Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction. Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend on her prediction of B’s beliefs and behavior; but B’s beliefs and behavior depend in turn on her prediction of A’s (...) beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior; but typically, there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning; but that this raises the puzzle of how the collective agent arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)