"Team reasoning"—understood as fundamentally different from individual instrumental reasoning—has been proposed as a solution to a problem of strategic interaction discussed in game theory. But this form of reasoning has been deployed recently in philosophical discussion about shared agency and joint action, in particular to characterize the special "participatory" intention an individual has when acting with another. The main point of the chapter is that constraints on intending raise some challenges for this approach to participatory intention. If team reasoning rationally yields a participatory intention to A, it would require a belief or presumption on the part of the agent regarding what fellow participants will do—namely, that they or enough of them will also employ team reasoning. But what warrants this assumption? I contend that some ways of defending it are incompatible with what originally motivates team reasoning as a solution to a problem of strategic interaction. I will argue that if, as its proponents insist, team reasoning is to be fundamentally distinct from individual instrumental reasoning, then it must invoke a notion of a rational yet non-evidential warrant for belief. The distinctiveness of team reasoning would require, in general, that a team reasoner's belief or expectation that other participants are also team reasoners is rational, but not acquired in the way that rational belief as it is usually understood should be acquired, that is, on the basis of evidence.