{
  "cells": [
    {
      "accuracy_relation": "equal",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "5/9",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "0",
      "planner_discovery": "5/9",
      "planner_profiles": [
        [
          0,
          0,
          2
        ],
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          1
        ],
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "5/9",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          0,
          2
        ],
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          1
        ],
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "2/3",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "0",
      "planner_discovery": "2/3",
      "planner_profiles": [
        [
          0,
          1,
          1
        ],
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "2/3",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          1,
          1
        ],
        [
          0,
          2,
          0
        ],
        [
          1,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "2/3",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "1/9",
      "planner_discovery": "7/9",
      "planner_profiles": [
        [
          0,
          1,
          1
        ],
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "7/9",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "3/4",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "1/12",
      "planner_discovery": "5/6",
      "planner_profiles": [
        [
          0,
          1,
          1
        ],
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "5/6",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "1/18",
      "planner_discovery": "8/9",
      "planner_profiles": [
        [
          0,
          1,
          1
        ],
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "8/9",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "3/4",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "3/4",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "3/4",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "3/4",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "3/4",
      "planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "3/4",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "5/6",
      "planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "5/6",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ],
        [
          1,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "3/4",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/8",
      "planner_discovery": "7/8",
      "planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "7/8",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/12",
      "planner_discovery": "11/12",
      "planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "11/12",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "8/9",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "8/9",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "8/9",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "8/9",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "8/9",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "8/9",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "8/9",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "8/9",
      "planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "8/9",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "11/12",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "11/12",
      "planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "unconditional_planner_discovery": "11/12",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/9",
      "planner_discovery": "17/18",
      "planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "17/18",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "15/16",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "15/16",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "15/16",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "15/16",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "23/24",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "23/24",
      "planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "unconditional_planner_discovery": "23/24",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "35/36",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "35/36",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "35/36",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "35/36",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "35/36",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "35/36",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "35/36",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "35/36",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "35/36",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "35/36",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "35/36",
      "planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "35/36",
      "unconditional_planner_profiles": [
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 2,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "35/36",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "35/36",
      "planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "35/36",
      "unconditional_planner_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "19/27",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "0",
      "planner_discovery": "19/27",
      "planner_profiles": [
        [
          0,
          0,
          3
        ],
        [
          0,
          1,
          2
        ],
        [
          1,
          0,
          2
        ],
        [
          1,
          1,
          1
        ],
        [
          2,
          0,
          1
        ],
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "19/27",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          0,
          3
        ],
        [
          0,
          1,
          2
        ],
        [
          1,
          0,
          2
        ],
        [
          1,
          1,
          1
        ],
        [
          2,
          0,
          1
        ],
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "2/3",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "1/9",
      "planner_discovery": "7/9",
      "planner_profiles": [
        [
          0,
          1,
          2
        ],
        [
          1,
          1,
          1
        ],
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "7/9",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          1
        ],
        [
          1,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "2/3",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "5/27",
      "planner_discovery": "23/27",
      "planner_profiles": [
        [
          0,
          1,
          2
        ],
        [
          1,
          1,
          1
        ],
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ],
      "unconditional_planner_discovery": "23/27",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "3/4",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "5/36",
      "planner_discovery": "8/9",
      "planner_profiles": [
        [
          0,
          1,
          2
        ],
        [
          1,
          1,
          1
        ],
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ],
      "unconditional_planner_discovery": "8/9",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "5/54",
      "planner_discovery": "25/27",
      "planner_profiles": [
        [
          0,
          1,
          2
        ],
        [
          1,
          1,
          1
        ],
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ],
      "unconditional_planner_discovery": "25/27",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "7/8",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "7/8",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "7/8",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "7/8",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "7/8",
      "planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "7/8",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/12",
      "planner_discovery": "11/12",
      "planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          1,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "11/12",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "7/8",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/16",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          3,
          0
        ],
        [
          1,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/8",
      "planner_discovery": "23/24",
      "planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ],
      "unconditional_planner_discovery": "23/24",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "26/27",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "26/27",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "26/27",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "26/27",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "26/27",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "26/27",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "26/27",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "26/27",
      "planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "26/27",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "35/36",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "35/36",
      "planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "unconditional_planner_discovery": "35/36",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "17/18",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/27",
      "planner_discovery": "53/54",
      "planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          1,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "53/54",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "63/64",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "63/64",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "63/64",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "63/64",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "63/64",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "63/64",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "63/64",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "63/64",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "63/64",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "63/64",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "63/64",
      "planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "63/64",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "95/96",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "95/96",
      "planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "95/96",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          2,
