Game Theory
1. Draw a payoff matrix for the one-shot prisoners' dilemma (one-shot PD); where the four payoffs (T, R, P, S) = (12, 10, 5, 3), and Ci means player i chooses to cooperate (C) and Di means player i defects (D), for i = 1, 2.
2. Draw a graph of player i's expected payoff line that results from player i choosing to cooperate, and the expected payoff line from choosing to defect; as the other player j’s probability of choosing to cooperate varies from 0 to 1. Explain why this diagram implies it is still a dominant strategy for player i to always defect even when player j can choose to randomly cooperate with any probability from 0 to 1.