logbook-files/outputs/executed/soccer.repeat.no-tex.executed.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1409da01",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-21T14:34:35.127195Z",
     "iopub.status.busy": "2026-07-21T14:34:35.126968Z",
     "iopub.status.idle": "2026-07-21T14:39:26.788782Z",
     "shell.execute_reply": "2026-07-21T14:39:26.787894Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Nash Policies (Noise=0.05)...\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import linprog\n",
    "\n",
    "# configuration\n",
    "\n",
    "width = 5               \n",
    "height = 4              \n",
    "gamma = 0.95            \n",
    "solver_iters = 100      \n",
    "actions = [(-1, 0), (1, 0), (0, 1), (0, -1), (0, 0)] # N, S, E, W, X\n",
    "num_acts = 5\n",
    "act_labels = [\"N\", \"S\", \"E\", \"W\", \"X\"]\n",
    "\n",
    "B_slip_prob = 0.25      \n",
    "step_cost = -0.05       \n",
    "noise_floor = 0.05 # 5% uniform noise added to Nash to ensure full support\n",
    "\n",
    "# visualization settings\n",
    "grid_color = '#e0e0e0'\n",
    "player_A_color = '#1f77b4' \n",
    "player_B_color = '#d62728' \n",
    "ball_color = '#ff7f0e'     \n",
    "\n",
    "np.random.seed(1)\n",
    "\n",
    "# game dynamics\n",
    "\n",
    "def get_state_idx(ax, ay, bx, by, poss):\n",
    "    return poss * (width*height)**2 + (ax*width+ay)*(width*height) + (bx*width+by)\n",
    "\n",
    "def parse_state_idx(idx):\n",
    "    poss = idx // ((width*height)**2)\n",
    "    rem = idx % ((width*height)**2)\n",
    "    a_idx = rem // (width*height)\n",
    "    b_idx = rem % (width*height)\n",
    "    ax, ay = a_idx // width, a_idx % width\n",
    "    bx, by = b_idx // width, b_idx % width\n",
    "    return ax, ay, bx, by, poss\n",
    "\n",
    "def get_next_state_reward_done(ax, ay, bx, by, poss, act_a, act_b):\n",
    "    dxa, dya = actions[act_a]; nax, nay = ax + dxa, ay + dya\n",
    "    dxb, dyb = actions[act_b]; nbx, nby = bx + dxb, by + dyb\n",
    "    \n",
    "    # walls\n",
    "    if nax < 0 or nax >= height or nay < 0 or nay >= width: nax, nay = ax, ay\n",
    "    if nbx < 0 or nbx >= height or nby < 0 or nby >= width: nbx, nby = bx, by\n",
    "    \n",
    "    # goals\n",
    "    if poss == 0 and nay == width-1: return (nax, nay, nbx, nby, poss), 100, True\n",
    "    if poss == 1 and nby == 0:       return (nax, nay, nbx, nby, poss), -100, True\n",
    "    \n",
    "    next_poss = poss\n",
    "    # collisions\n",
    "    if (nax == bx and nay == by and nbx == ax and nby == ay) or (nax == nbx and nay == nby):\n",
    "        nax, nay = ax, ay; nbx, nby = bx, by # bounce\n",
    "        if np.random.rand() < 0.5: next_poss = 1 - poss\n",
    "    elif nax == bx and nay == by and act_b == 4: nax, nay = ax, ay; next_poss = 1\n",
    "    elif nbx == ax and nby == ay and act_a == 4: nbx, nby = bx, by; next_poss = 0\n",
    "        \n",
    "    return (nax, nay, nbx, nby, next_poss), step_cost, False\n",
    "\n",
    "# solver (true Nash + smoothing)\n",
    "\n",
    "pi_NE_A = np.ones((2 * (width * height) ** 2, num_acts)) / num_acts\n",
    "pi_NE_B = np.ones((2 * (width * height) ** 2, num_acts)) / num_acts\n",
    "\n",
    "def solve_matrix_game(Q_table):\n",
