Polansky, Alan M.
Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
Path integrals are used to find an optimal strategy for a firm under a Walrasian system. We define dynamic optimal strategies and develop an integration method to capture all non-additive non-convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms' strategies fall into each other's influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semicooperation of the small firm in this case using a Liouville-Feynman path integral method. In later parts we use path integrals in different scenarios such as choosing a player in a cricket team.
Pramanik, Paramahansa, "Optimization of Dynamic Objective Functions Using Path integrals" (2021). Graduate Research Theses & Dissertations. 7563.
Northern Illinois University
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