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Global decarbonization demands a profound transformation of energy systems and the markets that govern them. The integration of variable renewable generation, storage, and sector coupling increases system complexity, while new market designs must ensure adequate investment incentives and fair welfare distribution. In this context, dispatch and investment decisions become increasingly intricate, and analytical decision-support models gain importance—both from a centralized system perspective and from the standpoint of individual market participants. Within this scope, this dissertation develops analytical tools to analyze dispatch and investment decisions in imperfect electricity and district heating markets. The focus is in two increasingly prominent forms of energy trade: thermal-electric local energy markets (LEMs) and corporate power purchase agreements (CPPAs). Market imperfections are deviations from the assumptions of perfect competition, that often create inefficiencies and welfare imbalances between producers and consumers. Three imperfections are considered in particular: (i) limited number of firms, (ii) market-entry barriers, and (iii) information asymmetries. First, this dissertation presents an abstract mathematical framework for modeling integrated energy systems. This framework jointly captures dispatch and investment decisions from a centralized perspective. It is based on a linear optimization problem, a well-established paradigm in energy system modeling, yet contributes novelty through its compact formulation, that simplifies data collection processes for producing model instances and allows for expansion for modeling more complex market dynamics. To study market imperfections in LEMs, two game-theoretic formulations are proposed. They are implemented as a mixed complementarity problem and an equilibrium problem with equilibrium constraints, respectively. Applied to illustrative scenarios, the models show that the limited number of suppliers makes LEMs highly vulnerable to market power, exercised not only through dispatch decisions but also via strategic investment—even under perfectly regulated and thus welfaremaximizing dispatch. With respect to entry barriers, we analytically demonstrate that their effects are regionally heterogeneous: investment in smaller, less profitable markets declines sharply as barriers to entry increase, with stronger effects for combined heat and power assets than for heat-only boilers. Finally, this dissertation examines the information requirements for assessing the profitability of CPPAs from the perspectives of both buyers and wind power plant investors. The analysis identifies the key actors and factors shaping profitability for each party, models their impact on contractual cash flows, and shows how access to—or reliable estimation of—third-party information can delineate negotiation ranges in which agreements are mutually profitable.