    "    c = np.zeros(num_acts + 1); c[-1] = -1 \n",
    "    A_eq = np.zeros((1, num_acts + 1)); A_eq[0, :num_acts] = 1; b_eq = [1.0]\n",
    "    A_ub = np.hstack([ -Q_table.T, np.ones((num_acts, 1)) ]); b_ub = np.zeros(num_acts)\n",
    "    bounds = [(0, 1) for _ in range(num_acts)] + [(None, None)]\n",
    "    res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds, method='highs')\n",
    "    if res.success:\n",
    "        policy = res.x[:num_acts]\n",
    "        policy[policy < 1e-8] = 0; policy /= np.sum(policy)\n",
    "        return res.x[-1], policy\n",
    "    return 0.0, np.ones(num_acts)/num_acts\n",
    "\n",
    "def compute_equilibrium():\n",
    "    global pi_NE_A, pi_NE_B\n",
    "    print(f\"Computing Nash Policies (Noise={noise_floor})...\")\n",
    "    V = np.zeros(2 * (width * height) ** 2)\n",
    "    # heuristic init\n",
    "    for idx in range(len(V)):\n",
    "        ax, ay, bx, by, p = parse_state_idx(idx)\n",
    "        V[idx] = (10.0 - ((width-1)-ay)) if p==0 else -(10.0 - by)\n",
    "\n",
    "    for it in range(solver_iters):\n",
    "        new_V = np.copy(V)\n",
    "        delta = 0\n",
    "        for idx in range(len(V)):\n",
    "            ax, ay, bx, by, poss = parse_state_idx(idx)\n",
    "            Q = np.zeros((num_acts, num_acts))\n",
    "            \n",
    "            for a in range(num_acts):\n",
    "                for b in range(num_acts):\n",
    "                    val_succ = 0; val_fail = 0\n",
    "                    for is_fail in [False, True]:\n",
    "                        eff_b = 4 if is_fail else b\n",
    "                        ns, r_step, _ = get_next_state_reward_done(ax,ay,bx,by,poss,a,eff_b)\n",
    "                        nax,nay,nbx,nby,nposs = ns\n",
    "                        \n",
    "                        term_r = r_step\n",
    "                        if poss==0 and nay==width-1: term_r += 100\n",
    "                        elif poss==1 and nby==0: term_r += -100\n",
    "                        else:\n",
    "                            if (nax==bx and nay==by and nbx==ax and nby==ay) or (nax==nbx and nay==nby):\n",
    "                                term_r += gamma * (0.5*V[get_state_idx(ax,ay,bx,by,0)] + 0.5*V[get_state_idx(ax,ay,bx,by,1)])\n",
    "                            elif nax==bx and nay==by and eff_b==4: term_r += gamma * V[get_state_idx(ax,ay,bx,by,1)]\n",
    "                            elif nbx==ax and nby==ay and a==4: term_r += gamma * V[get_state_idx(ax,ay,bx,by,0)]\n",
    "                            else: term_r += gamma * V[get_state_idx(nax,nay,nbx,nby,poss)]\n",
    "                        \n",
    "                        if is_fail: val_fail = term_r\n",
    "                        else: val_succ = term_r\n",
    "                    \n",
    "                    Q[a,b] = (1.0-B_slip_prob)*val_succ + B_slip_prob*val_fail\n",
    "            \n",
    "            val, pol_a = solve_matrix_game(Q)\n",
    "            _, pol_b = solve_matrix_game(-Q.T)\n",
    "            new_V[idx] = val; pi_NE_A[idx] = pol_a; pi_NE_B[idx] = pol_b\n",
    "            delta = max(delta, abs(V[idx]-val))\n",
    "        V = new_V\n",
    "        if delta < 1e-3: break\n",
    "    \n",
    "    # global smoothing\n",
