Download Differential Games in Economics and Management Science by Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, PDF

By Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, Gerhard Sorger

This publication is a complete, self-contained survey of the idea and functions of differential video games. No past wisdom of video game concept is thought, even though a simple wisdom of linear algebra, traditional differential equations and mathematical programming is needed. This ebook is designed as a examine source for researchers and students in addition to a textual content for complex undergraduates and primary yr graduate scholars. these in all facets of economics, in addition to in commercial companies, selection sciences, administration technology, advertising, operations learn and quantitative equipment will reap the benefits of this e-book.

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Sample text

The incumbent chooses an action from the set {'collude with entrant', 'fight the entrant'}. When player / has made his choice, the game terminates. 6 reflect that player E must pay an entry fee of 2 (million dollars) to enter the market. Total monopoly profits are 20 and this amount is equally shared if E enters and / colludes. 6. 6 enter stay out collude fight (8,10) (0,20) (-2,0) (0,20) If E enters and / fights the entrant, a price war is supposed to leave both firms with no profits at all. 2.

2. It shows that the players alternate in making decisions and there are four terminal histories, represented by the four terminal nodes. The assumption is that player / knows for sure in which of the two nodes (dots marked by /) he is when he must make his decision. 6 we show the strategic form of the entry game. The strategic form exhibits two Nash equilibria. One has payoffs (8,10), corresponding to the profile ('enter','collude'). The other equilibrium has payoffs (0,20) and corresponds to the pair ('stay out','fight').

Thus, one imposes the Markovian assumption that the game history in itself is not relevant for a choice of action at time t, only the consequences of the history are important and they are reflected in the current value of the state vector. Thus, the use of Markovian strategies is a natural choice in the setup of state space games where the history of the game till time t is summarized in the value of the state vector at time /. The choice of Markovian strategies is also motivated by their simplicity: players react only to factors which are payoff-relevant and constitute an intertemporal link in the game (namely, the state variables).

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