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Mixed Strategy Constraints in Continuous Games

Main:7 Pages
7 Figures
Bibliography:1 Pages
3 Tables
Abstract

Equilibrium problems representing interaction in physical environments typically require continuous strategies which satisfy opponent-dependent constraints, such as those modeling collision avoidance. However, as with finite games, mixed strategies are often desired, both from an equilibrium existence perspective as well as a competitive perspective. To that end, this work investigates a chance-constraint-based approach to coupled constraints in generalized Nash equilibrium problems which are solved over pure strategies and mixing weights simultaneously. We motivate these constraints in a discrete setting, placing them on tensor games (nn-player bimatrix games) as a justifiable approach to handling the probabilistic nature of mixing. Then, we describe a numerical solution method for these chance constrained tensor games with simultaneous pure strategy optimization. Finally, using a modified pursuit-evasion game as a motivating examples, we demonstrate the actual behavior of this solution method in terms of its fidelity, parameter sensitivity, and efficiency.

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@article{krusniak2025_2402.17874,
  title={ Mixed Strategy Constraints in Continuous Games },
  author={ Mel Krusniak and Forrest Laine },
  journal={arXiv preprint arXiv:2402.17874},
  year={ 2025 }
}
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