    "    # mix pure Nash with uniform noise to ensure full support\n",
    "    # this prevents \"infinite evidence\" jumps \n",
    "    pi_NE_A = (1 - noise_floor) * pi_NE_A + noise_floor * (np.ones_like(pi_NE_A)/num_acts)\n",
    "    pi_NE_B = (1 - noise_floor) * pi_NE_B + noise_floor * (np.ones_like(pi_NE_B)/num_acts)\n",
    "\n",
    "# \"afraid\" policy generation \n",
    "\n",
    "pi_afraid = None\n",
    "\n",
    "def generate_afraid_policy():\n",
    "    \"\"\"\n",
    "    Afraid Policy: Reduces 'East' (2) mass and distributes to 'West' (3) or 'Wait' (4).\n",
    "    Since Base is now smoothed, this acts as a 'Soft' deviation.\n",
    "    \"\"\"\n",
    "    global pi_afraid\n",
    "    pi_afraid = np.copy(pi_NE_A)\n",
    "    \n",
    "    for idx in range(len(pi_afraid)):\n",
    "        p = pi_afraid[idx]\n",
    "        east_prob = p[2]\n",
    "        \n",
    "        reduction = east_prob * 0.9\n",
    "        \n",
    "        p[2] -= reduction\n",
    "        p[3] += reduction * 0.5 # West\n",
    "        p[4] += reduction * 0.5 # Wait\n",
    "        \n",
    "        pi_afraid[idx] = p / np.sum(p)\n",
    "\n",
    "# run\n",
    "compute_equilibrium()\n",
    "generate_afraid_policy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "96d81f5b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-21T14:39:26.793489Z",
     "iopub.status.busy": "2026-07-21T14:39:26.793180Z",
     "iopub.status.idle": "2026-07-21T14:39:28.260829Z",
     "shell.execute_reply": "2026-07-21T14:39:28.259999Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilities Format: [N, S, E, W, X]\n",
      "Step 0:\n",
      "  A (E): [0.01 0.01 0.96 0.01 0.01]\n",
      "  B (W): [0.01 0.01 0.01 0.96 0.01] \n",
      "Step 1:\n",
      "  A (E): [0.06 0.59 0.33 0.01 0.01]\n",
      "  B (W): [0.01 0.05 0.01 0.47 0.45] **Slip!**\n",
      "Step 2:\n",
      "  A (N): [0.69 0.28 0.01 0.01 0.01]\n",
      "  B (X): [0.01 0.01 0.01 0.01 0.96] \n",
      "Step 3:\n",
      "  A (E): [0.01 0.01 0.96 0.01 0.01]\n",
      "  B (N): [0.96 0.01 0.01 0.01 0.01] \n",
      "Step 4:\n",
      "  A (E): [0.01 0.01 0.96 0.01 0.01]\n",
      "  B (N): [0.96 0.01 0.01 0.01 0.01] \n",
      "Step 5:\n",
      "  A (E): [0.01 0.01 0.96 0.01 0.01]\n",
      "  B (N): [0.96 0.01 0.01 0.01 0.01] \n",
      "Step 6:\n",
      "  A (S): [0.01 0.96 0.01 0.01 0.01]\n",
      "  B (N): [0.96 0.01 0.01 0.01 0.01] \n",
      "Step 7:\n",
      "  A (N): [0.96 0.01 0.01 0.01 0.01]\n",
      "  B (S): [0.01 0.96 0.01 0.01 0.01] **Slip!**\n",
      "Step 8:\n",
      "  A (X): [0.01 0.01 0.01 0.01 0.96]\n",
      "  B (X): [0.01 0.01 0.01 0.01 0.96] \n",
      "Step 9:\n",
      "  A (X): [0.01 0.01 0.01 0.01 0.96]\n",
      "  B (X): [0.01 0.01 0.01 0.01 0.96] \n",
      "Step 10:\n",
      "  A (X): [0.01 0.01 0.01 0.01 0.96]\n",
      "  B (X): [0.01 0.01 0.01 0.01 0.96] \n",
      "Step 11:\n",
      "  A (X): [0.01 0.01 0.01 0.01 0.96]\n",
      "  B (X): [0.01 0.01 0.01 0.01 0.96] \n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 1500x600 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import csv\n",
    "\n",
    "# visualization utils\n",
    "def plot_film_strip(history, save_filename=None):\n",
    "    n_steps = len(history)\n",
    "    max_cols = 6\n",
    "    n_rows = (n_steps + max_cols - 1) // max_cols\n",
    "    n_cols = min(n_steps, max_cols)\n",
    "    \n",
    "    fig, axes = plt.subplots(n_rows, n_cols, figsize=(n_cols*2.5, n_rows*3))\n",
    "    \n",
    "    if n_steps == 1: \n",
    "        axes_flat = [axes]\n",
    "    else:\n",
    "        axes_flat = axes.flatten()\n",
    "    \n",
    "    for t, state in enumerate(history):\n",
    "        ax_p, ay_p, bx_p, by_p, poss = state\n",
    "        ax = axes_flat[t]\n",
    "        \n",
    "        ax.set_xlim(-0.5, width-0.5)\n",
    "        ax.set_ylim(height-0.5, -0.5) \n",
    "        ax.set_xticks(np.arange(width))\n",
    "        ax.set_yticks(np.arange(height))\n",
    "        ax.grid(color=grid_color, linestyle='-', linewidth=2)\n",
    "        ax.set_xticklabels([]); ax.set_yticklabels([])\n",
    "        \n",
    "        # goal areas\n",
    "        ax.add_patch(plt.Rectangle((width-0.5, -0.5), 0.1, height, color=player_B_color, alpha=0.3))\n",
    "        ax.add_patch(plt.Rectangle((-0.6, -0.5), 0.1, height, color=player_A_color, alpha=0.3))\n",
    "\n",
    "        # players\n",
    "        ax.text(ay_p, ax_p, 'A', ha='center', va='center', fontsize=20, color='white', fontweight='bold',\n",
    "                bbox=dict(boxstyle=\"circle,pad=0.1\", fc=player_A_color, ec=player_A_color))\n",
    "        ax.text(by_p, bx_p, 'B', ha='center', va='center', fontsize=20, color='white', fontweight='bold',\n",
    "                bbox=dict(boxstyle=\"circle,pad=0.1\", fc=player_B_color, ec=player_B_color))\n",
    "        \n",
    "        # ball\n",
    "        if poss == 0: bx_ball, by_ball = ax_p - 0.3, ay_p + 0.3\n",
    "        else:         bx_ball, by_ball = bx_p - 0.3, by_p - 0.3\n",
    "        ax.plot(by_ball, bx_ball, 'o', color=ball_color, markersize=8, markeredgecolor='white')\n",
    "        \n",
    "        # axes title\n",
    "        ax.set_title(f\"Step {t}\", fontsize=12)\n",
    "        \n",
    "    for i in range(n_steps, len(axes_flat)):\n",
    "        axes_flat[i].axis('off')\n",
    "        \n",
    "    plt.tight_layout()\n",
    "    \n",
    "    # save figure\n",
    "    if save_filename:\n",
    "        plt.savefig(f'plots/{save_filename}', format='pdf', bbox_inches='tight')\n",
    "    \n",
    "    return fig\n",
    "\n",
    "def run_visual_episode(policy_a, save_csv_name=None):\n",
    "    ax, ay = 1, 0\n",
    "    bx, by = 1, width-1\n",
    "    poss = 0\n",
    "    history = []\n",
    "    log_rows = [] \n",
    "    \n",
    "    print(f\"Probabilities Format: [N, S, E, W, X]\")\n",
    "    \n",
    "    for step in range(12): \n",
    "        history.append((ax, ay, bx, by, poss))\n",
    "        s_idx = get_state_idx(ax, ay, bx, by, poss)\n",
    "        \n",
    "        p_a = policy_a[s_idx]\n",
    "        act_a = np.random.choice(num_acts, p=p_a)\n",
    "        \n",
    "        p_b = pi_NE_B[s_idx]\n",
    "        act_b = np.random.choice(num_acts, p=p_b)\n",
    "        \n",
    "        real_act_b = act_b\n",
    "        slip_txt = \"\"\n",
    "        is_slip = False\n",
    "        if np.random.rand() < B_slip_prob:\n",
    "            real_act_b = 4\n",
    "            if act_b != 4: \n",
