This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop nash equilibria are introduced. The existence of an...
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This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop nash equilibria are introduced. The existence of an open-loopnash equilibrium is characterized by the solvability of a system of mean-field forward-backward stochastic differential equations in an infinite horizon and the convexity of the cost functionals, and the closed-loop representation of an open-loopnash equilibrium is given through the solution to a system of two coupled non-symmetric algebraic Riccati equations. The existence of a closed-loopnash equilibrium is characterized by the solvability of a system of two coupled symmetric algebraic Riccati equations. Two-person mean-field linear-quadratic zero-sum stochastic differential games in an infinite horizon are also considered. Both the existence of open-loop and closed-loop saddle points are characterized by the solvability of a system of two coupled generalized algebraic Riccati equations with static stabilizing solutions. Mean-field linear-quadratic stochastic optimal control problems in an infinite horizon are discussed as well, for which it is proved that the open-loop solvability and closed-loop solvability are equivalent.
In this paper, the competition of dynamic oligopoly in the cruise line industry is modeled as an N-person nonzero-sum noncooperative dynamic game where a finite number of cruise lines compete to maximize their profits...
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In this paper, the competition of dynamic oligopoly in the cruise line industry is modeled as an N-person nonzero-sum noncooperative dynamic game where a finite number of cruise lines compete to maximize their profits over a fixed planning horizon. The noncooperative nash equilibrium capacity investment strategies of cruise lines are theoretically analyzed under the open-loop and closed-loop information structures. The optimality conditions for open-loop and closed-loopnash equilibrium solutions are derived using a Pontryagin-type maximum principle and given economic interpretations so as to demonstrate the differences between the open-loop and closed-loopnash equilibrium solutions. The dynamic oligopolistic competition of three cruise lines in a hypothetical setting is numerically analyzed by using the iterative algorithms for open-loop and closed-loop models. Numerical results provide a number of important managerial guidelines for cruise capacity investment decisions. The paper concludes with a discussion on future research directions.
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