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In the standard form of the equation (see later in article), and are respectively replaced by / and ; the advantage of this being that and have some understandable physical meaning, as they represent an integration time and a derivative time respectively.
The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory. In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method.
It studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems. The equation that describes the relationship between these subproblems is called the Bellman equation. Mathematical programming with equilibrium constraints is where the constraints include variational inequalities or ...
The possibility to fulfill different specifications varies from the model considered and the control strategy chosen. List of the main control techniques Optimal control is a particular control technique in which the control signal optimizes a certain "cost index": for example, in the case of a satellite, the jet thrusts needed to bring it to ...
Assume is increasing and concave in the player's own strategy . Under these assumptions, the two decisions are strategic complements if an increase in each player's own decision x i {\displaystyle \,x_{i}} raises the marginal payoff ∂ Π j ∂ x j {\displaystyle {\frac {\partial \Pi _{j}}{\partial x_{j}}}} of the other player.
Reward management is concerned with the formulation and implementation of strategies and policies that aim to reward people fairly, equitably and consistently in accordance with their value to the organization. [1] Reward management consists of analysing and controlling employee remuneration, compensation and all of the other benefits for the ...
A key property of a strategy-stealing argument is that it proves that the first player can win (or possibly draw) the game without actually constructing such a strategy. So, although it might prove the existence of a winning strategy, the proof gives no information about what that strategy is. The argument works by obtaining a contradiction. A ...
A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...