This work deals with problems where multiple actors simultaneously take control decisions and implement the corresponding actions in large multi-area power systems. The fact that those actions take place in the same transmission grid introduces a coupling between the various decision-making problems. First, transmission constraints involving all actors' controls must be satisfied, while, second, the satisfaction of an actor's operational objective depends, in general, not only on its own actions but on the others' too. Algorithms and/or operational procedures are, thus, developed seeking to reconcile the multiple actors' simultaneous decisions. The confidentiality and operational autonomy of the actors' decision-making procedures are preserved. In particular, two specific problems leading to such a multi-actor situation have been treated. The first is drawn from a recently emerging situation, at least in Europe, where several Transmission System Operators (TSOs) have installed and/or are planning to install Phase Shifting Transformers (PSTs) in such locations in their areas that, by properly adjusting the PST phase angle settings, they can significantly control the power flows entering and exiting their systems. A general framework is proposed for the control of PSTs owned by several TSOs, taking into account their interactions. The proposed solution is the Nash equilibrium of a sequence of optimizations performed by the various TSOs, each of them taking into account the other TSOs' control settings as well as operating constraints relative to the whole system. The method is applied to a linearized network model and illustrated on the IEEE 118-bus system. The second multi-actor situation dealt with in this work stems from the recently increasing amount of discussions and efforts made towards creating the right market structures and operational practices that would facilitate a seamless inter-area trade of electricity throughout large interconnections. In this respect, in accordance with European Union's goal of a fully functional Internal Electricity Market where ideally every consumer will be able to buy electric energy from every producer all across the interconnection, the possibility of every market participant to place its bid in whatever electricity market of an interconnection has been considered. This results in overlapping markets, each with its own schedule of power injections and withdraws, comprising buses all around the interconnection, that are cleared simultaneously by Transaction Schedulers (TSs). An iterative procedure is proposed to reconcile the various TS schedules such that congestion is managed in a fair and efficient way. The procedure converges to such schedules that the various TS market clearings are in a Nash equilibrium. The method is then extended towards several directions: enabling market participants to place their bids simultaneously in more than one TS's market, incorporating $N-1$ security constraints, allowing for joint energy-reserve dispatch, and, accounting for transmission losses. The corresponding iterative algorithms are thoroughly illustrated in detail on a 15-bus as well as the IEEE RTS-96 system.