Due to its theoretical virtues, several recent works propose the use of the incentive-compatible Vickrey-Clarke-Groves (VCG) mechanism for electricity markets. Coalitions of participants, however, can influence the VCG outcome to obtain higher collective utility. To address this issue, core-selecting mechanisms are proposed for their coalition-proofness. We show that core-selecting mechanisms generalize the economic rationale of the locational marginal pricing (LMP) mechanism. Namely, these mechanisms are the exact class of mechanisms that ensure the existence of a competitive equilibrium in linear/nonlinear prices. This implies that the LMP mechanism is also core-selecting, and hence coalition-proof. In contrast to the LMP mechanism, core-selecting mechanisms exist for a broad class of electricity markets, such as ones involving nonconvex costs and nonconvex constraint sets. In addition, they can approximate truthfulness without the price-taking assumption of the LMP mechanism. Finally, we show that they are also budget-balanced. Our results are verified with case studies based on OPF test systems and Swiss reserve market.