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This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and inter- dependent markets. This coordination represents a classic Stackelberg game and relies on the ex- change of sensitive information between the sys- tem agents. The paper is motivated by the observa- tion that the perturbation introduced by traditional DP mechanisms fundamentally changes the under- lying optimization problem and even leads to un- satisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stack- elberg Mechanism (PPSM), a framework that en- forces the notions of feasibility and fidelity (i.e. near-optimality) of the privacy-preserving informa- tion to the original problem objective. PPSM com- plies with the notion of differential privacy and en- sures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the proposed approach. A full version of this paper [Fioretto et al., 2020b] contains complete proofs and additional discussion on the motivating application.