In this paper, we extend the traditional formalization of a Distributed Constraint Satisfaction Problems (DisCSP) to a Quantified DisCSP. A Quantified DisCSP includes several universally quantified variables, while all of the variables in a traditional DisCSP are existentially quantified. A universally quantified variable represents a choice of the nature or an adversary. A Quantified DisCSP formalizes a situation where a team of agents is trying to make a robust plan against the nature or an adversary. In this paper, we present the formalization of such a Quantified DisCSP and develop an algorithm for solving it. This algorithm generalizes the asynchronous backtracking algorithm used for solving a DisCSP. In this algorithm, agents communicate a value assignment called a good in addition to the nogood used in asynchronous backtracking. Interestingly, the procedures executed by an adversarial/cooperative agent for good/nogood are totally symmetrical.