# A new quantum scheme for normal-form games

## TL;DR

This paper introduces a refined quantum game scheme that extends classical finite strategic form games, including extensive games, allowing for new strategic possibilities and outcomes in quantum settings.

## Contribution

It provides a rigorous mathematical framework for a refined quantum game scheme that generalizes classical and extensive games, enabling new strategic analysis.

## Key findings

- Quantum scheme generalizes classical normal-form games
- Rational choices can lead to different outcomes in quantum vs classical games
- Framework includes extensive games as special cases

## Abstract

We give a strict mathematical description for a refinement of the Marinatto-Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game induced by the scheme generalizes finite strategic form game. In particular, it covers normal representations of extensive games, i.e., strategic games generated by extensive ones. We illustrate our idea with an example of extensive game and prove that rational choices in the classical game and its quantum counterpart may lead to significantly different outcomes.