413Z", + "iopub.status.idle": "2026-10-04T05:59:20.868949Z", + "shell.execute_reply": "2026-10-04T05:59:20.868439Z" }, "papermill": { - "duration": 0.018367, - "end_time": "2026-08-23T16:04:29.278052+00:00", + "duration": 0.011277, + "end_time": "2026-10-04T05:59:20.870060+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.259685+00:00", + "start_time": "2026-10-04T05:59:20.858783+00:00", "status": "completed" }, "tags": [] @@ -171,7 +171,16 @@ { "cell_type": "markdown", "id": "23ef45a6", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.003432, + "end_time": "2026-10-04T05:59:20.877125+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:20.873693+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lecture de la sortie — l'instrument s'installe avant de jouer.** La ligne « Fonction shapley_value_exact definie. » n'affiche aucun resultat : la cellule pose l'outil, pas encore son usage. Ce que le contrat installe : le calcul exact par enumeration des n! permutations (chaque ordre d'arrivee des joueurs, contribution marginale moyenne), exact au sens ou aucune variance de sondage ne s'y glisse — a la difference des estimations Monte Carlo qu'on rencontre dans d'autres series du depot. La section suivante l'appliquera aussitot au jeu de gants : la premiere valeur chiffree viendra de la, pas d'ici.\n" ] @@ -181,10 +190,10 @@ "id": "c1c7ec32", "metadata": { "papermill": { - "duration": 0.005768, - "end_time": "2026-08-23T16:04:29.289787+00:00", + "duration": 0.003333, + "end_time": "2026-10-04T05:59:20.883802+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.284019+00:00", + "start_time": "2026-10-04T05:59:20.880469+00:00", "status": "completed" }, "tags": [] @@ -203,16 +212,16 @@ "id": "52c83b97", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.305570Z", - "iopub.status.busy": "2026-08-23T16:04:29.304571Z", - "iopub.status.idle": "2026-08-23T16:04:29.314691Z", - "shell.execute_reply": "2026-08-23T16:04:29.313682Z" + "iopub.execute_input": "2026-10-04T05:59:20.891596Z", + "iopub.status.busy": "2026-10-04T05:59:20.891596Z", + "iopub.status.idle": "2026-10-04T05:59:20.897159Z", + "shell.execute_reply": "2026-10-04T05:59:20.896642Z" }, "papermill": { - "duration": 0.019987, - "end_time": "2026-08-23T16:04:29.316215+00:00", + "duration": 0.010949, + "end_time": "2026-10-04T05:59:20.898052+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.296228+00:00", + "start_time": "2026-10-04T05:59:20.887103+00:00", "status": "completed" }, "tags": [] @@ -267,10 +276,10 @@ "id": "ebcebb55", "metadata": { "papermill": { - "duration": 0.00622, - "end_time": "2026-08-23T16:04:29.328497+00:00", + "duration": 0.003427, + "end_time": "2026-10-04T05:59:20.905575+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.322277+00:00", + "start_time": "2026-10-04T05:59:20.902148+00:00", "status": "completed" }, "tags": [] @@ -296,16 +305,16 @@ "id": "69170cd4", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.343571Z", - "iopub.status.busy": "2026-08-23T16:04:29.342566Z", - "iopub.status.idle": "2026-08-23T16:04:29.351557Z", - "shell.execute_reply": "2026-08-23T16:04:29.350549Z" + "iopub.execute_input": "2026-10-04T05:59:20.913400Z", + "iopub.status.busy": "2026-10-04T05:59:20.912781Z", + "iopub.status.idle": "2026-10-04T05:59:20.917530Z", + "shell.execute_reply": "2026-10-04T05:59:20.917023Z" }, "papermill": { - "duration": 0.018411, - "end_time": "2026-08-23T16:04:29.353821+00:00", + "duration": 0.009835, + "end_time": "2026-10-04T05:59:20.918907+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.335410+00:00", + "start_time": "2026-10-04T05:59:20.909072+00:00", "status": "completed" }, "tags": [] @@ -321,11 +330,7 @@ " L2 (gant gauche): 0.1667 = 1/6\n", " R1 (gant droit): 0.6667 = 4/6\n", "\n", - "Total : 1.0000 (= v(N) = 1)\n", - "\n", - "Interpretation :\n", - " - R1 (gant droit) a une valeur de 2/3 car il possede la ressource rare\n", - " - L1 et L2 se partagent 1/3 car ils sont en competition\n" + "Total : 1.0000 (= v(N) = 1)\n" ] } ], @@ -338,11 +343,7 @@ "for i, (label, val) in enumerate(zip(labels, shapley_glove)):\n", " print(f\" {label}: {val:.4f} = {int(val*6)}/6\")\n", "\n", - "print(f\"\\nTotal : {sum(shapley_glove):.4f} (= v(N) = 1)\")\n", - "\n", - "print(\"\\nInterpretation :\")\n", - "print(\" - R1 (gant droit) a une valeur de 2/3 car il possede la ressource rare\")\n", - "print(\" - L1 et L2 se partagent 1/3 car ils sont en competition\")" + "print(f\"\\nTotal : {sum(shapley_glove):.4f} (= v(N) = 1)\")" ] }, { @@ -350,10 +351,10 @@ "id": "ee963af9", "metadata": { "papermill": { - "duration": 0.007269, - "end_time": "2026-08-23T16:04:29.368257+00:00", + "duration": 0.003979, + "end_time": "2026-10-04T05:59:20.926909+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.360988+00:00", + "start_time": "2026-10-04T05:59:20.922930+00:00", "status": "completed" }, "tags": [] @@ -381,10 +382,10 @@ "id": "ex-glove-extended-md", "metadata": { "papermill": { - "duration": 0.007398, - "end_time": "2026-08-23T16:04:29.382757+00:00", + "duration": 0.003838, + "end_time": "2026-10-04T05:59:20.934974+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.375359+00:00", + "start_time": "2026-10-04T05:59:20.931136+00:00", "status": "completed" }, "tags": [] @@ -408,16 +409,16 @@ "id": "ex-glove-extended-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.401406Z", - "iopub.status.busy": "2026-08-23T16:04:29.401406Z", - "iopub.status.idle": "2026-08-23T16:04:29.410368Z", - "shell.execute_reply": "2026-08-23T16:04:29.409164Z" + "iopub.execute_input": "2026-10-04T05:59:20.942430Z", + "iopub.status.busy": "2026-10-04T05:59:20.942430Z", + "iopub.status.idle": "2026-10-04T05:59:20.947518Z", + "shell.execute_reply": "2026-10-04T05:59:20.947518Z" }, "papermill": { - "duration": 0.020031, - "end_time": "2026-08-23T16:04:29.412324+00:00", + "duration": 0.010768, + "end_time": "2026-10-04T05:59:20.949317+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.392293+00:00", + "start_time": "2026-10-04T05:59:20.938549+00:00", "status": "completed" }, "tags": [] @@ -460,7 +461,16 @@ { "cell_type": "markdown", "id": "d260abdb", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.003993, + "end_time": "2026-10-04T05:59:20.957106+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:20.953113+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lire la sortie d'un exercice non rempli.** « Exercice a completer » avec `Total: 0.0000` : le squelette `exercice_shapley_glove_etendu` rend l'etat vide, la ligne Total etant le format d'affichage attendu, pas un resultat. Le contrat, pose par l'enonce ci-dessus : etendre le jeu de gants de 3 a 4 joueurs (deux gants gauches L1, L2, deux droits R1, R2 selon le meme schema de gains) et recalculer les valeurs de Shapley exactes. La sortie remplie affichera quatre allocations sommant a v(N), et la question interessante de lecture : la rarete change-t-elle de camp quand les deux cotes passent a deux detenteurs ? L'indice de l'enonce oriente sans reveler.\n" ] @@ -471,16 +481,16 @@ "id": "443631a2", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.429655Z", - "iopub.status.busy": "2026-08-23T16:04:29.429095Z", - "iopub.status.idle": "2026-08-23T16:04:29.793061Z", - "shell.execute_reply": "2026-08-23T16:04:29.792054Z" + "iopub.execute_input": "2026-10-04T05:59:20.965534Z", + "iopub.status.busy": "2026-10-04T05:59:20.965534Z", + "iopub.status.idle": "2026-10-04T05:59:21.268777Z", + "shell.execute_reply": "2026-10-04T05:59:21.268777Z" }, "papermill": { - "duration": 0.374773, - "end_time": "2026-08-23T16:04:29.794323+00:00", + "duration": 0.309085, + "end_time": "2026-10-04T05:59:21.269985+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.419550+00:00", + "start_time": "2026-10-04T05:59:20.960900+00:00", "status": "completed" }, "tags": [] @@ -488,7 +498,7 @@ "outputs": [ { "data": { - "image/png": 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", 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" ] @@ -526,10 +536,10 @@ "id": "6e56fe89", "metadata": { "papermill": { - "duration": 0.008323, - "end_time": "2026-08-23T16:04:29.810373+00:00", + "duration": 0.003695, + "end_time": "2026-10-04T05:59:21.277705+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.802050+00:00", + "start_time": "2026-10-04T05:59:21.274010+00:00", "status": "completed" }, "tags": [] @@ -548,16 +558,16 @@ "id": "7a8740a6", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.826466Z", - "iopub.status.busy": "2026-08-23T16:04:29.826466Z", - "iopub.status.idle": "2026-08-23T16:04:29.835606Z", - "shell.execute_reply": "2026-08-23T16:04:29.834599Z" + "iopub.execute_input": "2026-10-04T05:59:21.284556Z", + "iopub.status.busy": "2026-10-04T05:59:21.284556Z", + "iopub.status.idle": "2026-10-04T05:59:21.289266Z", + "shell.execute_reply": "2026-10-04T05:59:21.288639Z" }, "papermill": { - "duration": 0.021327, - "end_time": "2026-08-23T16:04:29.837729+00:00", + "duration": 0.008724, + "end_time": "2026-10-04T05:59:21.289772+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.816402+00:00", + "start_time": "2026-10-04T05:59:21.281048+00:00", "status": "completed" }, "tags": [] @@ -603,10 +613,10 @@ "id": "8a8e5051", "metadata": { "papermill": { - "duration": 0.010465, - "end_time": "2026-08-23T16:04:29.858646+00:00", + "duration": 0.003349, + "end_time": "2026-10-04T05:59:21.296758+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.848181+00:00", + "start_time": "2026-10-04T05:59:21.293409+00:00", "status": "completed" }, "tags": [] @@ -630,16 +640,16 @@ "id": "91eaa7f5", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.883029Z", - "iopub.status.busy": "2026-08-23T16:04:29.882029Z", - "iopub.status.idle": "2026-08-23T16:04:29.890176Z", - "shell.execute_reply": "2026-08-23T16:04:29.889169Z" + "iopub.execute_input": "2026-10-04T05:59:21.302901Z", + "iopub.status.busy": "2026-10-04T05:59:21.302901Z", + "iopub.status.idle": "2026-10-04T05:59:21.307444Z", + "shell.execute_reply": "2026-10-04T05:59:21.307444Z" }, "papermill": { - "duration": 0.022757, - "end_time": "2026-08-23T16:04:29.892313+00:00", + "duration": 0.008685, + "end_time": "2026-10-04T05:59:21.308810+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.869556+00:00", + "start_time": "2026-10-04T05:59:21.300125+00:00", "status": "completed" }, "tags": [] @@ -649,55 +659,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "\n", - "PREUVE QUE LE CORE EST VIDE\n", - "==================================================\n", - "\n", - "Pour qu'une allocation (x1, x2, x3) soit dans le Core :\n", - "\n", - "1. Efficacite : x1 + x2 + x3 = v({1,2,3}) = 1\n", - "\n", - "2. Stabilite (aucune coalition ne peut bloquer) :\n", - " x1 + x2 >= v({1,2}) = 1\n", - " x1 + x3 >= v({1,3}) = 1\n", - " x2 + x3 >= v({2,3}) = 1\n", - "\n", - "En additionnant les trois contraintes de stabilite :\n", - " 2(x1 + x2 + x3) >= 3\n", - " 2 * 1 >= 3 (par efficacite x1+x2+x3=1)\n", - " 2 >= 3 CONTRADICTION!