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Strategic Dynamics of Firms via Path Integral Control

Paramahansa Pramanik

International Game Theory Review2026https://doi.org/10.1142/s0219198926500064article
AJG 1ABDC B
Weight
0.50

Abstract

We introduce a Euclidean path integral control approach to determine optimal strategies for firms operating under a Walrasian system, Pareto optimality, and a non-cooperative feedback Nash equilibrium. Our framework formulates a Lagrangian control problem with forward-looking stochastic dynamics, eliminating the need for a value function to derive optimal strategies. The method relies on a continuously differentiable Itô process generated by integrating factors, providing a computationally feasible alternative to solving complex market dynamics. Our approach facilitates the analysis of generalized nonlinear market dynamics, where constructing a Hamilton-Jacobi-Bellman (HJB) equation is particularly challenging. Similar to the Feynman-Kac approach, our solutions are not unique. Given the large number of firms considered, our method draws comparisons with mean-field game approach. The primary contribution of this work is the derivation of a non-cooperative feedback Nash equilibrium, offering a comparative perspective against solutions generated by mean-field interactions. We illustrate the effectiveness of our approach through various examples, contrasting it with the Pontryagin maximum principle.

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https://doi.org/https://doi.org/10.1142/s0219198926500064

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@article{paramahansa2026,
  title        = {{Strategic Dynamics of Firms via Path Integral Control}},
  author       = {Paramahansa Pramanik},
  journal      = {International Game Theory Review},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1142/s0219198926500064},
}

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0.50

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
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R · text relevance †0.50 × 0.4 = 0.20

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