In this paper, we propose a Quantified Distributed Constraint Optimization problem (QDCOP) that extends the framework of Distributed Constraint Optimization problems (DCOPs). DCOPs have been studied as a fundamental model of multi-agent cooperation. In traditional DCOPs, all agents cooperate to optimize the sum of their cost functions. However, in practical systems some agents may desire to select the value of their variables without cooperation. In special cases, such agents may take the values with the worst impact on the quality of the result reachable by the optimization process. We apply existential/universal quantifiers to distinct uncooperative variables. A universally quantified variable is left unassigned by the optimization as the result has to hold when it takes any value from its domain, while an existentially quantified variable takes exactly one of its values for each context. Similar classes of problems have recently been studied as (Distributed) Quantified Constraint P...