Abstract: (joined work with Dirk Becherer, https://doi.org/10.48550/arXiv.2408.01175) We study mean-field games where common noise dynamics are described by integer-valued random measures, for instance Poisson random measures, in addition to Brownian motions. In such a framework, we describe mean-field equilibria for mean-field portfolio games of both optimal investment and hedging under relative performance concerns with respect to exponential (CARA) utility preferences. Agents have independent individual risk aversions, competition weights and initial capital endowments, whereas their liabilities are described by contingent claims which can depend on both common and idiosyncratic risk factors. Liabilities may incorporate, for example, compound Poisson-like jump risks, which can only be hedged partially by trading in a common but incomplete financial market, where prices of risky assets evolve as It\^{o}-processes. Mean-field equilibria are fully characterized by solutions to suitable McKean-Vlasov backward SDEs with jumps, for which we prove existence and uniqueness of solutions, without restricting competition weights to be small. A novel change of measure argument and one-to-one relation to an auxiliary mean-field game play key roles for proof, helping among other things to avoid restrictive conditions for an approach by direct fixed point contraction.