  We formulate for the first time the economic dispatch problem in an
integrated electrical and gas distribution system as a game equilibrium problem
between distributed prosumers. Specifically, by approximating the non-linear
gas-flow equations either with a mixed-integer second order cone or a
piece-wise affine model and by assuming that electricity and gas prices depend
linearly on the total consumption we obtain a potential mixed-integer game. To
compute an approximate generalized Nash equilibrium, we propose an iterative
two-stage method that exploits a problem convexification and the gas flow
models. We quantify the quality of the computed solution and perform a
numerical study to evaluate the performance of our method.
