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2022 | Buch

# Theory and Applications of Dynamic Games

## A Course on Noncooperative and Cooperative Games Played over Event Trees

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

Buchreihe : Theory and Decision Library C

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SUCHEN

### Über dieses Buch

This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.

### Inhaltsverzeichnis

#### Static Games

##### Chapter 1. Noncooperative Games
Abstract
In this chapter, we review the basic concepts of noncooperative game theory. In Sect. 1.1, we deal with finite games in strategic form and, in Sect. 1.2, with continuous games in strategic form. In Sect. 1.3, games in extensive form are introduced, and the Stackelberg equilibrium is defined in Sect. 1.4. The chapter ends with a series of exercises.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
##### Chapter 2. Cooperative Games
Abstract
In this chapter, we review the main ingredients of cooperative games, which will be needed in the following chapters.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour

#### Deterministic Dynamic Games

##### Chapter 3. Multistage Games
Abstract
In this chapter, we provide a brief introduction to the theory of multistage games. We recall some properties of dynamical systems described in state-space formalism, and introduce the idea of information structure, which defines what the players know when they make their decisions.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
##### Chapter 4. Sustainability of Cooperation in Dynamic Games
Abstract
This chapter introduces the concepts of time consistency and cooperative equilibrium in cooperative dynamic games. To simplify the exposition, we retain a deterministic setup. In the next chapters, we extend the results to dynamic games played over event trees (DGPETs).
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour

#### Dynamic Games Played over Event Trees

##### Chapter 5. Noncooperative Dynamic Games Played over Event Trees
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.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
##### Chapter 6. Node-Consistent Single-Valued Solutions in DGPETs
Abstract
In this chapter, we examine the problem of the sustainability of cooperative solutions in dynamic games played over event trees (DGPETs). We introduce a cooperative version of the noncooperative DGPET defined in Chap. 5. We describe the problem of node inconsistency of cooperative solutions, which is a key issue in sustainable cooperation. We propose a procedure to define a node-consistent Shapley value and a Nash bargaining solution in DGPETs with a prescribed duration and with a random terminal time.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
##### Chapter 7. Node-Consistent Core in DGPETs
Abstract
This chapter deals with the node consistency of the core in cooperative dynamic games played over event trees. Being a set-valued solution, the core does not (in general) uniquely define the profile of payoffs to the players. This is the first major difference from the single-valued solutions discussed in the previous chapter. The second difference is that the core may be empty.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
##### Chapter 8. Cooperative Equilibria in DGPETs
Abstract
In this chapter, we extend to the class of dynamic games played over event trees (DGPETs) the concepts of subgame perfect $$\varepsilon$$-equilibrium and incentive equilibrium discussed in a deterministic framework in Chap. 4.
Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
##### Backmatter
Titel
Theory and Applications of Dynamic Games
verfasst von
Elena Parilina