 There are two players, Row and Column. Each has two possible moves, “cooperate” (\(\bC\)) or “defect” (\(\bD\)), corresponding, respectively, to the options of remaining silent or confessing in the illustrative anecdote above. For each possible pair of moves, the payoffs to Row and Column (in that order) are listed in the appropriate cell. \(R\) is the “reward” payoff that each player receives if both cooperate. \(P\) is the “punishment” that each receives if both defect. \(T\) is the “temptation” that each receives as sole defector and \(S\) is the “sucker” payoff that each receives as sole cooperator. We assume here that the game is symmetric, i.e., that the reward, punishment, temptation and sucker payoffs are the same for each player, and payoffs have only ordinal significance, i.e., they indicate whether one payoff is better than another, but tell us nothing about how much better. It is now easy to see that we have the structure of a dilemma like the one in the story. Suppose Column cooperates. Then Row gets \(R\) for cooperating and \(T\) for defecting, and so is better off defecting. Suppose Column defects. Then Row gets \(S\) for cooperating and \(P\) for defecting, and so is again better off defecting. The move \(\bD\) for Row is said to strictly dominate the move \(\bC\): whatever Column does, Row is better off choosing \(\bD\) than \(\bC\). By symmetry \(\bD\) also strictly dominates \(\bC\) for Column. Thus two “rational” players will defect and receive a payoff of \(P\), while two “irrational” players can cooperate and receive greater payoff \(R\). In standard treatments, game theory assumes rationality and common knowledge. Each player is rational, knows the other is rational, knows that the other knows he is rational, etc. Each player also knows how the other values the outcomes. But since \(\bD\) strictly dominates \(\bC\) for both players, the argument for dilemma here requires only that each player knows his own payoffs. (The argument remains valid, of course, under the stronger standard assumptions.) It is also worth noting that the outcome \((\bD, \bD)\) of both players defecting is the game's only strict nash equilibrium, i.e., it is the only outcome from which each player could only do worse by unilaterally changing its move. Flood and Dresher's interest in their dilemma seems to have stemmed from their view that it provided a counterexample to the claim that the nash equilibria of a game constitute its natural “solutions”.