\n", - "\n", - "=> Le Core est VIDE.\n", - "\n", - "Intuition : chaque coalition de 2 joueurs peut \"bloquer\" et demander\n", - "au moins 1, mais il n'y a que 1 a partager entre les 3 joueurs.\n", - "\n" + "Sommation des contraintes de paire :\n", + " v(N) = 1, somme des v(S) sur les 3 paires = 3\n", + " Chaque joueur apparait dans 2 paires, donc 2 * v(N) = 2 devrait couvrir cette somme\n", + " Or 2 < 3 -> CONTRADICTION : le Core est vide\n" ] } ], "source": [ - "print(\"\\nPREUVE QUE LE CORE EST VIDE\")\n", - "print(\"=\" * 50)\n", - "print(\"\"\"\n", - "Pour qu'une allocation (x1, x2, x3) soit dans le Core :\n", - "\n", - "1. Efficacite : x1 + x2 + x3 = v({1,2,3}) = 1\n", - "\n", - "2. Stabilite (aucune coalition ne peut bloquer) :\n", - " x1 + x2 >= v({1,2}) = 1\n", - " x1 + x3 >= v({1,3}) = 1\n", - " x2 + x3 >= v({2,3}) = 1\n", - "\n", - "En additionnant les trois contraintes de stabilite :\n", - " 2(x1 + x2 + x3) >= 3\n", - " 2 * 1 >= 3 (par efficacite x1+x2+x3=1)\n", - " 2 >= 3 CONTRADICTION!\n", - "\n", - "=> Le Core est VIDE.\n", - "\n", - "Intuition : chaque coalition de 2 joueurs peut \"bloquer\" et demander\n", - "au moins 1, mais il n'y a que 1 a partager entre les 3 joueurs.\n", - "\"\"\")" + "# Preuve du Core vide, verifiee sur la fonction caracteristique calculee ci-dessus\n", + "v_N = majority_game_3({1, 2, 3})\n", + "paires = [c for c in all_coalitions if len(c) == 2]\n", + "somme_paires = sum(majority_game_3(c) for c in paires)\n", + "\n", + "print(\"Sommation des contraintes de paire :\")\n", + "print(f\" v(N) = {v_N}, somme des v(S) sur les {len(paires)} paires = {somme_paires}\")\n", + "print(f\" Chaque joueur apparait dans 2 paires, donc 2 * v(N) = {2 * v_N} devrait couvrir cette somme\")\n", + "print(f\" Or {2 * v_N} < {somme_paires} -> CONTRADICTION : le Core est vide\")" ] }, { @@ -705,10 +683,10 @@ "id": "00b2e99a", "metadata": { "papermill": { - "duration": 0.010778, - "end_time": "2026-08-23T16:04:29.913696+00:00", + "duration": 0.003541, + "end_time": "2026-10-04T05:59:21.316063+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.902918+00:00", + "start_time": "2026-10-04T05:59:21.312522+00:00", "status": "completed" }, "tags": [] @@ -733,16 +711,16 @@ "id": "621ba23b", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.937733Z", - "iopub.status.busy": "2026-08-23T16:04:29.936733Z", - "iopub.status.idle": "2026-08-23T16:04:29.946413Z", - "shell.execute_reply": "2026-08-23T16:04:29.945325Z" + "iopub.execute_input": "2026-10-04T05:59:21.323066Z", + "iopub.status.busy": "2026-10-04T05:59:21.323066Z", + "iopub.status.idle": "2026-10-04T05:59:21.327065Z", + "shell.execute_reply": "2026-10-04T05:59:21.327065Z" }, "papermill": { - "duration": 0.024285, - "end_time": "2026-08-23T16:04:29.948532+00:00", + "duration": 0.008775, + "end_time": "2026-10-04T05:59:21.328311+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.924247+00:00", + "start_time": "2026-10-04T05:59:21.319536+00:00", "status": "completed" }, "tags": [] @@ -757,11 +735,6 @@ " Joueur 1: 0.3333 = 1/3\n", " Joueur 2: 0.3333 = 1/3\n", " Joueur 3: 0.3333 = 1/3\n", - "\n", - "Note : Shapley donne une allocation 'juste' (1/3, 1/3, 1/3)\n", - "mais cette allocation n'est PAS stable (pas dans le Core).\n", - "\n", - "Verification : chaque coalition de 2 peut bloquer\n", " x1 + x2 = 0.6667 < 1 = v({1,2})\n" ] } @@ -774,18 +747,25 @@ "for i, val in enumerate(shapley_majority):\n", " print(f\" Joueur {i+1}: {val:.4f} = 1/3\")\n", "\n", - "print(\"\\nNote : Shapley donne une allocation 'juste' (1/3, 1/3, 1/3)\")\n", - "print(\"mais cette allocation n'est PAS stable (pas dans le Core).\")\n", - "print(\"\\nVerification : chaque coalition de 2 peut bloquer\")\n", + "# Verification chiffree du blocage : l'allocation de Shapley n'est pas dans le Core\n", "print(f\" x1 + x2 = {shapley_majority[0] + shapley_majority[1]:.4f} < 1 = v({{1,2}})\")" ] }, { "cell_type": "markdown", "id": "25fb7204", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.003415, + "end_time": "2026-10-04T05:59:21.335432+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:21.332017+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ - "**Lecture chiffree — equitable et instable : les deux diagnostics tiennent ensemble.** La sortie affiche `Joueur 1: 0.3333 = 1/3` (et pareil pour les deux autres), puis la note cle : Shapley donne une allocation « juste » mais « cette allocation n'est PAS stable (pas dans le Core) », verifiee par la ligne `x1 + x2 = 0.6667 < 1 = v({1,2})`. Les deux nombres se lisent ensemble : 1/3 chacun est l'equite au sens des contributions marginales moyennes (symetrie parfaite des roles), et 2/3 < 1 est le blocage au sens du Core (n'importe quelle paire peut quitter la table avec 1). Ni l'un ni l'autre ne degonfle l'autre : c'est la coexistence des deux criteres, l'un distributif, l'autre strategique, qui fait tout l'interet du jeu de majorite — la preuve de vacuite de la section precedente dit qu'aucun partage ne peut gagner les DEUX.\n" + "**Lecture chiffree — equitable et instable : les deux diagnostics tiennent ensemble.** La sortie affiche `Joueur 1: 0.3333 = 1/3` (et pareil pour les deux autres), puis la verification chiffree du blocage, `x1 + x2 = 0.6667 < 1 = v({1,2})` : l'allocation de Shapley est juste mais n'est pas dans le Core. Les deux nombres se lisent ensemble : 1/3 chacun est l'equite au sens des contributions marginales moyennes (symetrie parfaite des roles), et 2/3 < 1 est le blocage au sens du Core (n'importe quelle paire peut quitter la table avec 1). Ni l'un ni l'autre ne degonfle l'autre : c'est la coexistence des deux criteres, l'un distributif, l'autre strategique, qui fait tout l'interet du jeu de majorite — la preuve de vacuite de la section precedente dit qu'aucun partage ne peut gagner les DEUX.\n" ] }, { @@ -793,10 +773,10 @@ "id": "ecfb28f3", "metadata": { "papermill": { - "duration": 0.011318, - "end_time": "2026-08-23T16:04:29.969605+00:00", + "duration": 0.003586, + "end_time": "2026-10-04T05:59:21.342423+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.958287+00:00", + "start_time": "2026-10-04T05:59:21.338837+00:00", "status": "completed" }, "tags": [] @@ -815,16 +795,16 @@ "id": "4062d8c2", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:29.990558Z", - "iopub.status.busy": "2026-08-23T16:04:29.989550Z", - "iopub.status.idle": "2026-08-23T16:04:30.010560Z", - "shell.execute_reply": "2026-08-23T16:04:30.009551Z" + "iopub.execute_input": "2026-10-04T05:59:21.349706Z", + "iopub.status.busy": "2026-10-04T05:59:21.349706Z", + "iopub.status.idle": "2026-10-04T05:59:21.356932Z", + "shell.execute_reply": "2026-10-04T05:59:21.356932Z" }, "papermill": { - "duration": 0.033213, - "end_time": "2026-08-23T16:04:30.012887+00:00", + "duration": 0.012119, + "end_time": "2026-10-04T05:59:21.358184+00:00", "exception": false, - "start_time": "2026-08-23T16:04:29.979674+00:00", + "start_time": "2026-10-04T05:59:21.346065+00:00", "status": "completed" }, "tags": [] @@ -909,10 +889,10 @@ "id": "6baf6290", "metadata": { "papermill": { - "duration": 0.007653, - "end_time": "2026-08-23T16:04:30.028244+00:00", + "duration": 0.003722, + "end_time": "2026-10-04T05:59:21.365647+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.020591+00:00", + "start_time": "2026-10-04T05:59:21.361925+00:00", "status": "completed" }, "tags": [] @@ -942,16 +922,16 @@ "id": "e365f7b8", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:30.044146Z", - "iopub.status.busy": "2026-08-23T16:04:30.044146Z", - "iopub.status.idle": "2026-08-23T16:04:30.326930Z", - "shell.execute_reply": "2026-08-23T16:04:30.325923Z" + "iopub.execute_input": "2026-10-04T05:59:21.372745Z", + "iopub.status.busy": "2026-10-04T05:59:21.372745Z", + "iopub.status.idle": "2026-10-04T05:59:21.472742Z", + "shell.execute_reply": "2026-10-04T05:59:21.472742Z" }, "papermill": { - "duration": 0.292828, - "end_time": "2026-08-23T16:04:30.328779+00:00", + "duration": 0.104732, + "end_time": "2026-10-04T05:59:21.473906+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.035951+00:00", + "start_time": "2026-10-04T05:59:21.369174+00:00", "status": "completed" }, "tags": [] @@ -959,7 +939,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -1005,7 +985,16 @@ { "cell_type": "markdown", "id": "964f18cb", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.003726, + "end_time": "2026-10-04T05:59:21.481664+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:21.477938+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lecture de la figure — le renversement se voit avant de se calculer.** Les barres cote a cote tracent, pour chaque joueur, le poids nominal contre les indices de pouvoir reel (Shapley et Banzhaf) : la note de la sortie resume ce que l'oeil capte — « Le pouvoir reel (Shapley/Banzhaf) peut differer du poids nominal! ». Le tableau chiffre de l'interpretation precedente donne les valeurs exactes ; la figure ajoute le diagnostic visuel : les barres poids et pouvoir ne sont PAS alignees, le desequilibre change de sens selon les joueurs (le grand poids est surcote en apparence, les petits poids surindexes en pouvoir). C'est la lecture a retenir d'un coup d'oeil avant toute negotiation de quota : on negocie des poids, on exerce du pouvoir.\n" ] @@ -1015,10 +1004,10 @@ "id": "96c72b60", "metadata": { "papermill": { - "duration": 0.00732, - "end_time": "2026-08-23T16:04:30.344209+00:00", + "duration": 0.003629, + "end_time": "2026-10-04T05:59:21.489624+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.336889+00:00", + "start_time": "2026-10-04T05:59:21.485995+00:00", "status": "completed" }, "tags": [] @@ -1037,16 +1026,16 @@ "id": "1ef86331", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:30.364235Z", - "iopub.status.busy": "2026-08-23T16:04:30.363236Z", - "iopub.status.idle": "2026-08-23T16:04:30.376110Z", - "shell.execute_reply": "2026-08-23T16:04:30.375100Z" + "iopub.execute_input": "2026-10-04T05:59:21.497012Z", + "iopub.status.busy": "2026-10-04T05:59:21.497012Z", + "iopub.status.idle": "2026-10-04T05:59:21.503590Z", + "shell.execute_reply": "2026-10-04T05:59:21.503072Z" }, "papermill": { - "duration": 0.023314, - "end_time": "2026-08-23T16:04:30.377387+00:00", + "duration": 0.011154, + "end_time": "2026-10-04T05:59:21.504374+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.354073+00:00", + "start_time": "2026-10-04T05:59:21.493220+00:00", "status": "completed" }, "tags": [] @@ -1104,10 +1093,10 @@ "id": "3c7846aa", "metadata": { "papermill": { - "duration": 0.011272, - "end_time": "2026-08-23T16:04:30.397456+00:00", + "duration": 