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• Nash and Stackelberg models to capture the interactions of DNO and SEV operator. • A best response-based algorithm is proposed to solve the bilevel problem. • Supply-demand equilibrium existence is proved and uniqueness is numerically tested. • Cruising traffic is increased with medium travel demand while reduced in other cases. This paper considers a group of shared electric vehicles (SEV) that provide transport and energy services through a ride-sourcing platform. Under the novel business model, the transport and power networks are coupled and the resulting market equilibrium depends on the pricing strategies of the distribution network operator (DNO) and the SEV platform operator. To capture the interaction between the DNO and the SEV platform operator, we develop two market competition models, including (a) a Stackelberg competition model where the DNO makes the decision first and the SEV operator reacts accordingly, and (b) a Nash competition model where the DNO and the SEV operator make decisions simultaneously. The strategic interactions of the DNO and the SEV platform operator are analyzed over a coupled transport and power network, which captures the routing and discharging behaviors of EV drivers, the matching process between passengers and drivers, and the corresponding traveler and power flows. We analytically prove that the supply and demand equilibrium between travelers and EV drivers over the transport network always exists. We also numerically validate that the equilibrium solution between the SEV operator and the DNO is stable and unique. By varying the transport demands, we show that the SEV platform operator, the DNO and EV drivers always benefit from the discharge business even though passengers may be slightly worse off. Surprisingly, we find that integrating the discharging service will have diverse impacts on the cruising traffic depending on the demand levels of the transport service: under low demand level, it will reduce the cruising traffic; under medium demand level, it will increase the cruising traffic; under high demand level, it has no impact on the cruising traffic. [ABSTRACT FROM AUTHOR]