    "                slip_txt = \"**Slip!**\"\n",
    "                is_slip = True\n",
    "            \n",
    "        p_a_str = \"[\" + \" \".join([f\"{p:.2f}\" for p in p_a]) + \"]\"\n",
    "        p_b_str = \"[\" + \" \".join([f\"{p:.2f}\" for p in p_b]) + \"]\"\n",
    "        \n",
    "        print(f\"Step {step}:\")\n",
    "        print(f\"  A ({act_labels[act_a]}): {p_a_str}\")\n",
    "        print(f\"  B ({act_labels[act_b]}): {p_b_str} {slip_txt}\")\n",
    "        \n",
    "        row = {\n",
    "            \"step\": step,\n",
    "            \"ax\": ax, \"ay\": ay, \"bx\": bx, \"by\": by, \"poss\": poss,\n",
    "            \"act_a\": act_labels[act_a],\n",
    "            \"act_b\": act_labels[act_b],\n",
    "            \"real_act_b\": act_labels[real_act_b],\n",
    "            \"slip\": is_slip,\n",
    "            \"p_a\": p_a.tolist(),\n",
    "            \"p_b\": p_b.tolist()\n",
    "        }\n",
    "        log_rows.append(row)\n",
    "        \n",
    "        next_s, r, done = get_next_state_reward_done(ax, ay, bx, by, poss, act_a, real_act_b)\n",
    "        ax, ay, bx, by, poss = next_s\n",
    "        \n",
    "        if done:\n",
    "            history.append((ax, ay, bx, by, poss))\n",
    "            print(f\"*** END: Reward {r} ***\")\n",
    "            log_rows.append({\n",
    "                \"step\": step + 1,\n",
    "                \"ax\": ax, \"ay\": ay, \"bx\": bx, \"by\": by, \"poss\": poss,\n",
    "                \"act_a\": \"END\", \"act_b\": \"END\", \"real_act_b\": \"END\", \"slip\": False,\n",
    "                \"p_a\": [], \"p_b\": []\n",
    "            })\n",
    "            break\n",
    "\n",
    "    # save csv\n",
    "    if save_csv_name:\n",
    "        csv_path = f'results/{save_csv_name}'\n",
    "        \n",
    "        with open(csv_path, 'w', newline='') as f:\n",
    "            writer = csv.writer(f)\n",
    "            header = [\"step\", \"ax\", \"ay\", \"bx\", \"by\", \"poss\", \"act_a\", \"act_b\", \"real_act_b\", \"slip\"]\n",
    "            header += [f\"p_a_{l}\" for l in act_labels]\n",
    "            header += [f\"p_b_{l}\" for l in act_labels]\n",
    "            \n",
    "            writer.writerow(header)\n",
    "            \n",
    "            for r in log_rows:\n",
    "                line = [r[\"step\"], r[\"ax\"], r[\"ay\"], r[\"bx\"], r[\"by\"], r[\"poss\"], \n",
    "                        r[\"act_a\"], r[\"act_b\"], r[\"real_act_b\"], r[\"slip\"]]\n",
    "                if r[\"p_a\"]:\n",
    "                    line += r[\"p_a\"] + r[\"p_b\"]\n",
    "                else:\n",
    "                    line += [\"\"] * (2 * num_acts)\n",
    "                writer.writerow(line)\n",
    "                            \n",
    "    return history\n",
    "\n",
    "hist_nash = run_visual_episode(pi_NE_A, save_csv_name=\"soccer/nash_history.csv\")\n",
    "fig = plot_film_strip(hist_nash, save_filename=\"soccer/nash_gameplay.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f48f496e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-21T14:39:28.265139Z",
     "iopub.status.busy": "2026-07-21T14:39:28.264821Z",
     "iopub.status.idle": "2026-07-21T14:39:29.140428Z",
