math-code-snippets

prisoners-dilemma-linear-program.py

import numpy as np
import cvxpy as cp

# Consider the Prisoner's Dilemma https://en.wikipedia.org/wiki/Prisoner%27s_dilemma

# Variable v is prisoner A's payoff in the worst case (minimum)
v = cp.Variable()  #  expected utility of prisoner A
c = cp.Variable(nonneg=True)  # probability that A cooperates
d = cp.Variable(nonneg=True)  # probability that A defects

obj = cp.Maximize(v)
constraints = [
               c + d == 1,
               v <= -c,
               v <= -3*c + -2 * d
]

prob = cp.Problem(obj, constraints)

prob.solve()
if prob.status == 'optimal':
    print(f'optimal value: {prob.value}')
    print(f'optimal solution: p(cooperate) = {c.value}, p(defect) = {d.value}')