          0
        ],
        [
          2,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "215/216",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "215/216",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "215/216",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "215/216",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "215/216",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "215/216",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "215/216",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "215/216",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "215/216",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "215/216",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "215/216",
      "planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "215/216",
      "unconditional_planner_profiles": [
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 3,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "215/216",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "215/216",
      "planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "215/216",
      "unconditional_planner_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          1,
          0
        ],
        [
          3,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "65/81",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "0",
      "planner_discovery": "65/81",
      "planner_profiles": [
        [
          0,
          0,
          4
        ],
        [
          0,
          1,
          3
        ],
        [
          1,
          0,
          3
        ],
        [
          1,
          1,
          2
        ],
        [
          2,
          0,
          2
        ],
        [
          2,
          1,
          1
        ],
        [
          3,
          0,
          1
        ],
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "65/81",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          0,
          4
        ],
        [
          0,
          1,
          3
        ],
        [
          1,
          0,
          3
        ],
        [
          1,
          1,
          2
        ],
        [
          2,
          0,
          2
        ],
        [
          2,
          1,
          1
        ],
        [
          3,
          0,
          1
        ],
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "7/9",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "2/27",
      "planner_discovery": "23/27",
      "planner_profiles": [
        [
          0,
          1,
          3
        ],
        [
          1,
          1,
          2
        ],
        [
          2,
          1,
          1
        ],
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "23/27",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          2,
          2
        ],
        [
          1,
          2,
          1
        ],
        [
          2,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "7/9",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "10/81",
      "planner_discovery": "73/81",
      "planner_profiles": [
        [
          0,
          1,
          3
        ],
        [
          1,
          1,
          2
        ],
        [
          2,
          1,
          1
        ],
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "73/81",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          3,
          1
        ],
        [
          0,
          4,
          0
        ],
        [
          1,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "3/4",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "19/108",
      "planner_discovery": "25/27",
      "planner_profiles": [
        [
          0,
          1,
          3
        ],
        [
          1,
          1,
          2
        ],
        [
          2,
          1,
          1
        ],
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          0,
          4,
          0
        ]
      ],
      "unconditional_planner_discovery": "25/27",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          4,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": true,
      "equilibrium_wedge": "19/162",
      "planner_discovery": "77/81",
      "planner_profiles": [
        [
          0,
          1,
          3
        ],
        [
          1,
          1,
          2
        ],
        [
          2,
          1,
          1
        ],
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/3",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          4,
          0
        ]
      ],
      "unconditional_planner_discovery": "77/81",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          4,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "15/16",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "15/16",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "15/16",
      "planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "15/16",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "11/12",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/24",
      "planner_discovery": "23/24",
      "planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          2,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "23/24",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "7/8",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "3/32",
      "planner_discovery": "31/32",
      "planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          1,
          3,
          0
        ]
      ],
      "unconditional_planner_discovery": "31/32",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "5/6",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "7/48",
      "planner_discovery": "47/48",
      "planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "1/2",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          0,
          4,
          0
        ]
      ],
      "unconditional_planner_discovery": "47/48",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          0,
          4,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "80/81",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "80/81",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "80/81",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "80/81",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "80/81",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "80/81",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "80/81",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "80/81",
      "planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "80/81",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "107/108",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "107/108",
      "planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "unconditional_planner_discovery": "107/108",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          1,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "17/18",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "4/81",
      "planner_discovery": "161/162",
      "planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "2/3",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          1,
          3,
          0
        ]
      ],
      "unconditional_planner_discovery": "161/162",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          1,
          3,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "255/256",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "255/256",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "255/256",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "255/256",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "255/256",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "255/256",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "255/256",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "255/256",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "255/256",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "255/256",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "255/256",
      "planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "255/256",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "shared-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": false,
      "best_equilibrium_discovery": "95/96",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "1/128",
      "planner_discovery": "383/384",
      "planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "private_accuracy": "3/4",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [
        [
          2,
          2,
          0
        ]
      ],
      "unconditional_planner_discovery": "383/384",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          2,
          2,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "1295/1296",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "1295/1296",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "1/3",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "1295/1296",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "1295/1296",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "1295/1296",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "1/2",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "1295/1296",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "1295/1296",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "1295/1296",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "2/3",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "1295/1296",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "private-higher",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "1295/1296",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "1295/1296",
      "planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "3/4",
      "strict_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "unconditional_planner_discovery": "1295/1296",
      "unconditional_planner_profiles": [
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          4,
          0,
          0
        ]
      ]
    },
    {
      "accuracy_relation": "equal",
      "agents": 4,
      "all_equilibria_planner_optimal": true,
      "best_equilibrium_discovery": "1295/1296",
      "conditional_gain": "0",
      "contrarian_is_planner_optimal": false,
      "equilibrium_wedge": "0",
      "planner_discovery": "1295/1296",
      "planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "private_accuracy": "5/6",
      "shared_accuracy": "5/6",
      "strict_equilibrium_profiles": [],
      "unconditional_planner_discovery": "1295/1296",
      "unconditional_planner_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ],
      "weak_equilibrium_profiles": [
        [
          3,
          1,
          0
        ],
        [
          4,
          0,
          0
        ]
      ]
    }
  ],
  "run_id": "20260721T222047Z_DD-014_f5f099a8_ea0276dd16",
  "schema_version": 1
}