  The wide adoption of gas fired units and power-to-gas technology brings
remarkable interdependency between natural gas and electricity infrastructures.
This paper studies the equilibria of coupled gas and electricity energy markets
driven by the strategic bidding behavior: each producer endeavours to maximizes
its own profit subjecting to the market clearing outcome. The market equilibria
is formulated as an equilibrium problem with equilibrium constraints (EPEC). A
special diagonalization algorithm (DA) is devised, in which the unilateral
equilibria of the gas or electricity market is found in the inner loop given
the rival's strategy; the interaction of the two markets are tackled in the
outer loop. Case studies on two test systems validates the proposed
methodology.
