 Another way that conditional moves can be introduced into the PD is by assuming that players have the property that David Gauthier has labeled transparency. A fully transparent player is one whose intentions are completely visible to others. Nobody holds that we humans are fully transparent, but the observation that we can often successfully predict what others will do suggests that we are at least “translucent.” Furthermore agents of larger scale, like firms or countries, which may have to publicly deliberate before acting, may be more transparent than we are. Thus there may be some theoretical interest in investigations of PDs with transparent players. Such players could presumably execute conditional strategies more sophisticated than those of the (non-transparent) extended game players, strategies, for example that are conditional on the conditional strategies employed by others. There is some difficulty, however, in determining exactly what strategies are feasible for such players. Suppose Row adopted the strategy “do the same as Column” and Column adopted the strategy “do the opposite of Row”. There is no way that both these strategies could be satisfied. On the other hand, if each adopted the strategy “imitate the other player”, there are two ways the strategies could be satisfied, and there is no way to determine which of the two they would adopt. Nigel Howard, who was probably the first to study such conditional strategies systematically, avoided this difficulty by insisting on a rigidly typed hierarchy of games. At the base level we have the ordinary PD game, where each player chooses between \(\bC\) and \(\bD\). For any game \(G\) in the hierarchy we can generate two new games \(RG\) and \(CG\). In \(RG\), Column has the same moves as in game \(G\) and Row can choose any function that assigns \(\bC\) or \(\bD\) to each of Column's possible moves. Similarly in \(CG\), Row has the same moves as in \(G\) and Column has a new set of conditional moves. For example, if [PD] is the base level game, then \(C\)[PD] is the game in which Column can choose from among the strategies \(\bCu\), \(\bDu\), \(\bI\) and \(\bO\) mentioned above. Howard observed that in the two third level games \(RC\)[PD] and \(CR\)[PD] (and in every higher level game) there is an equilibrium outcome giving each player \(R\). In particular, such an equilibrium is reached when one player plays \(\bI\) and the other cooperates when his opponent plays \(\bI\) and defects when his opponent plays \(\bCu\), \(\bDu\) or \(\bO\). Notice that this last strategy is tantamount to Danielson's reciprocal cooperation described in the last section.