Mechanism Design HW1

プログラム本体はここ



In [3]:

    
# !/usr/bin/python
# -*- encoding: utf-8 -*-

%matplotlib inline
from __future__ import division, print_function
import math
import numpy as np
from homework1 import *
np.set_printoptions(threshold=np.nan)

問1 プレイヤーが2人の場合の一位価格オークションのナッシュ均衡を求める

入札額は20の倍数に限る。プレイヤー1の財の私的価値は80, プレイヤー2は40とする。



In [5]:

    
players = [0, 1]
strategies = range(0, 101, 20)

def payoff_func(str_pattern):
    return [80 - str_pattern[0], 0] if str_pattern[0] >= str_pattern[1] else [0, 40 - str_pattern[1]]

print(find_nash_equilibrium(players, strategies, payoff_func))









    



strategy: [0, 0] deviate to: [0, 20]
strategy: [0, 20] deviate to: [20, 20]
strategy: [0, 40] deviate to: [40, 40]
strategy: [0, 60] deviate to: [60, 60]
strategy: [0, 80] deviate to: [0, 0]
strategy: [0, 100] deviate to: [0, 0]
strategy: [20, 0] deviate to: [0, 0]
strategy: (20, 20) deviate to: nothing
strategy: [20, 40] deviate to: [40, 40]
strategy: [20, 60] deviate to: [60, 60]
strategy: [20, 80] deviate to: [20, 0]
strategy: [20, 100] deviate to: [20, 0]
strategy: [40, 0] deviate to: [0, 0]
strategy: [40, 20] deviate to: [20, 20]
strategy: (40, 40) deviate to: nothing
strategy: [40, 60] deviate to: [60, 60]
strategy: [40, 80] deviate to: [40, 0]
strategy: [40, 100] deviate to: [40, 0]
strategy: [60, 0] deviate to: [0, 0]
strategy: [60, 20] deviate to: [20, 20]
strategy: [60, 40] deviate to: [40, 40]
strategy: (60, 60) deviate to: nothing
strategy: [60, 80] deviate to: [60, 0]
strategy: [60, 100] deviate to: [60, 0]
strategy: [80, 0] deviate to: [0, 0]
strategy: [80, 20] deviate to: [20, 20]
strategy: [80, 40] deviate to: [40, 40]
strategy: [80, 60] deviate to: [60, 60]
strategy: (80, 80) deviate to: nothing
strategy: [80, 100] deviate to: [80, 0]
strategy: [100, 0] deviate to: [0, 0]
strategy: [100, 20] deviate to: [0, 20]
strategy: [100, 40] deviate to: [0, 40]
strategy: [100, 60] deviate to: [0, 60]
strategy: [100, 80] deviate to: [0, 80]
strategy: [100, 100] deviate to: [0, 100]
[(20, 20), (40, 40), (60, 60), (80, 80)]

ナッシュ均衡は(20, 20), (40, 40), (60, 60), (80, 80)の4つ。入札額が離散的な値しかとれない場合、(20, 20)も均衡になる。

問2 プレイヤーが3人の場合の一位価格オークションのナッシュ均衡を求める

入札額は20の倍数に限る。プレイヤー1の財の私的価値は120, プレイヤー2は80, プレイヤー3は40とする。



In [7]:

    
player_num = 3
players = range(player_num)
strategies = range(0, 140, 20)

def payoff_func(str_pattern):
    # NumPyのargmaxはタイがある場合は最初の1つのindexを返すので、このままで大丈夫
    max_index = np.argmax(str_pattern)

    if max_index == 0:
        return [180 - str_pattern[0], 0, 0]

    elif max_index == 1:
        return [0, 140 - str_pattern[1], 0]

    elif max_index == 2:
        return [100 - str_pattern[2], 0, 0]

    else:
        print("ERROR")

print(find_nash_equilibrium(players, strategies, payoff_func))









