代码由我原创，有问题可以留言。本次分享会讲解怎么求解囚徒问题，囚徒问题本质上来讲是线性规划问题。
如上是北太天元的版本求解结果，代码可以扫码获取。（北太代码由老师原创）
下面这个是杉数求解器代码：
from coptpy import *env=Envr()# 创建一个新的模型model = env.createModel("two_prisoners_dilemma")# 创建变量x = model.addVars(2, vtype=COPT.BINARY, nameprefix="x")# 设置囚徒问题的奖励矩阵# CC 对应 (3, 3)# CD 对应 (0, 10)# DC 对应 (10, 0)# DD 对应 (9, 9)# 设置目标函数为囚徒A的奖励model.setObjective(3 * x[0] + 10 * (1 - x[0]), COPT.MAXIMIZE)# 添加约束条件，确保囚徒B的策略与囚徒A的策略相匹配model.addConstr(x[1] == 1 - x[0], "constraint")# 求解模型model.solve()# 打印结果if model.status == COPT.OPTIMAL:strategy_A = "Confess" if x[0].x > 0.5 else "Deny"strategy_B = "Confess" if x[1].x > 0.5 else "Deny"print(f"Optimal strategy for Prisoner A: {strategy_A}")print(f"Optimal strategy for Prisoner B: {strategy_B}")print(f"Objective value (Prisoner A's reward): {model.objVal}")else:print("No optimal solution found")
这个是杉数求解器代码，我们看看思路。
这个地方我们求解的思路和北太不一样，我们的思路是寻找利益最大化，然后反向求解这个问题。
现在我们来看看求解结果：
Cardinal Optimizer v7.1.3. Build date Apr 29 2024Copyright Cardinal Operations 2024. All Rights ReservedModel fingerprint: 1d5dbc9Using Cardinal Optimizer v7.1.3 on WindowsHardware has 4 cores and 8 threads. Using instruction set X86_AVX512_E1 (14)Maximizing a MIP problemThe original problem has:1 rows, 2 columns and 2 non-zero elements2 binariesStarting the MIP solver with 8 threads and 32 tasksPresolving the problemProblem was solved during presolveBest solution : 10.000000000Best bound : 10.000000000Best gap : 0.0000%Solve time : 0.02Solve node : 0MIP status : solvedSolution status : integer optimal (relative gap limit 0.0001)Violations : absolute relativebounds : 0 0rows : 0 0integrality : 0Optimal strategy for Prisoner A: DenyOptimal strategy for Prisoner B: ConfessObjective value (Prisoner A's reward): 10.0
这个是求解结果，我们反向思考这个问题如果A抗拒，对方利益就最大化了，所以应该选择坦白，B同理可得。
