455 research outputs found

    A Numerical Algorithm to find All Scalar Feedback Nash Equilibria

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    Abstract: In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on calculating the positive roots of a polynomial matrix.

    Algorithms for Computing Nash Equilibria in Deterministic LQ Games

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    In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.

    A Numerical Algorithm to find Soft-Constrained Nash Equilibria in Scalar LQ-Games

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    In this paper we provide a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game.The algorithm is based on the calculation of the eigenstructure of a certain matrix.The analysis follows the lines of the approach taken by Engwerda in [7] to calculate the solutions of a set of scalar coupled feedback Nash algebraic Riccati equations.

    Closed-Loop Nash Competition for Liquidity

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    We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values.Comment: 41 pages, 5 figures, supplementary appendi
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