     "shell.execute_reply": "2026-07-21T14:39:29.139423Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilities Format: [N, S, E, W, X]\n",
      "Step 0:\n",
      "  A (X): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (W): [0.01 0.01 0.01 0.96 0.01] \n",
      "Step 1:\n",
      "  A (E): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (X): [0.01 0.01 0.01 0.01 0.96] \n",
      "Step 2:\n",
      "  A (N): [0.06 0.59 0.03 0.16 0.16]\n",
      "  B (X): [0.01 0.05 0.01 0.47 0.45] \n",
      "Step 3:\n",
      "  A (X): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (E): [0.96 0.01 0.01 0.01 0.01] \n",
      "Step 4:\n",
      "  A (X): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (W): [0.01 0.01 0.01 0.96 0.01] \n",
      "Step 5:\n",
      "  A (X): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (N): [0.96 0.01 0.01 0.01 0.01] \n",
      "Step 6:\n",
      "  A (X): [0.01 0.61 0.04 0.17 0.17]\n",
      "  B (W): [0.01 0.32 0.01 0.65 0.01] \n",
      "Step 7:\n",
      "  A (S): [0.01 0.62 0.04 0.17 0.17]\n",
      "  B (N): [0.01 0.01 0.93 0.01 0.04] \n",
      "Step 8:\n",
      "  A (W): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (S): [0.01 0.96 0.01 0.01 0.01] \n",
      "Step 9:\n",
      "  A (E): [0.01 0.49 0.05 0.23 0.23]\n",
      "  B (W): [0.01 0.01 0.60 0.37 0.01] \n",
      "Step 10:\n",
      "  A (S): [0.01 0.49 0.05 0.23 0.23]\n",
      "  B (E): [0.01 0.01 0.60 0.37 0.01] \n",
      "Step 11:\n",
      "  A (W): [0.01 0.01 0.10 0.44 0.44]\n",
      "  B (S): [0.01 0.96 0.01 0.01 0.01] \n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x600 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# run episode using the global pi_afraid\n",
    "hist_afraid = run_visual_episode(\n",
    "    pi_afraid, \n",
    "    save_csv_name=\"soccer/afraid_history.csv\"\n",
    ")\n",
    "fig = plot_film_strip(\n",
    "    hist_afraid, \n",
    "    save_filename=\"soccer/afraid_gameplay.pdf\"\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "26c3a92d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-21T14:39:29.145144Z",
     "iopub.status.busy": "2026-07-21T14:39:29.144950Z",
     "iopub.status.idle": "2026-07-21T14:52:00.608549Z",
     "shell.execute_reply": "2026-07-21T14:52:00.607630Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running Martingale Test (Eps 0.05 -> 0.5)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eps=0.05 | Avg Time=1431.8 (+/- 103.3)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eps=0.10 | Avg Time=369.7 (+/- 39.2)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_100502/3243956245.py:30: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  martingale *= lr\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eps=0.20 | Avg Time=140.1 (+/- 18.0)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eps=0.30 | Avg Time=62.6 (+/- 8.4)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eps=0.50 | Avg Time=18.0 (+/- 3.3)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "def run_martingale_test(epsilon, threshold, max_steps=5000):\n",
    "    ax, ay = 1, 0\n",
    "    bx, by = 1, width-1\n",
    "    poss = 0\n",
    "    \n",
    "    martingale = 1.0\n",
    "    detected_step = None\n",
    "    steps = 0\n",
    "    \n",
    "    while steps < max_steps:\n",
