Abstract
Turn-based games on graphs are games where the states are controlled by one and only one player who decides which edge to follow. Each player has a temporal objective that he tries to achieve. One player is the designated 'controller', whose objective captures the desirable outcomes of the whole system. Cooperative rational synthesis is the problem of computing a Nash equilibrium that satisfies the controller's objective. In this paper, we tackle this problem in the context of a commons, where each action has a cost or a benefit on one shared common pool energy resource. The paper investigates the problem of synthesising the controller in a commons such that there exists an individually rational behaviour of all the agents in the commons that satisfies the controller's objective and does not deplete the resource. We consider two types of agents: careless and careful. Careless agents only care for their temporal objective, while careful agents also pay attention not to deplete the system's resource. We solve the problem of cooperative rational synthesis in these games, focusing on parity objectives.