    



strategy: [0, 0, 0] deviate to: [0, 20, 0]
strategy: [0, 0, 20] deviate to: [20, 0, 20]
strategy: [0, 0, 40] deviate to: [40, 0, 40]
strategy: [0, 0, 60] deviate to: [60, 0, 60]
strategy: [0, 0, 80] deviate to: [80, 0, 80]
strategy: [0, 0, 100] deviate to: [100, 0, 100]
strategy: [0, 0, 120] deviate to: [120, 0, 120]
strategy: [0, 20, 0] deviate to: [20, 20, 0]
strategy: [0, 20, 20] deviate to: [20, 20, 20]
strategy: [0, 20, 40] deviate to: [40, 20, 40]
strategy: [0, 20, 60] deviate to: [60, 20, 60]
strategy: [0, 20, 80] deviate to: [80, 20, 80]
strategy: [0, 20, 100] deviate to: [100, 20, 100]
strategy: [0, 20, 120] deviate to: [120, 20, 120]
strategy: [0, 40, 0] deviate to: [40, 40, 0]
strategy: [0, 40, 20] deviate to: [40, 40, 20]
strategy: [0, 40, 40] deviate to: [40, 40, 40]
strategy: [0, 40, 60] deviate to: [60, 40, 60]
strategy: [0, 40, 80] deviate to: [80, 40, 80]
strategy: [0, 40, 100] deviate to: [100, 40, 100]
strategy: [0, 40, 120] deviate to: [120, 40, 120]
strategy: [0, 60, 0] deviate to: [60, 60, 0]
strategy: [0, 60, 20] deviate to: [60, 60, 20]
strategy: [0, 60, 40] deviate to: [60, 60, 40]
strategy: [0, 60, 60] deviate to: [60, 60, 60]
strategy: [0, 60, 80] deviate to: [80, 60, 80]
strategy: [0, 60, 100] deviate to: [100, 60, 100]
strategy: [0, 60, 120] deviate to: [120, 60, 120]
strategy: [0, 80, 0] deviate to: [80, 80, 0]
strategy: [0, 80, 20] deviate to: [80, 80, 20]
strategy: [0, 80, 40] deviate to: [80, 80, 40]
strategy: [0, 80, 60] deviate to: [80, 80, 60]
strategy: [0, 80, 80] deviate to: [80, 80, 80]
strategy: [0, 80, 100] deviate to: [100, 80, 100]
strategy: [0, 80, 120] deviate to: [120, 80, 120]
strategy: [0, 100, 0] deviate to: [100, 100, 0]
strategy: [0, 100, 20] deviate to: [100, 100, 20]
strategy: [0, 100, 40] deviate to: [100, 100, 40]
strategy: [0, 100, 60] deviate to: [100, 100, 60]
strategy: [0, 100, 80] deviate to: [100, 100, 80]
strategy: [0, 100, 100] deviate to: [100, 100, 100]
strategy: [0, 100, 120] deviate to: [120, 100, 120]
strategy: [0, 120, 0] deviate to: [120, 120, 0]
strategy: [0, 120, 20] deviate to: [120, 120, 20]
strategy: [0, 120, 40] deviate to: [120, 120, 40]
strategy: [0, 120, 60] deviate to: [120, 120, 60]
strategy: [0, 120, 80] deviate to: [120, 120, 80]
strategy: [0, 120, 100] deviate to: [120, 120, 100]
strategy: [0, 120, 120] deviate to: [120, 120, 120]
strategy: [20, 0, 0] deviate to: [0, 0, 0]
strategy: [20, 0, 20] deviate to: [20, 40, 20]
strategy: [20, 0, 40] deviate to: [40, 0, 40]
strategy: [20, 0, 60] deviate to: [60, 0, 60]
strategy: [20, 0, 80] deviate to: [80, 0, 80]
strategy: [20, 0, 100] deviate to: [100, 0, 100]
strategy: [20, 0, 120] deviate to: [120, 0, 120]
strategy: [20, 20, 0] deviate to: [20, 40, 0]
strategy: [20, 20, 20] deviate to: [20, 40, 20]
strategy: [20, 20, 40] deviate to: [40, 20, 40]
