By Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, Gerhard Sorger
This publication is a accomplished, self-contained survey of the speculation and functions of differential video games. No earlier wisdom of video game thought is believed, even though a simple wisdom of linear algebra, usual differential equations and mathematical programming is needed. This e-book is designed as a learn source for researchers and students in addition to a textual content for complicated undergraduates and primary 12 months graduate scholars. these in all points of economics, in addition to in business enterprises, determination sciences, administration technology, advertising and marketing, operations study and quantitative equipment will reap the benefits of this ebook.
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Additional info for Differential Games in Economics and Management Science
In what follows we confine our interest to dynamic games in which all players' actions are observable by all players. The game is said to be one of perfect information. Hence, any player, when taking an action at time t, has perfect knowledge of all previous actions. These are his own past actions and those of his rivals, but can also include acts of nature (chance events) if there are exogenous uncertainties in the game. In such a game we say that players move simultaneously at time t if no player - when taking his action at time t - knows about the actions that the other players take at time t.
The standard interpretation of an incomplete information game is the following. 6 In a duopoly, for example, one firm is uncertain about the cost structure (in general: the 'type') of the second firm, and vice versa. Each firm knows its own cost (its own type) and it is common knowledge that each player must belong to a set of possible types. Which specific type, however, is not known for sure. Each player has an a priori probability distribution over the sets of possible types of all other players.
History consists of the restriction of control functions Uj(-),j e N, to the interval [0, i). Strategies based on action history are useful in problems in which the players should be given a chance to react if they observe deviations by their rivals from some tacitly agreed course of action. To observe deviations, the players normally need to know the action history. Strategies based on action history have been extensively used in dynamic games of tacit collusion where the players use threats of punishment as a means to sustain collusive behaviour.