models of reciprocity, which only attend to cooperative actions and not the deliberation

models of reciprocity, which only attend to cooperative actions and not the deliberation process leading up to the action. We develop a simple model to explain why “looking” at the costs of cooperation is viewed with suspicion. The explanation we suggest is quite intuitive: those who cooper- ate without looking (CWOL) can be trusted to cooperate even in times when there are temptations to defect. While this insight can be captured without the need for a formal model, it is less clear that cooperators will choose to not look, since they pay a price by cooperating blindly in tempting circumstances. Moreover, the formal model, as will be seen, helps explicate when CWOL will occur as well as what difference the ability to not look and to observe others not looking will make. We formalize this idea using what we call the envelope game (see figure 1). The envelope game distills an interaction between two individuals, or players, in an uncertain environment. Thus, we start by assuming there is a distribution of payoffs with two possibilities: one in which defection is relatively tempting, and another in which it is not. The temptation to defect is randomly determined. Defection is not tempting with probability p and tempting with probability 1—p. Both players know how likely it is that defection is tempting. However, at this point, neither player knows size of the temptation. That is, the temptation is placed inside an envelope and the envelope is sealed without the players knowing its content. Next, we assume that one of the players, player 1, chooses whether to learn the size of the temptation, either via mental deliberation or by gathering information. We model this in a simplified way by assuming that player 1 has a dichotomous choice: she can choose to open the envelope and look inside it, or not. If she opens the envelope and looks, she learns the size of the temptation. If she does not open the envelope and look, she only knows the distribution of payoffs. Player 1 then chooses whether to cooperate or defect. We model cooperation as costly to player 1, regardless HOUSE_OVERSIGHT_026523