For an optimal control problem of an Ito's type stochastic differential equation, the control process could be taken in open-loop or closed-loop forms. In the standard literature, provided appropriate regularity, ...
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For an optimal control problem of an Ito's type stochastic differential equation, the control process could be taken in open-loop or closed-loop forms. In the standard literature, provided appropriate regularity, the value functions under these two types of controls are equal and are the unique (viscosity) solution to the corresponding (path-dependent) HJB equation. In this short note, we provide a counterexample in the path dependent setting showing that these value functions can be different in general. (C) 2021 Elsevier B.V. All rights reserved.
We reformulate the Verhulst-Lotka-Volterra model of natural resource extraction under the alternative assumptions of Cournot behaviour and perfect competition, to revisit the tragedy of commons vs the possibility of s...
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We reformulate the Verhulst-Lotka-Volterra model of natural resource extraction under the alternative assumptions of Cournot behaviour and perfect competition, to revisit the tragedy of commons vs the possibility of sustainable harvesting. After a brief layout of the open-loop solution including the Ramsey rule, we rely on the state-redundancy property and the consequent strong time consistency of the static equilibrium output to investigate the different impact of demand elasticity on the regulator's possibility of driving industry harvest to the maximum sustainable yield in the two settings. The presence of a flat demand function offers the authority a fully effective regulatory tool in the form of the exogenous price faced by perfectly competitive firms, to drive their collective harvest rate to the maximum sustainable yield. The same cannot happen under Cournot competition, as in this case the price is endogenous and the regulator's policy is confined to limiting access to the common pool. (C) 2019 Elsevier Ltd. All rights reserved.
A new approach to two-player zero-sum differential games with convex-concave cost function is presented. It employs the tools of convex and variational analysis. A necessary and sufficient condition on controls to be ...
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A new approach to two-player zero-sum differential games with convex-concave cost function is presented. It employs the tools of convex and variational analysis. A necessary and sufficient condition on controls to be an open-loop saddle point of the game is given. Explicit formulas for saddle controls are derived in terms of the subdifferential of the function conjugate to the cost. Existence of saddle controls is concluded under very general assumptions, not requiring the compactness of control sets. A Hamiltonian inclusion, new to the field of differential games, is shown to describe equilibrium trajectories of the game.
This paper deals with a class ofN-person nonzero-sum differential games where the control variables enter into the state equations as well as the payoff functionals in an exponential way. Due to the structure of the g...
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This paper deals with a class ofN-person nonzero-sum differential games where the control variables enter into the state equations as well as the payoff functionals in an exponential way. Due to the structure of the game, Nash-optimal controls are easily determined. The equilibrium in open-loop controls is also a closed-loop equilibrium. An example of optimal exploitation of an exhaustible resource is presented.
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