João P. Hespanha
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175218
- eISBN:
- 9781400885442
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175218.003.0014
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter discusses a new class of games known as dynamic games. It begins by considering a two-player multi-stage game in extensive form in which the overall tree structure can be mathematically ...
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This chapter discusses a new class of games known as dynamic games. It begins by considering a two-player multi-stage game in extensive form in which the overall tree structure can be mathematically described in a manner that actually allows for games that are more general than those typically described in extensive form. These include games described by graphs that are not trees, games with infinitely many stages, and games with action spaces that are not finite sets. The equation for solving dynamic games is often called the dynamics of the game. The chapter also examines the information structures of dynamic games and concludes with an overview of continuous time differential games and differential games with variable termination time.Less
This chapter discusses a new class of games known as dynamic games. It begins by considering a two-player multi-stage game in extensive form in which the overall tree structure can be mathematically described in a manner that actually allows for games that are more general than those typically described in extensive form. These include games described by graphs that are not trees, games with infinitely many stages, and games with action spaces that are not finite sets. The equation for solving dynamic games is often called the dynamics of the game. The chapter also examines the information structures of dynamic games and concludes with an overview of continuous time differential games and differential games with variable termination time.
Thomas A. Weber
- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.003.0004
- Subject:
- Mathematics, Probability / Statistics
This chapter provides an introduction to games in discrete time with complete and incomplete information. Based on this body of classical game theory, it goes on to discuss continuous-time ...
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This chapter provides an introduction to games in discrete time with complete and incomplete information. Based on this body of classical game theory, it goes on to discuss continuous-time differential games.Less
This chapter provides an introduction to games in discrete time with complete and incomplete information. Based on this body of classical game theory, it goes on to discuss continuous-time differential games.
Anastasios Xepapadeas
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199692873
- eISBN:
- 9780191738371
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692873.003.0006
- Subject:
- Economics and Finance, Development, Growth, and Environmental
Robust policy rules and precaution might be called for, under conditions of scientific uncertainty, when a policy maker is concerned about possible misspecification of the natural system that is used ...
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Robust policy rules and precaution might be called for, under conditions of scientific uncertainty, when a policy maker is concerned about possible misspecification of the natural system that is used to model pollution dynamics. Precaution, however, could be costly. The present chapter develops a conceptual framework for designing robust policy rules and estimating the cost of being precautious in the context of an international pollution control problem. Cooperative and non-cooperative robust policy rules are determined and the cost, in terms of value loss, of being robust relative to conventional policy rules is estimated.Less
Robust policy rules and precaution might be called for, under conditions of scientific uncertainty, when a policy maker is concerned about possible misspecification of the natural system that is used to model pollution dynamics. Precaution, however, could be costly. The present chapter develops a conceptual framework for designing robust policy rules and estimating the cost of being precautious in the context of an international pollution control problem. Cooperative and non-cooperative robust policy rules are determined and the cost, in terms of value loss, of being robust relative to conventional policy rules is estimated.
Thomas A. Weber
- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.001.0001
- Subject:
- Mathematics, Probability / Statistics
This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and ...
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This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations is the backbone of the theory developed in the book, and Chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendices provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer’s creation of an environment in which players interact to maximize the designer’s objective. The book focuses on applications; the problems are an integral part of the text.Less
This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations is the backbone of the theory developed in the book, and Chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendices provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer’s creation of an environment in which players interact to maximize the designer’s objective. The book focuses on applications; the problems are an integral part of the text.
Darko Jus and Volker Meier
- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780262027885
- eISBN:
- 9780262319836
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027885.003.0009
- Subject:
- Economics and Finance, Development, Growth, and Environmental
Employing a Stackelberg differential game approach, the chapter derives the carbon tax chosen by a climate coalition of resource consuming countries which purchase the fossil resource from a ...
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Employing a Stackelberg differential game approach, the chapter derives the carbon tax chosen by a climate coalition of resource consuming countries which purchase the fossil resource from a representative competitive resource supplier. The global climate coalition reduces the speed at which the global fossil resource stock is depleted over time to the socially efficient level by levying the Pigou tax on resource consumption. If the climate coalition is incomplete, the chosen unilateral carbon tax falls short of the Pigou tax. Furthermore, international carbon leakage undermines the effectiveness of the unilateral carbon tax in slowing down the speed of global resource extraction. Nevertheless, under the assumptions made, also the incomplete climate coalition is able to slow down the speed of global extraction to some extent because the chosen carbon tax is time-consistent, irrespective of whether the coalition is global or incomplete.Less
Employing a Stackelberg differential game approach, the chapter derives the carbon tax chosen by a climate coalition of resource consuming countries which purchase the fossil resource from a representative competitive resource supplier. The global climate coalition reduces the speed at which the global fossil resource stock is depleted over time to the socially efficient level by levying the Pigou tax on resource consumption. If the climate coalition is incomplete, the chosen unilateral carbon tax falls short of the Pigou tax. Furthermore, international carbon leakage undermines the effectiveness of the unilateral carbon tax in slowing down the speed of global resource extraction. Nevertheless, under the assumptions made, also the incomplete climate coalition is able to slow down the speed of global extraction to some extent because the chosen carbon tax is time-consistent, irrespective of whether the coalition is global or incomplete.
