Mixed Strategy Constraints in Continuous Games
<|reference_start|>Mixed Strategy Constraints in Continuous Games: 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 ($n$-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.<|reference_end|>
@article{krusniak2024mixed,
    title={Mixed Strategy Constraints in Continuous Games},
    author={Mel Krusniak and Forrest Laine},
    journal={arXiv preprint arXiv:2402.17874},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17874},
    primaryClass={cs.GT}
}