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2022 | OriginalPaper | Buchkapitel

5. Noncooperative Dynamic Games Played over Event Trees

verfasst von : Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour

Erschienen in: Theory and Applications of Dynamic Games

Verlag: Springer International Publishing

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Abstract

In this chapter, we introduce a class of dynamic games played over event trees (DGPETs). We define the elements of the game, in particular the S-adapted information structure, and the corresponding concepts. We state the existence and uniqueness of the equilibrium results and a maximum principle for this class of games. Also, we extend the formalism to DGPETs that can terminate at any intermediate node. An example and some additional readings are provided.

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Vorheriges Kapitel Sustainability of Cooperation in Dynamic Games

Nächstes Kapitel Node-Consistent Single-Valued Solutions in DGPETs

Modeling uncertainty with scenario trees is a common practice in the stochastic programming literature.

Other information structures can be considered; see, e.g., Haurie et al. (2012).

We refer interested readers to Carlson and Haurie (2000), Haurie (1995), Haurie and Zaccour (1995) for a more detailed treatment of (deterministic) dynamic game models with coupled constraints.

In optimal control problems involving constraints the pseudo-Lagrangian is obtained by adding the penalty for violating the constraints to the Hamiltonian; see Sethi and Thompson (2000).

In international pollution control, such an authority does not exist and the players (countries) need to agree on a particular vector of weights. Therefore, the game with coupled constraints cannot be considered as a purely noncooperative game.

By setting probabilities \(\tau _{n_{t}}\) for any \(n_{t}\in \textbf{n}_{t}\) for all \(t=0,\dots ,T\) we determine the probability distribution of the process termination over the set of nodes. For the distribution, it holds that \(\sum _{\nu \in \textbf{n}_{0}^{++}}\tau _{\nu }=1\).

The cooperative version of this game is examined in Sect. 6.3.2.

For a background on this class of games, see the survey in Jørgensen et al. (2010).

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Titel: Noncooperative Dynamic Games Played over Event Trees
verfasst von: Elena Parilina
Puduru Viswanadha Reddy
Georges Zaccour
Verlag: Springer International Publishing
Buch: Theory and Applications of Dynamic Games
Print ISBN: 978-3-031-16454-5

Electronic ISBN: 978-3-031-16455-2

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-031-16455-2_5

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