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Matrix-Valued Mean-Field-Type Games: Risk-Sensitive, Adversarial, and Risk-Neutral Linear-Quadratic Case

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      Abstract

      In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a semi-explicit solution for both problems by means of a direct method. The state dynamics is described by a matrix-valued linear jump-diffusion-regime switching system of conditional mean-field type where the conditioning is with respect to common noise which is a regime switching process. The optimal strategies are in a state-and-conditional mean-field feedback form. Semi-explicit solutions of equilibrium costs and strategies are also provided for the full cooperative, adversarial teams, risk-sensitive full cooperative and risk-sensitive adversarial team cases. It is shown that full cooperation increases the well-posedness domain under risk-sensitive decision-makers by means of population risk-sharing. Finally, relationship between risk-sensitivity and robustness are established in the mean-field type context.

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            Author and article information

            Journal
            23 April 2019
            1904.11346

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            40 pages. arXiv admin note: text overlap with arXiv:1412.0037 by other authors
            math.OC cs.GT

            Theoretical computer science, Numerical methods

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