The Theory of Sequential Decision Making

• Applicant: Professor Dr. Carlos Alós-Ferrer
• Subject Area: Economic Theory
• Term: from 2009 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 157248499

• Final Report Year: 2024

Final Report Abstract

The development of interactive decision theory, also known as game theory, began during the middle of the last century. In the meantime game theory has become the dominant methodology in the social sciences, in particular in economics. The necessities of economic theory, however, have generated applications that transcended the traditional framework of finite game theory. Hence, this project has tackled the task of putting game theory on new foundations that are appropriate for modern economic theory. This concerns in particular the generalization of the key classical results without resorting to the finiteness assumptions, which were originally adopted for simplicity. In the now completed, second part of this research project we have proposed a general theory of dynamic games, also known as extensive form games. This theory encompasses nor only representations that can do without any cardinality assumptions, but also a generalization of one of the fundamental building blocks of solution theory: The existence of subgame perfect equilibrium for games of perfect information. More precisely, we offer a characterization of the existence of equilibria, because the conditions that we propose are not only sufficient for existence but also necessary. Since these conditions apply to the topology on the universal set of plays, this result defines the framework in which game theory can be operative. While pursuing this we have also found a number of new results that are relevant for applications. For instance, we were able to characterize when the one-shot deviation principle holds true. Another example is a novel characterization of the concept of perfect recall, which we can now define purely in terms of the primitives of the game, instead via derived objects like strategies.

Publications

• Some Remarks on Pseudotrees. Order, 22(1), 1-9.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• Trees and decisions. Economic Theory, 25(4).
  Alós-Ferrer, Carlo & Ritzberger, Klaus
  
• Trees and extensive forms. Journal of Economic Theory, 143(1), 216-250.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• Comment on “Trees and extensive forms” [J. Econ. Theory 143 (1) (2008) 216–250]. Journal of Economic Theory, 146(5), 2165-2168.
  Alós-Ferrer, Carlos; Kern, Johannes & Ritzberger, Klaus
  
• Large extensive form games. Economic Theory, 52(1), 75-102.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• On the characterization of preference continuity by chains of sets. Economic Theory Bulletin, 3(2), 115-128.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• Characterizing existence of equilibrium for large extensive form games: a necessity result. Economic Theory, 63(2), 407-430.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• Repeated games in continuous time as extensive form games. Journal of Mathematical Economics, 61, 34-57.
  Alós-Ferrer, Carlos & Kern, Johannes
  
• Characterizations of perfect recall. International Journal of Game Theory, 46(2), 311-326.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• Equilibrium existence for large perfect information games. Journal of Mathematical Economics, 62, 5-18.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• The Theory of Extensive Form Games. Springer Series in Game Theory. Springer Berlin Heidelberg.
  Alós-Ferrer, Carlos & Ritzberger, Klaus
  
• Does backwards induction imply subgame perfection?. Games and Economic Behavior, 103, 19-29.
  Alós-Ferrer, Carlos & Ritzberger, Klaus