In this paper we present a general model of organizational problem‐solving in which we explore the relationship between problem complexity, decentralization of tasks and reward schemes. When facing complex problems that require the co‐ordination of large numbers of interdependent elements, organizations face a decomposition problem that has both cognitive dimensions and reward and incentive dimensions. The former relate to the decomposition and allocation of the process of generation of new solutions: since the search space is too vast to be searched extensively, organizations employ heuristics for reducing it. The decomposition heuristic takes the form of division of cognitive labour and determines which solutions are generated and become candidates for selection. The reward and incentive dimensions fundamentally shape the selection environment which chooses over alternative solutions. The model we present begins to study the interrelationships between these two domains of analysis: in particular, we compare the problem‐solving performance of organizations characterized by various decompositions (of coarser or finer grain) and various reward schemes (at the level of the entire organization, team and individual). Moreover we investigate extensions of our model in order to account for (admittedly rudimentary) power and authority relationships (giving some parts of the organization the power to stop changes in other parts), and discuss the interaction of problem representations and incentive mechanisms.