0.003633, + "end_time": "2026-10-04T05:59:21.512238+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.386184+00:00", + "start_time": "2026-10-04T05:59:21.508605+00:00", "status": "completed" }, "tags": [] @@ -1132,16 +1121,16 @@ "id": "4cf40a9d", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:30.419827Z", - "iopub.status.busy": "2026-08-23T16:04:30.418826Z", - "iopub.status.idle": "2026-08-23T16:04:30.432870Z", - "shell.execute_reply": "2026-08-23T16:04:30.431862Z" + "iopub.execute_input": "2026-10-04T05:59:21.519932Z", + "iopub.status.busy": "2026-10-04T05:59:21.519932Z", + "iopub.status.idle": "2026-10-04T05:59:21.526267Z", + "shell.execute_reply": "2026-10-04T05:59:21.525509Z" }, "papermill": { - "duration": 0.025306, - "end_time": "2026-08-23T16:04:30.434496+00:00", + "duration": 0.011055, + "end_time": "2026-10-04T05:59:21.526925+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.409190+00:00", + "start_time": "2026-10-04T05:59:21.515870+00:00", "status": "completed" }, "tags": [] @@ -1206,7 +1195,16 @@ { "cell_type": "markdown", "id": "21ae35db", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.003799, + "end_time": "2026-10-04T05:59:21.534610+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:21.530811+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lecture chiffree — le theoreme verifies sur ses deux cotes.** La sortie aligne le jeu convexe `v(S) = |S|^2 / 9` puis son contre-exemple. Cote theoreme : `Convexe ? True` et `Shapley : [0.3333, 0.3333, 0.3333]` avec `Dans le Core ? True` — sur un jeu convexe, la valeur de Shapley APPARTIENT au Core, l'allocation equitable est ici aussi stable. Cote contre-exemple : le jeu de majorite repond `False` avec la cause nominmee — `Coalition (0, 1) peut bloquer`. La paire de verdicts fait le travail pedagogique : la convexite est precisement l'hypothese qui soude equite et stabilite, et le jeu de majorite (non convexe) montre les deux critieres se separer a nouveau, comme en section 3.\n" ] @@ -1216,10 +1214,10 @@ "id": "ex-convex-core-md", "metadata": { "papermill": { - "duration": 0.007572, - "end_time": "2026-08-23T16:04:30.449350+00:00", + "duration": 0.003595, + "end_time": "2026-10-04T05:59:21.541934+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.441778+00:00", + "start_time": "2026-10-04T05:59:21.538339+00:00", "status": "completed" }, "tags": [] @@ -1243,16 +1241,16 @@ "id": "ex-convex-core-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:30.467322Z", - "iopub.status.busy": "2026-08-23T16:04:30.466319Z", - "iopub.status.idle": "2026-08-23T16:04:30.478068Z", - "shell.execute_reply": "2026-08-23T16:04:30.476550Z" + "iopub.execute_input": "2026-10-04T05:59:21.548469Z", + "iopub.status.busy": "2026-10-04T05:59:21.548469Z", + "iopub.status.idle": "2026-10-04T05:59:21.554174Z", + "shell.execute_reply": "2026-10-04T05:59:21.554174Z" }, "papermill": { - "duration": 0.023086, - "end_time": "2026-08-23T16:04:30.479472+00:00", + "duration": 0.009974, + "end_time": "2026-10-04T05:59:21.555508+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.456386+00:00", + "start_time": "2026-10-04T05:59:21.545534+00:00", "status": "completed" }, "tags": [] @@ -1307,7 +1305,16 @@ { "cell_type": "markdown", "id": "fe3e9680", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.003786, + "end_time": "2026-10-04T05:59:21.563209+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:21.559423+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lire la sortie d'un exercice non rempli — et reconnaitre un artefact.** Les lignes `Convexe: False` sur le Jeu 1 (convexe attendu) ne sont pas un verdict mathematique : `Shapley: []` le revele, le squelette ne calcule rien, et le False par defaut s'affiche pour les deux jeux a l'identique. L'etat reel est « Exercice a completer ». Le contrat : construire deux jeux de 3 joueurs (un convexe, un non convexe), appliquer `is_convex` puis le test d'appartenance au Core, et lire la PAIRE de verdicts — convexe attendu True/True a la maniere de la cellule precedente, non convexe attendu False/False. La sortie remplie devra rompre la symetrie artefactuelle des deux False actuels : c'est justement le signe que la solution vit.\n" ] @@ -1317,10 +1324,10 @@ "id": "gt15c-lp-intro", "metadata": { "papermill": { - "duration": 0.008328, - "end_time": "2026-08-23T16:04:30.495570+00:00", + "duration": 0.003687, + "end_time": "2026-10-04T05:59:21.570636+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.487242+00:00", + "start_time": "2026-10-04T05:59:21.566949+00:00", "status": "completed" }, "tags": [] @@ -1362,16 +1369,16 @@ "id": "gt15c-lp-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:30.514588Z", - "iopub.status.busy": "2026-08-23T16:04:30.513590Z", - "iopub.status.idle": "2026-08-23T16:04:36.685547Z", - "shell.execute_reply": "2026-08-23T16:04:36.684541Z" + "iopub.execute_input": "2026-10-04T05:59:21.578252Z", + "iopub.status.busy": "2026-10-04T05:59:21.578252Z", + "iopub.status.idle": "2026-10-04T05:59:26.970040Z", + "shell.execute_reply": "2026-10-04T05:59:26.969525Z" }, "papermill": { - "duration": 6.183225, - "end_time": "2026-08-23T16:04:36.686950+00:00", + "duration": 5.396811, + "end_time": "2026-10-04T05:59:26.971185+00:00", "exception": false, - "start_time": "2026-08-23T16:04:30.503725+00:00", + "start_time": "2026-10-04T05:59:21.574374+00:00", "status": "completed" }, "tags": [] @@ -1442,10 +1449,10 @@ "id": "gt15c-lp-interp", "metadata": { "papermill": { - "duration": 0.00659, - "end_time": "2026-08-23T16:04:36.701015+00:00", + "duration": 0.004637, + "end_time": "2026-10-04T05:59:26.980598+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.694425+00:00", + "start_time": "2026-10-04T05:59:26.975961+00:00", "status": "completed" }, "tags": [] @@ -1475,10 +1482,10 @@ "id": "gt15c-bal-md", "metadata": { "papermill": { - "duration": 0.007454, - "end_time": "2026-08-23T16:04:36.715575+00:00", + "duration": 0.005682, + "end_time": "2026-10-04T05:59:26.990729+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.708121+00:00", + "start_time": "2026-10-04T05:59:26.985047+00:00", "status": "completed" }, "tags": [] @@ -1514,16 +1521,16 @@ "id": "gt15c-bal-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:36.732482Z", - "iopub.status.busy": "2026-08-23T16:04:36.731476Z", - "iopub.status.idle": "2026-08-23T16:04:36.750840Z", - "shell.execute_reply": "2026-08-23T16:04:36.749835Z" + "iopub.execute_input": "2026-10-04T05:59:27.003815Z", + "iopub.status.busy": "2026-10-04T05:59:27.003815Z", + "iopub.status.idle": "2026-10-04T05:59:27.017449Z", + "shell.execute_reply": "2026-10-04T05:59:27.016441Z" }, "papermill": { - "duration": 0.029681, - "end_time": "2026-08-23T16:04:36.752388+00:00", + "duration": 0.022731, + "end_time": "2026-10-04T05:59:27.018943+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.722707+00:00", + "start_time": "2026-10-04T05:59:26.996212+00:00", "status": "completed" }, "tags": [] @@ -1596,10 +1603,10 @@ "id": "gt15c-bal-interp-md", "metadata": { "papermill": { - "duration": 0.008182, - "end_time": "2026-08-23T16:04:36.767647+00:00", + "duration": 0.00447, + "end_time": "2026-10-04T05:59:27.028768+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.759465+00:00", + "start_time": "2026-10-04T05:59:27.024298+00:00", "status": "completed" }, "tags": [] @@ -1632,16 +1639,16 @@ "id": "gt15c-bal-dual-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:36.784138Z", - "iopub.status.busy": "2026-08-23T16:04:36.783552Z", - "iopub.status.idle": "2026-08-23T16:04:36.801316Z", - "shell.execute_reply": "2026-08-23T16:04:36.800306Z" + "iopub.execute_input": "2026-10-04T05:59:27.042821Z", + "iopub.status.busy": "2026-10-04T05:59:27.042821Z", + "iopub.status.idle": "2026-10-04T05:59:27.055327Z", + "shell.execute_reply": "2026-10-04T05:59:27.054265Z" }, "papermill": { - "duration": 0.027637, - "end_time": "2026-08-23T16:04:36.802824+00:00", + "duration": 0.02104, + "end_time": "2026-10-04T05:59:27.056660+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.775187+00:00", + "start_time": "2026-10-04T05:59:27.035620+00:00", "status": "completed" }, "tags": [] @@ -1706,7 +1713,16 @@ { "cell_type": "markdown", "id": "40f1f6a7", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.005833, + "end_time": "2026-10-04T05:59:27.067520+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:27.061687+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lecture chiffree — le solveur rend le certificat gratuitement.** La sortie part des marges duales du LP de least-core (`res.ineqlin.marginal`) et les transforme en certificat de Bondareva-Shapley. Jeu de gants : `epsilon* = -0.0000`, les trois paires portent `|m| = 0.3333` chacune ; la renormalisation `k = 1.5000` (chaque joueur apparait dans deux paires) donne `w({i,j}) = 0.5000` et `somme_S w(S)*v(S) = +1.0000` — pile `v(N)` : la collection equilibree explicite de la cellule precedente, reconstruite par le dual sans qu'on la fournisse. Jeu de majorite : `epsilon* = -0.3333` et la meme mecanique conduit a la somme `3/2 > 1` de la preuve manuelle. La lecon d'ingenierie : primal et dual d'un meme LP livrent le verdict ET son certificat — deux preuves pour le prix d'un solve.\n" ] @@ -1716,10 +1732,10 @@ "id": "gt15c-bal-ex-md", "metadata": { "papermill": { - "duration": 0.010564, - "end_time": "2026-08-23T16:04:36.821569+00:00", + "duration": 0.006036, + "end_time": "2026-10-04T05:59:27.081245+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.811005+00:00", + "start_time": "2026-10-04T05:59:27.075209+00:00", "status": "completed" }, "tags": [] @@ -1747,16 +1763,16 @@ "id": "gt15c-bal-ex-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:36.838032Z", - "iopub.status.busy": "2026-08-23T16:04:36.838032Z", - "iopub.status.idle": "2026-08-23T16:04:36.846870Z", - "shell.execute_reply": "2026-08-23T16:04:36.845290Z" + "iopub.execute_input": "2026-10-04T05:59:27.095690Z", + "iopub.status.busy": "2026-10-04T05:59:27.095690Z", + "iopub.status.idle": "2026-10-04T05:59:27.101143Z", + "shell.execute_reply": "2026-10-04T05:59:27.100179Z" }, "papermill": { - "duration": 0.018697, - "end_time": "2026-08-23T16:04:36.847907+00:00", + "duration": 0.013583, + "end_time": "2026-10-04T05:59:27.102170+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.829210+00:00", + "start_time": "2026-10-04T05:59:27.088587+00:00", "status": "completed" }, "tags": [] @@ -1797,7 +1813,16 @@ { "cell_type": "markdown", "id": "90b74d47", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.006698, + "end_time": "2026-10-04T05:59:27.116425+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:27.109727+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lire la sortie d'un exercice non rempli — l'artefact du jeu nul.