Electricity markets with high installed capacities of Variable Renewable Energy Sources (VRES) experience periods of supply and demand mismatch, resulting in near-zero and even negative prices, or energy spilling due to surplus. The participation of emerging Power-to-X solutions in a sector coupling paradigm, such as Power-to-Gas (PTG), has been envisioned to provide a source of demand flexibility to the power sector and decarbonize the gas sector. We advance a long-run equilibrium model to study the PTG investment decision from the point of view of a perfectly competitive electricity and gas system where each sector’s market is cleared separately but coupled by PTG. Under scenarios combining PTG technology costs and electricity RES targets, we study whether or not there is a convergence in the optimal deployment of PTG capacity and what is the welfare distribution across both sectors. We observe that PTG can play an important price-setting role in the electricity market, but PTG revenues from arbitrage opportunities erodes as more PTG capacity is installed. We find that the electricity and gas sector have aligned incentives to cooperate around PTG, and instead find an issue of misaligned incentives related to the PTG actor. Although not the focus of our analysis, in some scenarios we find that the welfare optimal PTG capacity results in a loss for the PTG actor, which reveals some intuition that subsidizing PTG can make sense to reduce the cost of RES subsidies. A sensitivity analysis is conducted to contextualize these findings for system specificities.