strategy: [20, 20, 60] deviate to: [60, 20, 60]
strategy: [20, 20, 80] deviate to: [80, 20, 80]
strategy: [20, 20, 100] deviate to: [100, 20, 100]
strategy: [20, 20, 120] deviate to: [120, 20, 120]
strategy: [20, 40, 0] deviate to: [40, 40, 0]
strategy: [20, 40, 20] deviate to: [40, 40, 20]
strategy: [20, 40, 40] deviate to: [40, 40, 40]
strategy: [20, 40, 60] deviate to: [60, 40, 60]
strategy: [20, 40, 80] deviate to: [80, 40, 80]
strategy: [20, 40, 100] deviate to: [100, 40, 100]
strategy: [20, 40, 120] deviate to: [120, 40, 120]
strategy: [20, 60, 0] deviate to: [60, 60, 0]
strategy: [20, 60, 20] deviate to: [60, 60, 20]
strategy: [20, 60, 40] deviate to: [60, 60, 40]
strategy: [20, 60, 60] deviate to: [60, 60, 60]
strategy: [20, 60, 80] deviate to: [80, 60, 80]
strategy: [20, 60, 100] deviate to: [100, 60, 100]
strategy: [20, 60, 120] deviate to: [120, 60, 120]
strategy: [20, 80, 0] deviate to: [80, 80, 0]
strategy: [20, 80, 20] deviate to: [80, 80, 20]
strategy: [20, 80, 40] deviate to: [80, 80, 40]
strategy: [20, 80, 60] deviate to: [80, 80, 60]
strategy: [20, 80, 80] deviate to: [80, 80, 80]
strategy: [20, 80, 100] deviate to: [100, 80, 100]
strategy: [20, 80, 120] deviate to: [120, 80, 120]
strategy: [20, 100, 0] deviate to: [100, 100, 0]
strategy: [20, 100, 20] deviate to: [100, 100, 20]
strategy: [20, 100, 40] deviate to: [100, 100, 40]
strategy: [20, 100, 60] deviate to: [100, 100, 60]
strategy: [20, 100, 80] deviate to: [100, 100, 80]
strategy: [20, 100, 100] deviate to: [100, 100, 100]
strategy: [20, 100, 120] deviate to: [120, 100, 120]
strategy: [20, 120, 0] deviate to: [120, 120, 0]
strategy: [20, 120, 20] deviate to: [120, 120, 20]
strategy: [20, 120, 40] deviate to: [120, 120, 40]
strategy: [20, 120, 60] deviate to: [120, 120, 60]
strategy: [20, 120, 80] deviate to: [120, 120, 80]
strategy: [20, 120, 100] deviate to: [120, 120, 100]
strategy: [20, 120, 120] deviate to: [120, 120, 120]
strategy: [40, 0, 0] deviate to: [0, 0, 0]
strategy: [40, 0, 20] deviate to: [20, 0, 20]
strategy: [40, 0, 40] deviate to: [40, 60, 40]
strategy: [40, 0, 60] deviate to: [60, 0, 60]
strategy: [40, 0, 80] deviate to: [80, 0, 80]
strategy: [40, 0, 100] deviate to: [100, 0, 100]
strategy: [40, 0, 120] deviate to: [120, 0, 120]
strategy: [40, 20, 0] deviate to: [20, 20, 0]
strategy: [40, 20, 20] deviate to: [20, 20, 20]
strategy: [40, 20, 40] deviate to: [40, 60, 40]
strategy: [40, 20, 60] deviate to: [60, 20, 60]
strategy: [40, 20, 80] deviate to: [80, 20, 80]
strategy: [40, 20, 100] deviate to: [100, 20, 100]
strategy: [40, 20, 120] deviate to: [120, 20, 120]
strategy: [40, 40, 0] deviate to: [40, 60, 0]
strategy: [40, 40, 20] deviate to: [40, 60, 20]
strategy: [40, 40, 40] deviate to: [40, 60, 40]
strategy: [40, 40, 60] deviate to: [60, 40, 60]
strategy: [40, 40, 80] deviate to: [80, 40, 80]
