 How will a population of individuals that plays the Prisoner’s Dilemma evolve over time? We cannot answer that question without introducing a few assumptions concerning the nature of the population. First, assume that the population is quite large and that the probability of interacting with a Cooperator or Defector equals the proportion of the population following that strategy. This allows us to represent the state of the population by simply keeping track of what proportion follow the strategies Cooperate and Defect. Let \(p_C\) and \(p_D\) denote these proportions. Denote the expected fitness of cooperators and defectors by \(W_C\) and \(W_D\), respectively, and let \(\overline{W}\) denote the average fitness of the entire population. (These quantities may vary over time; the time-dependency has been suppressed for clarity of notation.) Given these assumptions, the values of \(W_C, W_D\), and \(\overline{W}\) can be expressed in terms of the population proportions and payoff values as follows, where \(F_0\) stands for the base fitness level of an individual prior to any interaction: