Quantum information approach to normal representation of extensive games

TL;DR

This paper introduces a quantum information framework for representing extensive games, enabling the analysis of finite extensive games through quantum concepts, demonstrated on classic game examples using established quantization methods.

Contribution

It develops a quantum-based method for the normal representation of extensive games, bridging quantum information theory with game theory analysis.

Findings

Successfully applied quantum representation to Selten's Horse game

Extended the approach to two-stage extensive games with perfect information

Demonstrated equivalence of quantum and classical game outcomes in examples

Abstract

We modify the concept of quantum strategic game to make it useful for extensive form games. We prove that our modification allows to consider the normal representation of any finite extensive game using the fundamental concepts of quantum information. The Selten's Horse game and the general form of two-stage extensive game with perfect information are studied to illustrate a potential application of our idea. In both examples we use Eisert-Wilkens-Lewenstein approach as well as Marinatto-Weber approach to quantization of games.