Modeling foundations of economic property rights theory

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This volume serves as an introduction to the foundations of economic property rights theory (EPRT), marking the initial step in its research program. It explores rules related to economic property rights (e.p.r.s), entrepreneurial agreements, and enterprises. The concept of e.p.r.s extends the traditional pairing of residual rights of control and returns within economic theory. Its significance arises from the general impossibility of crafting complete contracts for nontrivial economic transactions involving e.p.r.s. The work presents a theoretical framework rooted in mathematical economics, utilizing recent advancements in Hopf algebras, quasi-Hopf algebras, representation theory, category theory, and deformation theories. This aims to establish a mathematical methodology for economic property rights and the foundations of economic agreements. The goal is to develop a mathematical application where fundamental entities and operations have empirical economic interpretations. This approach addresses the complexity of economic phenomena and emphasizes the need for precise model formulations, ensuring that meaningful solutions arise from rigorous analysis. The proposed extensions in mathematical economics and property rights theory seek to provide robust foundations that can adequately address the intricacies of economic property rights and identify appropriate methodologies for problem-solving.