Discrete-Time Dynamic Noncooperative Game Theory

TL;DR

This paper refines and extends theoretical results in discrete-time affine-quadratic dynamic noncooperative game theory, providing more concise proofs and exploring equilibrium solutions under various conditions.

Contribution

It corrects existing results, offers shorter proofs, and extends equilibrium solution frameworks for discrete-time affine-quadratic dynamic games.

Findings

Corrected some existing theoretical results.

Provided shorter, more convenient proofs.

Extended equilibrium solution analysis for multiple scenarios.

Abstract

Dynamic noncooperative game theory is a field of mathematics and economics in which a lot of research is being carried out at present featuring a great number of applications in many different areas of economics and management science like capital accumulation and investments, R&D and technological innovations, macroeconomics, microeconomics, pricing and advertising decisions in marketing, natural resource extraction, pollution control. The aim of this diploma thesis is to correct some results for discrete-time affine-quadratic dynamic games of prespecified fixed duration with open-loop and feedback information patterns and to give shorter and more convenient proofs for some results already stated in the literature. Additionally we present some extensions for the open-loop and feedback Stackelberg equilibrium solutions of discrete-time affine-quadratic dynamic games of prespecified fixed duration, concerning the number of followers, the structure of the cost und state functions and the possibility of an algorithmic disintegration.