strategy: [40, 40, 100] deviate to: [100, 40, 100]
strategy: [40, 40, 120] deviate to: [120, 40, 120]
strategy: [40, 60, 0] deviate to: [60, 60, 0]
strategy: [40, 60, 20] deviate to: [60, 60, 20]
strategy: [40, 60, 40] deviate to: [60, 60, 40]
strategy: [40, 60, 60] deviate to: [60, 60, 60]
strategy: [40, 60, 80] deviate to: [80, 60, 80]
strategy: [40, 60, 100] deviate to: [100, 60, 100]
strategy: [40, 60, 120] deviate to: [120, 60, 120]
strategy: [40, 80, 0] deviate to: [80, 80, 0]
strategy: [40, 80, 20] deviate to: [80, 80, 20]
strategy: [40, 80, 40] deviate to: [80, 80, 40]
strategy: [40, 80, 60] deviate to: [80, 80, 60]
strategy: [40, 80, 80] deviate to: [80, 80, 80]
strategy: [40, 80, 100] deviate to: [100, 80, 100]
strategy: [40, 80, 120] deviate to: [120, 80, 120]
strategy: [40, 100, 0] deviate to: [100, 100, 0]
strategy: [40, 100, 20] deviate to: [100, 100, 20]
strategy: [40, 100, 40] deviate to: [100, 100, 40]
strategy: [40, 100, 60] deviate to: [100, 100, 60]
strategy: [40, 100, 80] deviate to: [100, 100, 80]
strategy: [40, 100, 100] deviate to: [100, 100, 100]
strategy: [40, 100, 120] deviate to: [120, 100, 120]
strategy: [40, 120, 0] deviate to: [120, 120, 0]
strategy: [40, 120, 20] deviate to: [120, 120, 20]
strategy: [40, 120, 40] deviate to: [120, 120, 40]
strategy: [40, 120, 60] deviate to: [120, 120, 60]
strategy: [40, 120, 80] deviate to: [120, 120, 80]
strategy: [40, 120, 100] deviate to: [120, 120, 100]
strategy: [40, 120, 120] deviate to: [120, 120, 120]
strategy: [60, 0, 0] deviate to: [0, 0, 0]
strategy: [60, 0, 20] deviate to: [20, 0, 20]
strategy: [60, 0, 40] deviate to: [40, 0, 40]
strategy: [60, 0, 60] deviate to: [60, 80, 60]
strategy: [60, 0, 80] deviate to: [80, 0, 80]
strategy: [60, 0, 100] deviate to: [100, 0, 100]
strategy: [60, 0, 120] deviate to: [120, 0, 120]
strategy: [60, 20, 0] deviate to: [20, 20, 0]
strategy: [60, 20, 20] deviate to: [20, 20, 20]
strategy: [60, 20, 40] deviate to: [40, 20, 40]
strategy: [60, 20, 60] deviate to: [60, 80, 60]
strategy: [60, 20, 80] deviate to: [80, 20, 80]
strategy: [60, 20, 100] deviate to: [100, 20, 100]
strategy: [60, 20, 120] deviate to: [120, 20, 120]
strategy: [60, 40, 0] deviate to: [40, 40, 0]
strategy: [60, 40, 20] deviate to: [40, 40, 20]
strategy: [60, 40, 40] deviate to: [40, 40, 40]
strategy: [60, 40, 60] deviate to: [60, 80, 60]
strategy: [60, 40, 80] deviate to: [80, 40, 80]
strategy: [60, 40, 100] deviate to: [100, 40, 100]
strategy: [60, 40, 120] deviate to: [120, 40, 120]
strategy: [60, 60, 0] deviate to: [60, 80, 0]
strategy: [60, 60, 20] deviate to: [60, 80, 20]
strategy: [60, 60, 40] deviate to: [60, 80, 40]
strategy: [60, 60, 60] deviate to: [60, 80, 60]
strategy: [60, 60, 80] deviate to: [80, 60, 80]
strategy: [60, 60, 100] deviate to: [100, 60, 100]
strategy: [60, 60, 120] deviate to: [120, 60, 120]
