A Short Note on: Optimal Control in Matching Pennies Game
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Page Numbers:
752-755
Digital Object Identifier:
10.58578/mjms.v3i3.7336
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Authors:
Reza Habibi1* 
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Abstract
This short note explores the application of optimal control theory in identifying mixed equilibrium strategies within the context of the Matching Pennies game. The study emphasizes the role of gradient descent as a fundamental mechanism in the players' learning dynamics. By formulating the game as an optimal control problem, the approach enables systematic analysis of strategic adaptation over time. In addition to the theoretical framework, simulation results are presented to illustrate and validate the effectiveness of the method in converging toward mixed equilibrium. The findings highlight the potential of control-theoretic techniques in advancing game-theoretic learning models.
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Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Kamien, M. I. (2013). Dynamic Optimization: the Calculus of Variations and Optimal Control in Economics and Management. Dover Publications. USA.
Singh, S., Kearns, M., and Mansour, Y. (2000). Nash convergence of gradient dynamics in general-sum games. Technical Report. AT&T Labs and Tel Aviv University.