** `Collection equilibree : {}` avec `somme_S w(S)*v(S) = +0.0000 vs v(N) = 0.0` puis `Core vide ? False` : tout vient du jeu par defaut (nul) et de la collection vide — le verdict False mesure un objet absent, pas le jeu de majorite. L'etat reel : « Exercice a completer ». Le contrat : exhiber une collection equilibree qui prouve la vacuite du Core du jeu de majorite, c'est-a-dire des poids `w` sur des coalitions avec `somme_{S contient i} w(S) = 1` pour chaque joueur et `somme_S w(S) v(S) > v(N)`. La reponse existe deja dans ce notebook — les trois paires a `1/2` de la section precedente ; l'exercice demande de la retrouver par la methode, pas de la recopier.\n" ] @@ -1807,10 +1832,10 @@ "id": "gt15c-nuc-intro", "metadata": { "papermill": { - "duration": 0.007035, - "end_time": "2026-08-23T16:04:36.862349+00:00", + "duration": 0.006681, + "end_time": "2026-10-04T05:59:27.130135+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.855314+00:00", + "start_time": "2026-10-04T05:59:27.123454+00:00", "status": "completed" }, "tags": [] @@ -1839,16 +1864,16 @@ "id": "gt15c-nuc-code", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:36.881777Z", - "iopub.status.busy": "2026-08-23T16:04:36.880177Z", - "iopub.status.idle": "2026-08-23T16:04:36.913853Z", - "shell.execute_reply": "2026-08-23T16:04:36.912845Z" + "iopub.execute_input": "2026-10-04T05:59:27.146354Z", + "iopub.status.busy": "2026-10-04T05:59:27.145791Z", + "iopub.status.idle": "2026-10-04T05:59:27.168556Z", + "shell.execute_reply": "2026-10-04T05:59:27.167956Z" }, "papermill": { - "duration": 0.044414, - "end_time": "2026-08-23T16:04:36.915682+00:00", + "duration": 0.032509, + "end_time": "2026-10-04T05:59:27.170174+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.871268+00:00", + "start_time": "2026-10-04T05:59:27.137665+00:00", "status": "completed" }, "tags": [] @@ -1859,7 +1884,13 @@ "output_type": "stream", "text": [ "NUCLEOLE vs VALEUR DE SHAPLEY\n", - "========================================================\n", + "========================================================\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "\n", "Jeu de gants (2 LP resolus)\n", " Nucleole = [-0.0, -0.0, 1.0] -> dans le Core : True\n", @@ -1928,7 +1959,16 @@ { "cell_type": "markdown", "id": "4395bde8", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.005681, + "end_time": "2026-10-04T05:59:27.181928+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:27.176247+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lecture chiffree — trois jeux font un banc complet pour le nucleole.** La sortie croise nucleole et Shapley sur les trois jeux du notebook. Jeu de gants : `Nucleole = [-0.0, -0.0, 1.0] -> Core : True` contre `Shapley = [0.1667, 0.1667, 0.6667] -> False` — le nucleole selections l'unique point du Core (le detenteur du gant droit rafle tout), la Shapley equitable reste dehors : stabilite contre equite, tranchees. Jeu de majorite : les DEUX valent `(0.3333, 0.3333, 0.3333)` et TOUS DEUX hors Core — la symetrie force l'egalite des deux concepts, et le nucleole existe meme sans Core (propriete « existe toujours » verifiee sur ce cas). Jeu convexe : les deux coincident encore, cette fois DANS le Core. Le detail final compte : « 2 LP resolus » pour gants et majorite contre « 1 LP resolus » pour le convexe — l'algorithme sequentiel de Maschler s'arrete des la premiere etape quand le Core a un interieur, il ne s'y enlise que sur les cas limites.\n" ] @@ -1939,16 +1979,16 @@ "id": "gt15c-fig", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:36.933856Z", - "iopub.status.busy": "2026-08-23T16:04:36.933856Z", - "iopub.status.idle": "2026-08-23T16:04:37.330926Z", - "shell.execute_reply": "2026-08-23T16:04:37.330415Z" + "iopub.execute_input": "2026-10-04T05:59:27.197020Z", + "iopub.status.busy": "2026-10-04T05:59:27.196424Z", + "iopub.status.idle": "2026-10-04T05:59:27.423465Z", + "shell.execute_reply": "2026-10-04T05:59:27.422737Z" }, "papermill": { - "duration": 0.409017, - "end_time": "2026-08-23T16:04:37.332644+00:00", + "duration": 0.236884, + "end_time": "2026-10-04T05:59:27.424789+00:00", "exception": false, - "start_time": "2026-08-23T16:04:36.923627+00:00", + "start_time": "2026-10-04T05:59:27.187905+00:00", "status": "completed" }, "tags": [] @@ -1956,7 +1996,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -2000,10 +2040,10 @@ "id": "gt15c-interp", "metadata": { "papermill": { - "duration": 0.007806, - "end_time": "2026-08-23T16:04:37.348611+00:00", + "duration": 0.005113, + "end_time": "2026-10-04T05:59:27.435046+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.340805+00:00", + "start_time": "2026-10-04T05:59:27.429933+00:00", "status": "completed" }, "tags": [] @@ -2031,10 +2071,10 @@ "id": "ab51184f", "metadata": { "papermill": { - "duration": 0.009214, - "end_time": "2026-08-23T16:04:37.365413+00:00", + "duration": 0.004961, + "end_time": "2026-10-04T05:59:27.445327+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.356199+00:00", + "start_time": "2026-10-04T05:59:27.440366+00:00", "status": "completed" }, "tags": [] @@ -2071,10 +2111,10 @@ "id": "89d42c89", "metadata": { "papermill": { - "duration": 0.012292, - "end_time": "2026-08-23T16:04:37.386760+00:00", + "duration": 0.00546, + "end_time": "2026-10-04T05:59:27.455581+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.374468+00:00", + "start_time": "2026-10-04T05:59:27.450121+00:00", "status": "completed" }, "tags": [] @@ -2107,16 +2147,16 @@ "id": "83115469", "metadata": { "execution": { - "iopub.execute_input": "2026-08-23T16:04:37.410242Z", - "iopub.status.busy": "2026-08-23T16:04:37.408690Z", - "iopub.status.idle": "2026-08-23T16:04:37.418944Z", - "shell.execute_reply": "2026-08-23T16:04:37.417936Z" + "iopub.execute_input": "2026-10-04T05:59:27.466427Z", + "iopub.status.busy": "2026-10-04T05:59:27.466427Z", + "iopub.status.idle": "2026-10-04T05:59:27.471970Z", + "shell.execute_reply": "2026-10-04T05:59:27.471102Z" }, "papermill": { - "duration": 0.023017, - "end_time": "2026-08-23T16:04:37.421220+00:00", + "duration": 0.012485, + "end_time": "2026-10-04T05:59:27.473288+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.398203+00:00", + "start_time": "2026-10-04T05:59:27.460803+00:00", "status": "completed" }, "tags": [] @@ -2161,7 +2201,16 @@ { "cell_type": "markdown", "id": "c8049152", - "metadata": {}, + "metadata": { + "papermill": { + "duration": 0.005021, + "end_time": "2026-10-04T05:59:27.483507+00:00", + "exception": false, + "start_time": "2026-10-04T05:59:27.478486+00:00", + "status": "completed" + }, + "tags": [] + }, "source": [ "**Lire la sortie d'un exercice non rempli.** La ligne « Exercice a completer » ouvre l'espace des exemples guides de la section Exercices : le premier (jeu de l'aeroport, enonce ci-dessus) attend sa solution ici. Le terrain est pose par le notebook entier : `shapley_value_exact` (section 1) calcule les allocations, le LP de least-core (section 6) teste l'appartenance au Core, et le modele du jeu de gants montre comment encoder une fonction caracteristique par petites regles. Une solution remplie affichera la fonction de cout de l'aeroport, les parts Shapley par joueur, et leur lecture — qui paie quoi du runway commun quand les avions n'ont pas la meme taille.\n" ] @@ -2171,10 +2220,10 @@ "id": "c36229aa", "metadata": { "papermill": { - "duration": 0.01076, - "end_time": "2026-08-23T16:04:37.444159+00:00", + "duration": 0.005374, + "end_time": "2026-10-04T05:59:27.495007+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.433399+00:00", + "start_time": "2026-10-04T05:59:27.489633+00:00", "status": "completed" }, "tags": [] @@ -2194,10 +2243,10 @@ "id": "33ad7247", "metadata": { "papermill": { - "duration": 0.011264, - "end_time": "2026-08-23T16:04:37.466418+00:00", + "duration": 0.005431, + "end_time": "2026-10-04T05:59:27.506583+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.455154+00:00", + "start_time": "2026-10-04T05:59:27.501152+00:00", "status": "completed" }, "tags": [] @@ -2213,10 +2262,10 @@ "id": "43bdd0a8", "metadata": { "papermill": { - "duration": 0.012627, - "end_time": "2026-08-23T16:04:37.490860+00:00", + "duration": 0.005329, + "end_time": "2026-10-04T05:59:27.517057+00:00", "exception": false, - "start_time": "2026-08-23T16:04:37.478233+00:00", + "start_time": "2026-10-04T05:59:27.511728+00:00", "status": "completed" }, "tags": [] @@ -2263,21 +2312,21 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.15" + "version": "3.11.16" }, "papermill": { "default_parameters": {}, - "duration": 16.377676, - "end_time": "2026-08-23T16:04:37.966995+00:00", + "duration": 12.808068, + "end_time": "2026-10-04T05:59:27.874685+00:00", "environment_variables": {}, "exception": null, - "input_path": "MyIA.AI.Notebooks/GameTheory/GameTheory-15c-CooperativeGames-Python.ipynb", - "output_path": "MyIA.AI.Notebooks/GameTheory/GameTheory-15c-CooperativeGames-Python.ipynb", + "input_path": "GameTheory-15c-CooperativeGames-Python.ipynb", + "output_path": "GameTheory-15c-CooperativeGames-Python.ipynb", "parameters": {}, - "start_time": "2026-08-23T16:04:21.589319+00:00", + "start_time": "2026-10-04T05:59:15.066617+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file From 21b8b74a108c8fca61e09616109e41a755ac43fd Mon Sep 17 00:00:00 2001 From: jsboige Date: Sun, 4 Oct 2026 08:09:09 +0200 Subject: [PATCH 2/2] fix(twin-parity,#18874): reattester la paire GameTheory-15c apres re-execution C.2 La PR modifie le carnet (4 cellules), donc le blob SHA a change et l'attestation de paire est tombee en DRIFT : l'organe twin parity exige une nouvelle attestation a chaque modification, c'est son role. Re-attestation a la tete b1fcf9859c via --update --pair, apres la normalisation papermill (ordre #8957 : strip d'abord, attester en dernier). La paire repasse [OK] en local. Co-Authored-By: Claude Sonnet 5.5 --- .../0010-2026-10-04-myia-po-2023-CoursIA.yaml | 6 ++++++ 1 file changed, 6 insertions(+) create mode 100644 scripts/notebook_tools/twin_pairs.d/gametheory-15c-cooperativegames/0010-2026-10-04-myia-po-2023-CoursIA.yaml diff --git a/scripts/notebook_tools/twin_pairs.d/gametheory-15c-cooperativegames/0010-2026-10-04-myia-po-2023-CoursIA.yaml b/scripts/notebook_tools/twin_pairs.d/gametheory-15c-cooperativegames/0010-2026-10-04-myia-po-2023-CoursIA.yaml new file mode 100644 index 0000000000..e8ec9d93e1 --- /dev/null +++ b/scripts/notebook_tools/twin_pairs.d/gametheory-15c-cooperativegames/0010-2026-10-04-myia-po-2023-CoursIA.yaml @@ -0,0 +1,6 @@ +date: '2026-10-04' +by: myia-po-2023:CoursIA +python_sha: 392926099f8c709e4fb5ba873f47e8ac2a52a3cb +csharp_sha: 9c8f03f3a5e979e066a88eee80e7c8c3509ab643 +content_python_sha: 6374911a2a8a8b04d32ad87742603a4e4143c1b73206b779ab15dd125c13ceaa +content_csharp_sha: ac581e30a530a8fa6e0b1fae0465c8627c9b96a6b53e9f3f22ac0cf6ded1f2c4