strategy: [60, 80, 0] deviate to: [80, 80, 0]
strategy: [60, 80, 20] deviate to: [80, 80, 20]
strategy: [60, 80, 40] deviate to: [80, 80, 40]
strategy: [60, 80, 60] deviate to: [80, 80, 60]
strategy: [60, 80, 80] deviate to: [80, 80, 80]
strategy: [60, 80, 100] deviate to: [100, 80, 100]
strategy: [60, 80, 120] deviate to: [120, 80, 120]
strategy: [60, 100, 0] deviate to: [100, 100, 0]
strategy: [60, 100, 20] deviate to: [100, 100, 20]
strategy: [60, 100, 40] deviate to: [100, 100, 40]
strategy: [60, 100, 60] deviate to: [100, 100, 60]
strategy: [60, 100, 80] deviate to: [100, 100, 80]
strategy: [60, 100, 100] deviate to: [100, 100, 100]
strategy: [60, 100, 120] deviate to: [120, 100, 120]
strategy: [60, 120, 0] deviate to: [120, 120, 0]
strategy: [60, 120, 20] deviate to: [120, 120, 20]
strategy: [60, 120, 40] deviate to: [120, 120, 40]
strategy: [60, 120, 60] deviate to: [120, 120, 60]
strategy: [60, 120, 80] deviate to: [120, 120, 80]
strategy: [60, 120, 100] deviate to: [120, 120, 100]
strategy: [60, 120, 120] deviate to: [120, 120, 120]
strategy: [80, 0, 0] deviate to: [0, 0, 0]
strategy: [80, 0, 20] deviate to: [20, 0, 20]
strategy: [80, 0, 40] deviate to: [40, 0, 40]
strategy: [80, 0, 60] deviate to: [60, 0, 60]
strategy: [80, 0, 80] deviate to: [80, 100, 80]
strategy: [80, 0, 100] deviate to: [100, 0, 100]
strategy: [80, 0, 120] deviate to: [120, 0, 120]
strategy: [80, 20, 0] deviate to: [20, 20, 0]
strategy: [80, 20, 20] deviate to: [20, 20, 20]
strategy: [80, 20, 40] deviate to: [40, 20, 40]
strategy: [80, 20, 60] deviate to: [60, 20, 60]
strategy: [80, 20, 80] deviate to: [80, 100, 80]
strategy: [80, 20, 100] deviate to: [100, 20, 100]
strategy: [80, 20, 120] deviate to: [120, 20, 120]
strategy: [80, 40, 0] deviate to: [40, 40, 0]
strategy: [80, 40, 20] deviate to: [40, 40, 20]
strategy: [80, 40, 40] deviate to: [40, 40, 40]
strategy: [80, 40, 60] deviate to: [60, 40, 60]
strategy: [80, 40, 80] deviate to: [80, 100, 80]
strategy: [80, 40, 100] deviate to: [100, 40, 100]
strategy: [80, 40, 120] deviate to: [120, 40, 120]
strategy: [80, 60, 0] deviate to: [60, 60, 0]
strategy: [80, 60, 20] deviate to: [60, 60, 20]
strategy: [80, 60, 40] deviate to: [60, 60, 40]
strategy: [80, 60, 60] deviate to: [60, 60, 60]
strategy: [80, 60, 80] deviate to: [80, 100, 80]
strategy: [80, 60, 100] deviate to: [100, 60, 100]
strategy: [80, 60, 120] deviate to: [120, 60, 120]
strategy: [80, 80, 0] deviate to: [80, 100, 0]
strategy: [80, 80, 20] deviate to: [80, 100, 20]
strategy: [80, 80, 40] deviate to: [80, 100, 40]
strategy: [80, 80, 60] deviate to: [80, 100, 60]
strategy: [80, 80, 80] deviate to: [80, 100, 80]
strategy: [80, 80, 100] deviate to: [100, 80, 100]
strategy: [80, 80, 120] deviate to: [120, 80, 120]
strategy: [80, 100, 0] deviate to: [100, 100, 0]
strategy: [80, 100, 20] deviate to: [100, 100, 20]