    "        s_idx = get_state_idx(ax, ay, bx, by, poss)\n",
    "        \n",
    "        # get base policies\n",
    "        pi_nash = pi_NE_A[s_idx]\n",
    "        # pi_afraid = pi_afraid[s_idx]\n",
    "        p_afraid = pi_afraid[s_idx]\n",
    "        \n",
    "        # construct true mixture strategy\n",
    "        pi_true = (1 - epsilon) * pi_nash + epsilon * p_afraid\n",
    "        \n",
    "        # sample action\n",
    "        act_a = np.random.choice(num_acts, p=pi_true)\n",
    "        \n",
    "        # detector\n",
    "        prob_h0 = pi_nash[act_a]\n",
    "        prob_h1 = (1 - epsilon) * pi_nash[act_a] + epsilon * p_afraid[act_a]\n",
    "        lr = prob_h1 / prob_h0\n",
    "        martingale *= lr\n",
    "            \n",
    "        # check threshold\n",
    "        if detected_step is None and martingale > threshold:\n",
    "            detected_step = steps + 1\n",
    "            \n",
    "        # opponent\n",
    "        act_b = np.random.choice(num_acts, p=pi_NE_B[s_idx])\n",
    "        real_act_b = act_b\n",
    "        if np.random.rand() < B_slip_prob: real_act_b = 4\n",
    "            \n",
    "        next_s, _, done = get_next_state_reward_done(ax, ay, bx, by, poss, act_a, real_act_b)\n",
    "        ax, ay, bx, by, poss = next_s\n",
    "        steps += 1\n",
    "        if done: \n",
    "             ax, ay = 1, 0; bx, by = 1, width-1; poss = 0\n",
    "            \n",
    "    if detected_step is None: detected_step = max_steps\n",
    "    return detected_step\n",
    "\n",
    "# parameters\n",
    "threshold = 20.0 \n",
    "epsilons = [0.05, 0.1, 0.2, 0.3, 0.5] \n",
    "n_trials = 150\n",
    "max_steps = 25000\n",
    "\n",
    "empirical_times = []\n",
    "std_errs = []\n",
    "\n",
    "print(f\"\\nRunning Martingale Test (Eps 0.05 -> 0.5)\")\n",
    "\n",
    "for eps in epsilons:\n",
    "    detections = []\n",
    "    for _ in range(n_trials):\n",
    "        dt = run_martingale_test(eps, threshold, max_steps)\n",
    "        detections.append(dt)\n",
    "    \n",
    "    mean_time = np.mean(detections)\n",
    "    std_err = np.std(detections) / np.sqrt(n_trials)\n",
    "    empirical_times.append(mean_time)\n",
    "    std_errs.append(std_err)\n",
    "    print(f\"Eps={eps:.2f} | Avg Time={mean_time:.1f} (+/- {std_err:.1f})\")\n",
    "\n",
    "# theoretical scaling: T ~ K / epsilon^2\n",
    "# Anchor to the last point\n",
    "anchor_idx = -1 \n",
    "K = empirical_times[anchor_idx] * (epsilons[anchor_idx]**2)\n",
    "theoretical_times = [K / (e**2) for e in epsilons]\n",
    "\n",
    "# plotting\n",
    "plt.figure(figsize=(5, 3))\n",
    "plt.errorbar(epsilons, empirical_times, yerr=std_errs, fmt='o-', label='Empirical', color='#1f77b4', capsize=5)\n",
    "plt.plot(epsilons, theoretical_times, '--', label='Theoretical', color='#2ca02c', linewidth=2)\n",
    "\n",
    "plt.ylim(10,2000)\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.xscale('linear')\n",
    "plt.xlabel(r'Mixture Parameter $\\varepsilon$')\n",
    "plt.ylabel('Avg Detection Time')\n",
    "plt.grid(True, which='both', alpha=0.3)\n",
    "plt.legend()\n",
    "\n",
    "plt.savefig('plots/soccer/scaling.pdf')"
   ]
  }
 ],
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