strategy: [80, 100, 40] deviate to: [100, 100, 40]
strategy: [80, 100, 60] deviate to: [100, 100, 60]
strategy: [80, 100, 80] deviate to: [100, 100, 80]
strategy: [80, 100, 100] deviate to: [100, 100, 100]
strategy: [80, 100, 120] deviate to: [120, 100, 120]
strategy: [80, 120, 0] deviate to: [120, 120, 0]
strategy: [80, 120, 20] deviate to: [120, 120, 20]
strategy: [80, 120, 40] deviate to: [120, 120, 40]
strategy: [80, 120, 60] deviate to: [120, 120, 60]
strategy: [80, 120, 80] deviate to: [120, 120, 80]
strategy: [80, 120, 100] deviate to: [120, 120, 100]
strategy: [80, 120, 120] deviate to: [120, 120, 120]
strategy: [100, 0, 0] deviate to: [0, 0, 0]
strategy: [100, 0, 20] deviate to: [20, 0, 20]
strategy: [100, 0, 40] deviate to: [40, 0, 40]
strategy: [100, 0, 60] deviate to: [60, 0, 60]
strategy: [100, 0, 80] deviate to: [80, 0, 80]
strategy: [100, 0, 100] deviate to: [100, 120, 100]
strategy: [100, 0, 120] deviate to: [120, 0, 120]
strategy: [100, 20, 0] deviate to: [20, 20, 0]
strategy: [100, 20, 20] deviate to: [20, 20, 20]
strategy: [100, 20, 40] deviate to: [40, 20, 40]
strategy: [100, 20, 60] deviate to: [60, 20, 60]
strategy: [100, 20, 80] deviate to: [80, 20, 80]
strategy: [100, 20, 100] deviate to: [100, 120, 100]
strategy: [100, 20, 120] deviate to: [120, 20, 120]
strategy: [100, 40, 0] deviate to: [40, 40, 0]
strategy: [100, 40, 20] deviate to: [40, 40, 20]
strategy: [100, 40, 40] deviate to: [40, 40, 40]
strategy: [100, 40, 60] deviate to: [60, 40, 60]
strategy: [100, 40, 80] deviate to: [80, 40, 80]
strategy: [100, 40, 100] deviate to: [100, 120, 100]
strategy: [100, 40, 120] deviate to: [120, 40, 120]
strategy: [100, 60, 0] deviate to: [60, 60, 0]
strategy: [100, 60, 20] deviate to: [60, 60, 20]
strategy: [100, 60, 40] deviate to: [60, 60, 40]
strategy: [100, 60, 60] deviate to: [60, 60, 60]
strategy: [100, 60, 80] deviate to: [80, 60, 80]
strategy: [100, 60, 100] deviate to: [100, 120, 100]
strategy: [100, 60, 120] deviate to: [120, 60, 120]
strategy: [100, 80, 0] deviate to: [80, 80, 0]
strategy: [100, 80, 20] deviate to: [80, 80, 20]
strategy: [100, 80, 40] deviate to: [80, 80, 40]
strategy: [100, 80, 60] deviate to: [80, 80, 60]
strategy: [100, 80, 80] deviate to: [80, 80, 80]
strategy: [100, 80, 100] deviate to: [100, 120, 100]
strategy: [100, 80, 120] deviate to: [120, 80, 120]
strategy: [100, 100, 0] deviate to: [100, 120, 0]
strategy: [100, 100, 20] deviate to: [100, 120, 20]
strategy: [100, 100, 40] deviate to: [100, 120, 40]
strategy: [100, 100, 60] deviate to: [100, 120, 60]
strategy: [100, 100, 80] deviate to: [100, 120, 80]
strategy: [100, 100, 100] deviate to: [100, 120, 100]
strategy: [100, 100, 120] deviate to: [120, 100, 120]
strategy: [100, 120, 0] deviate to: [120, 120, 0]
strategy: [100, 120, 20] deviate to: [120, 120, 20]
strategy: [100, 120, 40] deviate to: [120, 120, 40]
strategy: [100, 120, 60] deviate to: [120, 120, 60]
strategy: [100, 120, 80] deviate to: [120, 120, 80]
strategy: [100, 120, 100] deviate to: [120, 120, 100]
strategy: [100, 120, 120] deviate to: [120, 120, 120]
strategy: [120, 0, 0] deviate to: [0, 0, 0]
strategy: [120, 0, 20] deviate to: [0, 0, 20]
strategy: [120, 0, 40] deviate to: [40, 0, 40]
strategy: [120, 0, 60] deviate to: [60, 0, 60]
strategy: [120, 0, 80] deviate to: [80, 0, 80]
strategy: [120, 0, 100] deviate to: [100, 0, 100]
strategy: (120, 0, 120) deviate to: nothing
strategy: [120, 20, 0] deviate to: [20, 20, 0]
strategy: [120, 20, 20] deviate to: [20, 20, 20]
strategy: [120, 20, 40] deviate to: [40, 20, 40]
strategy: [120, 20, 60] deviate to: [60, 20, 60]
strategy: [120, 20, 80] deviate to: [80, 20, 80]
strategy: [120, 20, 100] deviate to: [100, 20, 100]
strategy: (120, 20, 120) deviate to: nothing
strategy: [120, 40, 0] deviate to: [40, 40, 0]
strategy: [120, 40, 20] deviate to: [40, 40, 20]
strategy: [120, 40, 40] deviate to: [40, 40, 40]
strategy: [120, 40, 60] deviate to: [60, 40, 60]
strategy: [120, 40, 80] deviate to: [80, 40, 80]
strategy: [120, 40, 100] deviate to: [100, 40, 100]
strategy: (120, 40, 120) deviate to: nothing
strategy: [120, 60, 0] deviate to: [60, 60, 0]
strategy: [120, 60, 20] deviate to: [60, 60, 20]
strategy: [120, 60, 40] deviate to: [60, 60, 40]
strategy: [120, 60, 60] deviate to: [60, 60, 60]
strategy: [120, 60, 80] deviate to: [80, 60, 80]
strategy: [120, 60, 100] deviate to: [100, 60, 100]
strategy: (120, 60, 120) deviate to: nothing
strategy: [120, 80, 0] deviate to: [80, 80, 0]
strategy: [120, 80, 20] deviate to: [80, 80, 20]
strategy: [120, 80, 40] deviate to: [80, 80, 40]
strategy: [120, 80, 60] deviate to: [80, 80, 60]
strategy: [120, 80, 80] deviate to: [80, 80, 80]
strategy: [120, 80, 100] deviate to: [100, 80, 100]
strategy: (120, 80, 120) deviate to: nothing
strategy: [120, 100, 0] deviate to: [100, 100, 0]
strategy: [120, 100, 20] deviate to: [100, 100, 20]
strategy: [120, 100, 40] deviate to: [100, 100, 40]
strategy: [120, 100, 60] deviate to: [100, 100, 60]
strategy: [120, 100, 80] deviate to: [100, 100, 80]
strategy: [120, 100, 100] deviate to: [100, 100, 100]
strategy: (120, 100, 120) deviate to: nothing
strategy: (120, 120, 0) deviate to: nothing
strategy: (120, 120, 20) deviate to: nothing
strategy: (120, 120, 40) deviate to: nothing
strategy: (120, 120, 60) deviate to: nothing
strategy: (120, 120, 80) deviate to: nothing
strategy: (120, 120, 100) deviate to: nothing
strategy: (120, 120, 120) deviate to: nothing
[(120, 0, 120), (120, 20, 120), (120, 40, 120), (120, 60, 120), (120, 80, 120), (120, 100, 120), (120, 120, 0), (120, 120, 20), (120, 120, 40), (120, 120, 60), (120, 120, 80), (120, 120, 100), (120, 120, 120)]



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